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id="sc_sccoursedescs"> <h2 class="sectionhead">Programming & Software Engineering</h2><div class="courseblock"> <h4 class="courseblocktitle">6.100A Introduction to Computer Science Programming in Python</h4> Prereq: None U (Fall, Spring; first half of term) 2-0-4 units Credit cannot also be received for <a href="/search/?P=6.100L" title="6.100L" class="bubblelink code" onclick="return showCourse(this, '6.100L');">6.100L</a> Introduction to computer science and programming for students with little or no programming experience. Students develop skills to program and use computational techniques to solve problems. Topics include the notion of computation, Python, simple algorithms and data structures, testing and debugging, and algorithmic complexity. Combination of <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and <a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a> or <a href="/search/?P=16.C20" title="16.C20[J]" class="bubblelink code" onclick="return showCourse(this, '16.C20');">16.C20[J]</a> counts as REST subject. Final given in the seventh week of the term. A. Bell </div><div class="courseblock"> <h4 class="courseblocktitle">6.100B Introduction to Computational Thinking and Data Science</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> or permission of instructor U (Fall, Spring; second half of term) 2-0-4 units Credit cannot also be received for <a href="/search/?P=9.C20" title="9.C20[J]" class="bubblelink code" onclick="return showCourse(this, '9.C20');">9.C20[J]</a>, <a href="/search/?P=16.C20" title="16.C20[J]" class="bubblelink code" onclick="return showCourse(this, '16.C20');">16.C20[J]</a>, <a href="/search/?P=18.C20" title="18.C20[J]" class="bubblelink code" onclick="return showCourse(this, '18.C20');">18.C20[J]</a>, <a href="/search/?P=CSE.C20" title="CSE.C20[J]" class="bubblelink code" onclick="return showCourse(this, 'CSE.C20');">CSE.C20[J]</a> Provides an introduction to using computation to understand real-world phenomena. Topics include plotting, stochastic programs, probability and statistics, random walks, Monte Carlo simulations, modeling data, optimization problems, and clustering. Combination of <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and <a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a> counts as REST subject. A. Bell, J. V. Guttag </div><div class="courseblock"> <h4 class="courseblocktitle">6.100L Introduction to Computer Science and Programming</h4> Prereq: None U (Fall, Spring) 2-0-4 units Credit cannot also be received for <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> Introduction to computer science and programming for students with no programming experience. Presents content taught in <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> over an entire semester. Students develop skills to program and use computational techniques to solve problems. Topics include the notion of computation, Python, simple algorithms and data structures, testing and debugging, and algorithmic complexity. Lectures are viewed outside of class; in-class time is dedicated to problem-solving and discussion. Combination of <a href="/search/?P=6.100L" title="6.100L" class="bubblelink code" onclick="return showCourse(this, '6.100L');">6.100L</a> and <a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a> or <a href="/search/?P=16.C20" title="16.C20[J]" class="bubblelink code" onclick="return showCourse(this, '16.C20');">16.C20[J]</a> counts as REST subject. A. Bell, J. V. Guttag </div><div class="courseblock"> <h4 class="courseblocktitle">6.1010 Fundamentals of Programming</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> U (Fall, Spring) 2-4-6 units. Institute LAB Introduces fundamental concepts of programming. Designed to develop skills in applying basic methods from programming languages to abstract problems. Topics include programming and Python basics, computational concepts, software engineering, algorithmic techniques, data types, and recursion. 聽Lab component consists of software design, construction, and implementation of design. Enrollment may be limited. D. S. Boning, A. Chlipala, S. Devadas, A. Hartz </div><div class="courseblock"> <h4 class="courseblocktitle">6.1020 Software Construction</h4> Prereq: <a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> U (Spring) 3-0-12 units Introduces fundamental principles and techniques of software development: how to write software that is safe from bugs, easy to understand, and ready for change. Topics include specifications and invariants; testing, test-case generation, and coverage; abstract data types and representation independence; design patterns for object-oriented programming; concurrent programming, including message passing and shared memory concurrency, and defending against races and deadlock; and functional programming with immutable data and higher-order functions. Includes weekly programming exercises and larger group programming projects. M. Goldman, R. C. Miller </div><div class="courseblock"> <h4 class="courseblocktitle">6.1040 Software Design</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> and <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> U (Fall) 4-0-14 units Provides design-focused instruction on how to build complex software applications. Design topics include classic human-computer interaction (HCI) design tactics (need finding, heuristic evaluation, prototyping, user testing), conceptual design (inventing, modeling and evaluating constituent concepts), social and ethical implications, abstract data modeling, and visual design. Implementation topics include reactive front-ends, web services, and databases. Students work both on individual projects and a larger team project in which they design and build full-stack web applications. D. N. Jackson, A. Satyanarayan </div><div class="courseblock"> <h4 class="courseblocktitle">6.1060 Software Performance Engineering</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a>, <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>, and <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Fall) 3-12-3 units Project-based introduction to building efficient, high-performance and scalable software systems. Topics include performance analysis, algorithmic techniques for high performance, instruction-level optimizations, vectorization, cache and memory hierarchy optimization, and parallel programming. S. Amarasinghe, C. E. Leiserson </div><div class="courseblock"> <h4 class="courseblocktitle">6.5060 Algorithm Engineering</h4> Prereq: <a href="/search/?P=6.1060" title="6.1060" class="bubblelink code" onclick="return showCourse(this, '6.1060');">6.1060</a> and <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> G (Spring) 3-0-9 units Covers the theory and practice of algorithms and data structures. Topics include models of computation, algorithm design and analysis, and performance engineering of algorithm implementations. Presents the design and implementation of sequential, parallel, cache-efficient, and external-memory algorithms. Illustrates many of the principles of algorithm engineering in the context of parallel algorithms and graph problems. J. Shun </div><div class="courseblock"> <h4 class="courseblocktitle">6.5080 Multicore Programming</h4> Subject meets with <a href="/search/?P=6.5081" title="6.5081" class="bubblelink code" onclick="return showCourse(this, '6.5081');">6.5081</a> Prereq: <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> G (Spring) 4-0-8 units Introduces principles and core techniques for programming multicore machines. Topics include locking, scalability, concurrent data structures, multiprocessor scheduling, load balancing, and state-of-the-art synchronization techniques, such as transactional memory. Includes sequence of programming assignments on a large multicore machine, culminating with the design of a highly concurrent application. Students taking graduate version complete additional assignments. N. Shavit </div><div class="courseblock"> <h4 class="courseblocktitle">6.5081 Multicore Programming</h4> Subject meets with <a href="/search/?P=6.5080" title="6.5080" class="bubblelink code" onclick="return showCourse(this, '6.5080');">6.5080</a> Prereq: <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> U (Spring) 4-0-8 units Introduces principles and core techniques for programming multicore machines. Topics include locking, scalability, concurrent data structures, multiprocessor scheduling, load balancing, and state-of-the-art synchronization techniques, such as transactional memory. Includes sequence of programming assignments on a large multicore machine, culminating with the design of a highly concurrent application. Students taking graduate version complete additional assignments. N. Shavit </div><h2 class="sectionhead">Programming Languages</h2><div class="courseblock"> <h4 class="courseblocktitle">6.1100 Computer Language Engineering</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> and <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Spring) 4-4-4 units Analyzes issues associated with the implementation of higher-level programming languages. Fundamental concepts, functions, and structures of compilers. The interaction of theory and practice. Using tools in building software. Includes a multi-person project on compiler design and implementation. M. C. Rinard </div><div class="courseblock"> <h4 class="courseblocktitle">6.1120 Dynamic Computer Language Engineering</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> or <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Fall) 4-4-4 units Studies the design and implementation of modern, dynamic programming languages. Topics include fundamental approaches for parsing, semantics and interpretation, virtual machines, garbage collection, just-in-time machine code generation, and optimization. Includes a semester-long, group project that delivers a virtual machine that spans all of these topics. M. Carbin </div><div class="courseblock"> <h4 class="courseblocktitle">6.5110 Foundations of Program Analysis</h4> Prereq: <a href="/search/?P=6.1100" title="6.1100" class="bubblelink code" onclick="return showCourse(this, '6.1100');">6.1100</a> G (Fall) Not offered regularly; consult department 3-0-9 units Presents major principles and techniques for program analysis. Includes formal semantics, type systems and type-based program analysis, abstract interpretation and model checking and synthesis. Emphasis on Haskell and Ocaml, but no prior experience in these languages is assumed. Student assignments include implementing of techniques covered in class, including building simple verifiers. A. Solar-Lezama </div><div class="courseblock"> <h4 class="courseblocktitle">6.5120 Formal Reasoning About Programs</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> and <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units Surveys techniques for rigorous mathematical reasoning about correctness of software, emphasizing commonalities across approaches. Introduces interactive computer theorem proving with the Coq proof assistant, which is used for all assignments, providing immediate feedback on soundness of logical arguments. Covers common program-proof techniques, including operational semantics, model checking, abstract interpretation, type systems, program logics, and their applications to functional, imperative, and concurrent programs. Develops a common conceptual framework based on invariants, abstraction, and modularity applied to state and labeled transition systems. A. Chlipala </div><div class="courseblock"> <h4 class="courseblocktitle">6.5150 Large-scale Symbolic Systems</h4> Subject meets with <a href="/search/?P=6.5151" title="6.5151" class="bubblelink code" onclick="return showCourse(this, '6.5151');">6.5151</a> Prereq: <a href="/search/?P=6.4100" title="6.4100" class="bubblelink code" onclick="return showCourse(this, '6.4100');">6.4100</a> or permission of instructor G (Spring) 3-0-9 units Concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Covers means for decoupling goals from strategy, mechanisms for implementing additive data-directed invocation, work with partially-specified entities, and how to manage multiple viewpoints. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. Students taking graduate version complete additional assignments. G. J. Sussman </div><div class="courseblock"> <h4 class="courseblocktitle">6.5151 Large-scale Symbolic Systems</h4> Subject meets with <a href="/search/?P=6.5150" title="6.5150" class="bubblelink code" onclick="return showCourse(this, '6.5150');">6.5150</a> Prereq: <a href="/search/?P=6.4100" title="6.4100" class="bubblelink code" onclick="return showCourse(this, '6.4100');">6.4100</a> or permission of instructor U (Spring) 3-0-9 units Concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Covers means for decoupling goals from strategy, mechanisms for implementing additive data-directed invocation, work with partially-specified entities, and how to manage multiple viewpoints. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. Students taking graduate version complete additional assignments. G. J. Sussman </div><div class="courseblock"> <h4 class="courseblocktitle">6.5160[J] Classical Mechanics: A Computational Approach</h4> Same subject as <a href="/search/?P=8.351J" title="8.351[J]" class="bubblelink code" onclick="return showCourse(this, '8.351J');">8.351[J]</a>, <a href="/search/?P=12.620J" title="12.620[J]" class="bubblelink code" onclick="return showCourse(this, '12.620J');">12.620[J]</a> Prereq: <a href="/search/?P=8.01|8.01L|8.011|8.012" onclick="return showCourse(this, '8.01|8.01L|8.011|8.012');">Physics I (GIR)</a>, <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, and permission of instructor G (Fall) 3-3-6 units See description under subject <a href="/search/?P=12.620J" title="12.620[J]" class="bubblelink code" onclick="return showCourse(this, '12.620J');">12.620[J]</a>. J. Wisdom, G. J. Sussman </div><h2 class="sectionhead">Theoretical Computer Science</h2><div class="courseblock"> <h4 class="courseblocktitle">6.1200[J] Mathematics for Computer Science</h4> Same subject as <a href="/search/?P=18.062J" title="18.062[J]" class="bubblelink code" onclick="return showCourse(this, '18.062J');">18.062[J]</a> Prereq: <a href="/search/?P=18.01|18.01A|18.014" onclick="return showCourse(this, '18.01|18.01A|18.014');">Calculus I (GIR)</a> U (Fall, Spring) 5-0-7 units. REST Elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability. Z. R.聽Abel,聽F. T. Leighton,聽A. Moitra </div><div class="courseblock"> <h4 class="courseblocktitle">6.120A Discrete Mathematics and Proof for Computer Science</h4> Prereq: <a href="/search/?P=18.01|18.01A|18.014" onclick="return showCourse(this, '18.01|18.01A|18.014');">Calculus I (GIR)</a> U (Spring; second half of term) 3-0-3 units Subset of elementary discrete mathematics for science and engineering useful in computer science. Topics may include logical notation, sets, done relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.1210 Introduction to Algorithms</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or (<a href="/search/?P=6.120A" title="6.120A" class="bubblelink code" onclick="return showCourse(this, '6.120A');">6.120A</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>, or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a>))) U (Fall, Spring) 5-0-7 units Introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. Emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Enrollment may be limited. E. Demaine, S. Devadas </div><div class="courseblock"> <h4 class="courseblocktitle">6.1220[J] Design and Analysis of Algorithms</h4> Same subject as <a href="/search/?P=18.410J" title="18.410[J]" class="bubblelink code" onclick="return showCourse(this, '18.410J');">18.410[J]</a> Prereq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> and <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> U (Fall, Spring) 4-0-8 units Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing. E. Demaine, M. Goemans, S. Raghuraman </div><div class="courseblock"> <h4 class="courseblocktitle">6.1400[J] Computability and Complexity Theory</h4> Same subject as <a href="/search/?P=18.400J" title="18.400[J]" class="bubblelink code" onclick="return showCourse(this, '18.400J');">18.400[J]</a> Prereq: (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> and <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>) or permission of instructor U (Spring) 4-0-8 units Mathematical introduction to the theory of computing. Rigorously explores what kinds of tasks can be efficiently solved with computers by way of finite automata, circuits, Turing machines, and communication complexity, introducing students to some major open problems in mathematics. Builds skills in classifying computational tasks in terms of their difficulty. Discusses other fundamental issues in computing, including the Halting Problem, the Church-Turing Thesis, the P versus NP problem, and the power of randomness.聽聽 R. Williams, R. Rubinfeld </div><div class="courseblock"> <h4 class="courseblocktitle">6.1420 Fixed Parameter and Fine-grained Computation</h4> Prereq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a>, <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>, and (<a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a>, <a href="/search/?P=6.1400" title="6.1400[J]" class="bubblelink code" onclick="return showCourse(this, '6.1400');">6.1400[J]</a>, or <a href="/search/?P=18.404" title="18.404" class="bubblelink code" onclick="return showCourse(this, '18.404');">18.404</a>) Acad Year 2024-2025: U (Fall) Acad Year 2025-2026: Not offered 3-0-9 units An overview of the theory of parameterized algorithms and the "problem-centric" theory of fine-grained complexity, both of which reconsider how to measure the difficulty and feasibility of solving computational problems. Topics include: fixed-parameter tractability (FPT) and its characterizations, the W-hierarchy (W[1], W[2], W[P], etc.), 3-sum-hardness, all-pairs shortest paths (APSP)-equivalences, strong exponential time hypothesis (SETH) hardness of problems, and the connections to circuit complexity and other aspects of computing. R. Williams, V. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.5210[J] Advanced Algorithms</h4> Same subject as <a href="/search/?P=18.415J" title="18.415[J]" class="bubblelink code" onclick="return showCourse(this, '18.415J');">18.415[J]</a> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> and (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a>, <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a>) G (Fall) 5-0-7 units First-year graduate subject in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Surveys a variety of computational models and the algorithms for them. Data structures, network flows, linear programming, computational geometry, approximation algorithms, online algorithms, parallel algorithms, external memory, streaming algorithms. A. Moitra, D. R. Karger </div><div class="courseblock"> <h4 class="courseblocktitle">6.5220[J] Randomized Algorithms</h4> Same subject as <a href="/search/?P=18.416J" title="18.416[J]" class="bubblelink code" onclick="return showCourse(this, '18.416J');">18.416[J]</a> Prereq: (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>) and (<a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> or <a href="/search/?P=6.5210" title="6.5210[J]" class="bubblelink code" onclick="return showCourse(this, '6.5210');">6.5210[J]</a>) Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 5-0-7 units Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and minimum cuts. Geometric algorithms: convex hulls, linear programming in fixed or arbitrary dimension. Approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms. D. R. Karger </div><div class="courseblock"> <h4 class="courseblocktitle">6.5230 Advanced Data Structures</h4> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units More advanced and powerful data structures for answering several queries on the same data. Such structures are crucial in particular for designing efficient algorithms. Dictionaries; hashing; search trees. Self-adjusting data structures; linear search; splay trees; dynamic optimality. Integer data structures; word RAM. Predecessor problem; van Emde Boas priority queues; y-fast trees; fusion trees. Lower bounds; cell-probe model; round elimination. Dynamic graphs; link-cut trees; dynamic connectivity. Strings; text indexing; suffix arrays; suffix trees. Static data structures; compact arrays; rank and select. Succinct data structures; tree encodings; implicit data structures. External-memory and cache-oblivious data structures; B-trees; buffer trees; tree layout; ordered-file maintenance. Temporal data structures; persistence; retroactivity. E. D. Demaine </div><div class="courseblock"> <h4 class="courseblocktitle">6.5240 Sublinear Time Algorithms</h4> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> or permission of instructor Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units Sublinear time algorithms understand parameters and properties of input data after viewing only a minuscule fraction of it. Tools from number theory, combinatorics, linear algebra, optimization theory, distributed algorithms, statistics, and probability are covered. Topics include: testing and estimating properties of distributions, functions, graphs, strings, point sets, and various combinatorial objects. R. Rubinfeld </div><div class="courseblock"> <h4 class="courseblocktitle">6.5250[J] Distributed Algorithms</h4> Same subject as <a href="/search/?P=18.437J" title="18.437[J]" class="bubblelink code" onclick="return showCourse(this, '18.437J');">18.437[J]</a> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units Design and analysis of algorithms, emphasizing those suitable for use in distributed networks. Covers various topics including聽distributed graph algorithms, locality constraints,聽bandwidth limitations and communication complexity,聽process synchronization, allocation of computational resources, fault tolerance, and asynchrony. No background in distributed systems required. M. Ghaffari, N. A. Lynch </div><div class="courseblock"> <h4 class="courseblocktitle">6.5310 Geometric Folding Algorithms: Linkages, Origami, Polyhedra</h4> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Covers discrete geometry and algorithms underlying the reconfiguration of foldable structures, with applications to robotics, manufacturing, and biology. Linkages made from one-dimensional rods connected by hinges: constructing polynomial curves, characterizing rigidity, characterizing unfoldable versus locked, protein folding. Folding two-dimensional paper (origami): characterizing flat foldability, algorithmic origami design, one-cut magic trick. Unfolding and folding three-dimensional polyhedra: edge unfolding, vertex unfolding, gluings, Alexandrov's Theorem, hinged dissections. E. D. Demaine </div><div class="courseblock"> <h4 class="courseblocktitle">6.5320 Geometric Computing</h4> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units Introduction to the design and analysis of algorithms for geometric problems, in low- and high-dimensional spaces. Algorithms: convex hulls, polygon triangulation, Delaunay triangulation, motion planning, pattern matching. Geometric data structures: point location, Voronoi diagrams, Binary Space Partitions. Geometric problems in higher dimensions: linear programming, closest pair problems. High-dimensional nearest neighbor search and low-distortion embeddings between metric spaces. Geometric algorithms for massive data sets: external memory and streaming algorithms. Geometric optimization. P. Indyk </div><div class="courseblock"> <h4 class="courseblocktitle">6.5340 Topics in Algorithmic Game Theory</h4> Prereq: <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> or <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> G (Spring) 3-0-9 units Presents research topics at the interface of computer science and game theory, with an emphasis on algorithms and computational complexity. Explores the types of game-theoretic tools that are applicable to computer systems, the loss in system performance due to the conflicts of interest of users and administrators, and the design of systems whose performance is robust with respect to conflicts of interest inside the system. Algorithmic focus is on algorithms for equilibria, the complexity of equilibria and fixed points, algorithmic tools in mechanism design, learning in games, and the price of anarchy. K. Daskalakis </div><div class="courseblock"> <h4 class="courseblocktitle">6.5350 Matrix Multiplication and Graph Algorithms</h4> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> G (Fall) Not offered regularly; consult department 3-0-9 units Explores topics around matrix multiplication (MM) and its use in the design of graph algorithms. Focuses on problems such as transitive closure, shortest paths, graph matching, and other classical graph problems. Explores fast approximation algorithms when MM techniques are too expensive. V. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.5400[J] Theory of Computation</h4> Same subject as <a href="/search/?P=18.4041J" title="18.4041[J]" class="bubblelink code" onclick="return showCourse(this, '18.4041J');">18.4041[J]</a> Subject meets with <a href="/search/?P=18.404" title="18.404" class="bubblelink code" onclick="return showCourse(this, '18.404');">18.404</a> Prereq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=18.200" title="18.200" class="bubblelink code" onclick="return showCourse(this, '18.200');">18.200</a> G (Fall) 4-0-8 units See description under subject <a href="/search/?P=18.4041J" title="18.4041[J]" class="bubblelink code" onclick="return showCourse(this, '18.4041J');">18.4041[J]</a>. M. Sipser </div><div class="courseblock"> <h4 class="courseblocktitle">6.5410[J] Advanced Complexity Theory</h4> Same subject as <a href="/search/?P=18.405J" title="18.405[J]" class="bubblelink code" onclick="return showCourse(this, '18.405J');">18.405[J]</a> Prereq: <a href="/search/?P=18.404" title="18.404" class="bubblelink code" onclick="return showCourse(this, '18.404');">18.404</a> G (Spring) 3-0-9 units See description under subject <a href="/search/?P=18.405J" title="18.405[J]" class="bubblelink code" onclick="return showCourse(this, '18.405J');">18.405[J]</a>. R. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.5420 Randomness and Computation</h4> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a> and <a href="/search/?P=18.4041" title="18.4041[J]" class="bubblelink code" onclick="return showCourse(this, '18.4041');">18.4041[J]</a> Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units The power and sources of randomness in computation. Connections and applications to computational complexity, computational learning theory, cryptography and combinatorics. Topics include: probabilistic proofs, uniform generation and approximate counting, Fourier analysis of Boolean functions, computational learning theory, expander graphs, pseudorandom generators, derandomization. R. Rubinfeld </div><div class="courseblock"> <h4 class="courseblocktitle">6.5430 Quantum Complexity Theory</h4> Prereq: <a href="/search/?P=6.1400" title="6.1400[J]" class="bubblelink code" onclick="return showCourse(this, '6.1400');">6.1400[J]</a>, <a href="/search/?P=18.4041" title="18.4041[J]" class="bubblelink code" onclick="return showCourse(this, '18.4041');">18.4041[J]</a>, and <a href="/search/?P=18.435" title="18.435[J]" class="bubblelink code" onclick="return showCourse(this, '18.435');">18.435[J]</a> G (Spring) 3-0-9 units Introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs and advice, and interactive proof systems in the quantum world; classical simulation of quantum circuits. The objective is to bring students to the research frontier. Staff </div><h2 class="sectionhead">Security & Cryptography</h2><div class="courseblock"> <h4 class="courseblocktitle">6.1600 Foundations of Computer Security</h4> Prereq: (<a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> and (<a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or <a href="/search/?P=6.1810" title="6.1810" class="bubblelink code" onclick="return showCourse(this, '6.1810');">6.1810</a>)) or permission of instructor U (Fall) 4-0-8 units Fundamental notions and big ideas for achieving security in computer systems. Topics include cryptographic foundations (pseudorandomness, collision-resistant hash functions, authentication codes, signatures, authenticated encryption, public-key encryption), systems ideas (isolation, non-interference, authentication, access control, delegation, trust), and implementation techniques (privilege separation, fuzzing, symbolic execution, runtime defenses, side-channel attacks). Case studies of how these ideas are realized in deployed systems. Lab assignments apply ideas from lectures to learn how to build secure systems and how they can be attacked. H. Corrigan-Gibbs, S. Devadas, S. Goldwasser, Y. Kalai, S. Micali, R. Rivest, V. Vaikuntanathan, N. Zeldovich </div><div class="courseblock"> <h4 class="courseblocktitle">6.5610 Applied Cryptography and Security</h4> Prereq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> and <a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> G (Spring) 4-0-8 units Emphasis on applied cryptography. May include: basic notion of systems security, cryptographic hash functions, symmetric cryptography (one-time pad,聽block ciphers,聽stream ciphers, message authentication codes), hash functions, key-exchange, public-key cryptography (encryption, digital signatures), elliptic curve cryptography,聽 secret-sharing, fully homomorphic encryption, zero-knowledge proofs, and electronic voting. Assignments include a final group project. Topics may vary year to year. H. Corrigan-Gibbs, Y. Kalai </div><div class="courseblock"> <h4 class="courseblocktitle">6.5620[J] Foundations of Cryptography</h4> Same subject as <a href="/search/?P=18.425J" title="18.425[J]" class="bubblelink code" onclick="return showCourse(this, '18.425J');">18.425[J]</a> Prereq: <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a>, <a href="/search/?P=6.1400" title="6.1400[J]" class="bubblelink code" onclick="return showCourse(this, '6.1400');">6.1400[J]</a>, or <a href="/search/?P=18.4041" title="18.4041[J]" class="bubblelink code" onclick="return showCourse(this, '18.4041');">18.4041[J]</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units A rigorous introduction to modern cryptography. Emphasis on the fundamental cryptographic primitives such as public-key encryption, digital signatures, and pseudo-random number generation, as well as advanced cryptographic primitives such as zero-knowledge proofs, homomorphic encryption, and secure multiparty computation. S. Goldwasser, S. Micali, V. Vaikuntanathan </div><div class="courseblock"> <h4 class="courseblocktitle">6.5630 Advanced Topics in Cryptography</h4> Prereq: <a href="/search/?P=6.5620" title="6.5620[J]" class="bubblelink code" onclick="return showCourse(this, '6.5620');">6.5620[J]</a> G (Fall) 3-0-9 units Can be repeated for credit. In-depth exploration of recent results in cryptography. S. Goldwasser, Y. Kalai, S. Micali, V. Vaikuntanathan </div><div class="courseblock"> <h4 class="courseblocktitle">6.5660 Computer Systems Security</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> and (<a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or <a href="/search/?P=6.1810" title="6.1810" class="bubblelink code" onclick="return showCourse(this, '6.1810');">6.1810</a>) G (Spring) 3-6-3 units Design and implementation of secure computer systems. Lectures cover attacks that compromise security as well as techniques for achieving security, based on recent research papers. Topics include operating system security, privilege separation, capabilities, language-based security, cryptographic network protocols, trusted hardware, and security in web applications and mobile phones. Labs involve implementing and compromising a web application that sandboxes arbitrary code, and a group final project. N. B. Zeldovich </div><h2 class="sectionhead">Computer Systems</h2><div class="courseblock"> <h4 class="courseblocktitle">6.1800 Computer Systems Engineering</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Spring) 5-1-6 units Topics on the engineering of computer software and hardware systems: techniques for controlling complexity; strong modularity using client-server design, operating systems; performance, networks; naming; security and privacy; fault-tolerant systems, atomicity and coordination of concurrent activities, and recovery; impact of computer systems on society. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Includes a single, semester-long design project. Students engage in extensive written communication exercises. Enrollment may be limited. K. LaCurts </div><div class="courseblock"> <h4 class="courseblocktitle">6.1810 Operating System Engineering</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Fall) 3-0-9 units Design and implementation of operating systems, and their use as a foundation for systems programming. Topics include virtual memory, file systems, threads, context switches, kernels, interrupts, system calls, interprocess communication, coordination, and interaction between software and hardware. A multi-processor operating system for RISC-V, xv6, is used to illustrate these topics. Individual laboratory assignments involve extending the xv6 operating system, for example to support sophisticated virtual memory features and networking. A. Belay, M. F. Kaashoek, R. T. Morris </div><div class="courseblock"> <h4 class="courseblocktitle">6.1820[J] Mobile and Sensor Computing</h4> Same subject as <a href="/search/?P=MAS.453J" title="MAS.453[J]" class="bubblelink code" onclick="return showCourse(this, 'MAS.453J');">MAS.453[J]</a> Prereq: <a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or permission of instructor U (Spring) Not offered regularly; consult department 3-0-9 units Focuses on "Internet of Things" (IoT) systems and technologies, sensing, computing, and communication. Explores fundamental design and implementation issues in the engineering of mobile and sensor computing systems. Topics include battery-free sensors, seeing through wall, robotic sensors, vital sign sensors (breathing, heartbeats, emotions), sensing in cars and autonomous vehicles, subsea IoT, sensor security, positioning technologies (including GPS and indoor WiFi), inertial sensing (accelerometers, gyroscopes, inertial measurement units, dead-reckoning), embedded and distributed system architectures, sensing with radio signals, sensing with microphones and cameras, wireless sensor networks, embedded and distributed system architectures, mobile libraries and APIs to sensors, and application case studies. Includes readings from research literature, as well as laboratory assignments and a significant term project. H. Balakrishnan, S. Madden, F. Adib </div><div class="courseblock"> <h4 class="courseblocktitle">6.1850 Computer Systems and Society</h4> Prereq: <a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> U (Fall) 3-0-9 units Explores the impact of computer systems on individual humans, society, and the environment. Examines large- and small-scale power structures that stem from low-level technical design decisions, the consequences of those structures on society, and how they can limit or provide access to certain technologies. Students learn to assess design decisions within an ethical framework and consider the impact of their decisions on non-users. Case studies of working systems and readings from the current literature provide comparisons and contrasts. Possible topics include the implications of hierarchical designs (e.g., DNS) for scale; how layered models influence what parts of a network have the power to take certain actions; and the environmental impact of proof-of-work-based systems such as Bitcoin. Enrollment may be limited. K. LaCurts </div><div class="courseblock"> <h4 class="courseblocktitle">6.5810 Operating System Engineering</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> and (<a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or <a href="/search/?P=6.1810" title="6.1810" class="bubblelink code" onclick="return showCourse(this, '6.1810');">6.1810</a>) Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-6-3 units Fundamental design and implementation issues in the engineering of operating systems. Lectures based on the study of a symmetric multiprocessor version of UNIX version 6 and research papers. Topics include virtual memory; file system; threads; context switches; kernels; interrupts; system calls; interprocess communication; coordination, and interaction between software and hardware. Individual laboratory assignments accumulate in the construction of a minimal operating system (for an x86-based personal computer) that implements the basic operating system abstractions and a shell. Knowledge of programming in the C language is a prerequisite. M. F. Kaashoek </div><div class="courseblock"> <h4 class="courseblocktitle">6.5820 Computer Networks</h4> Prereq: <a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or permission of instructor G (Fall) 4-0-8 units Topics on the engineering and analysis of network protocols and architecture, including architectural principles for designing heterogeneous networks; transport protocols; Internet routing; router design; congestion control and network resource management; wireless networks; network security; naming; overlay and peer-to-peer networks. Readings from original research papers. Semester-long project and paper. H. Balakrishnan, D. Katabi </div><div class="courseblock"> <h4 class="courseblocktitle">6.5830 Database Systems</h4> Subject meets with <a href="/search/?P=6.5831" title="6.5831" class="bubblelink code" onclick="return showCourse(this, '6.5831');">6.5831</a> Prereq: ((<a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> or <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a>) and (<a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or <a href="/search/?P=6.1810" title="6.1810" class="bubblelink code" onclick="return showCourse(this, '6.1810');">6.1810</a>)) or permission of instructor G (Fall) 3-0-9 units Topics related to the engineering and design of database systems, including data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel and heterogeneous databases; adaptive databases; trigger systems; pub-sub systems; semi structured data and XML querying. Lecture and readings from original research papers. Semester-long project and paper. Students taking graduate version complete different assignments. Enrollment may be limited. S. R. Madden </div><div class="courseblock"> <h4 class="courseblocktitle">6.5831 Database Systems</h4> Subject meets with <a href="/search/?P=6.5830" title="6.5830" class="bubblelink code" onclick="return showCourse(this, '6.5830');">6.5830</a> Prereq: ((<a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> or <a href="/search/?P=6.1220" title="6.1220[J]" class="bubblelink code" onclick="return showCourse(this, '6.1220');">6.1220[J]</a>) and (<a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a> or <a href="/search/?P=6.1810" title="6.1810" class="bubblelink code" onclick="return showCourse(this, '6.1810');">6.1810</a>)) or permission of instructor U (Fall) 3-0-9 units Topics related to the engineering and design of database systems, including data models; database and schema design; schema normalization and integrity constraints; query processing; query optimization and cost estimation; transactions; recovery; concurrency control; isolation and consistency; distributed, parallel and heterogeneous databases; adaptive databases; trigger systems; pub-sub systems; semi structured data and XML querying. Lecture and readings from original research papers. Semester-long project and paper. Students taking graduate version complete different assignments. Enrollment may be limited. S. R. Madden </div><div class="courseblock"> <h4 class="courseblocktitle">6.5840 Distributed Computer Systems Engineering</h4> Prereq: <a href="/search/?P=6.1800" title="6.1800" class="bubblelink code" onclick="return showCourse(this, '6.1800');">6.1800</a>, <a href="/search/?P=6.1810" title="6.1810" class="bubblelink code" onclick="return showCourse(this, '6.1810');">6.1810</a>, or permission of instructor G (Spring) 3-0-9 units Abstractions and implementation techniques for engineering distributed systems: remote procedure call, threads and locking, client/server, peer-to-peer, consistency, fault tolerance, and security. Readings from current literature. Individual laboratory assignments culminate in the construction of a fault-tolerant and scalable network file system. Programming experience with C/C++ required. Enrollment limited. R. T. Morris, M. F. Kaashoek </div><div class="courseblock"> <h4 class="courseblocktitle">6.5850 Principles of Computer Systems</h4> Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Introduction to the basic principles of computer systems with emphasis on the use of rigorous techniques as an aid to understanding and building modern computing systems. Particular attention paid to concurrent and distributed systems. Topics include: specification and verification, concurrent algorithms, synchronization, naming, Networking, replication techniques (including distributed cache management), and principles and algorithms for achieving reliability. M. F. Kaashoek, B. Lampson, N. B. Zeldovich </div><h2 class="sectionhead">Computer Architecture</h2><div class="courseblock"> <h4 class="courseblocktitle">6.1903 Introduction to Low-level Programming in C and Assembly</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> U (Spring; first half of term) 2-2-2 units Credit cannot also be received for <a href="/search/?P=6.1904" title="6.1904" class="bubblelink code" onclick="return showCourse(this, '6.1904');">6.1904</a> Introduction to C and assembly language for students coming from a Python background (<a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions. J. D. Steinmeyer, S. Z. Hanono Wachman </div><div class="courseblock"> <h4 class="courseblocktitle">6.1904 Introduction to Low-level Programming in C and Assembly</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> U (Spring; second half of term) 2-2-2 units Credit cannot also be received for <a href="/search/?P=6.1903" title="6.1903" class="bubblelink code" onclick="return showCourse(this, '6.1903');">6.1903</a> Introduction to C and assembly language for students coming from a Python background (<a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>). Studies the C language, focusing on memory and associated topics including pointers, how different data structures are stored in memory, the stack, and the heap in order to build a strong understanding of the constraints involved in manipulating complex data structures in modern computational systems. Studies assembly language to facilitate a firm understanding of how high-level languages are translated to machine-level instructions. J. D. Steinmeyer, S. Z. Hanono Wachman </div><div class="courseblock"> <h4 class="courseblocktitle">6.1910 Computation Structures</h4> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a>, <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>, and (Coreq: <a href="/search/?P=6.1903" title="6.1903" class="bubblelink code" onclick="return showCourse(this, '6.1903');">6.1903</a> or <a href="/search/?P=6.1904" title="6.1904" class="bubblelink code" onclick="return showCourse(this, '6.1904');">6.1904</a>); or permission of instructor U (Fall, Spring) 4-0-8 units. REST Provides an introduction to the design of digital systems and computer architecture. Emphasizes expressing all hardware designs in a high-level hardware description language and synthesizing the designs. Topics include combinational and sequential circuits, instruction set abstraction for programmable hardware, single-cycle and pipelined processor implementations, multi-level memory hierarchies, virtual memory, exceptions and I/O, and parallel systems. S. Z. Hanono Wachman, D. Sanchez </div><div class="courseblock"> <h4 class="courseblocktitle">6.1920 Constructive Computer Architecture</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Spring) 3-8-1 units Illustrates a constructive (as opposed to a descriptive) approach to computer architecture. Topics include combinational and pipelined arithmetic-logic units (ALU), in-order pipelined microarchitectures, branch prediction, blocking and unblocking caches, interrupts, virtual memory support, cache coherence and multicore architectures. Labs in a modern Hardware Design Language (HDL) illustrate various aspects of microprocessor design, culminating in a term project in which students present a multicore design running on an FPGA board. Arvind </div><div class="courseblock"> <h4 class="courseblocktitle">6.5900 Computer System Architecture</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> G (Fall) 4-0-8 units Introduction to the principles underlying modern computer architecture. Emphasizes the relationship among technology, hardware organization, and programming systems in the evolution of computer architecture. Topics include pipelined, out-of-order, and speculative execution; caches, virtual memory and exception handling, superscalar, very long instruction word (VLIW), vector, and multithreaded processors; on-chip networks, memory models, synchronization, and cache coherence protocols for multiprocessors. J. S. Emer, D. Sanchez </div><div class="courseblock"> <h4 class="courseblocktitle">6.5910 Complex Digital Systems Design</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> G (Spring) Not offered regularly; consult department 5-5-2 units Introduction to the design and implementation of large-scale digital systems using hardware description languages and high-level synthesis tools in conjunction with standard commercial electronic design automation (EDA) tools. Emphasizes modular and robust designs, reusable modules, correctness by construction, architectural exploration, meeting area and timing constraints, and developing functional field-programmable gate array (FPGA) prototypes. Extensive use of CAD tools in weekly labs serve as preparation for a multi-person design project on multi-million gate FPGAs. Enrollment may be limited. Arvind </div><div class="courseblock"> <h4 class="courseblocktitle">6.5920 Parallel Computing</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> or permission of instructor G (Spring) Not offered regularly; consult department 3-0-9 units Introduction to parallel and multicore computer architecture and programming. Topics include the design and implementation of multicore processors; networking, video, continuum, particle and graph applications for multicores; communication and synchronization algorithms and mechanisms; locality in parallel computations; computational models, including shared memory, streams, message passing, and data parallel; multicore mechanisms for synchronization, cache coherence, and multithreading. Performance evaluation of multicores; compilation and runtime systems for parallel computing. Substantial project required. A. Agarwal </div><div class="courseblock"> <h4 class="courseblocktitle">6.5930 Hardware Architecture for Deep Learning</h4> Subject meets with <a href="/search/?P=6.5931" title="6.5931" class="bubblelink code" onclick="return showCourse(this, '6.5931');">6.5931</a> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> and (<a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> or <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>) G (Spring) 3-3-6 units Introduction to the design and implementation of hardware architectures for efficient processing of deep learning algorithms and tensor algebra in AI systems. Topics include basics of deep learning, optimization principles for programmable platforms, design principles of accelerator architectures, co-optimization of algorithms and hardware (including sparsity) and use of advanced technologies (including memristors and optical computing). Includes labs involving modeling and analysis of hardware architectures, architecting deep learning inference systems, and an open-ended design project. Students taking graduate version complete additional assignments. V. Sze, J. Emer </div><div class="courseblock"> <h4 class="courseblocktitle">6.5931 Hardware Architecture for Deep Learning</h4> Subject meets with <a href="/search/?P=6.5930" title="6.5930" class="bubblelink code" onclick="return showCourse(this, '6.5930');">6.5930</a> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> and (<a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> or <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>) U (Spring) 3-3-6 units Introduction to the design and implementation of hardware architectures for efficient processing of deep learning algorithms and tensor algebra in AI systems. Topics include basics of deep learning, optimization principles for programmable platforms, design principles of accelerator architectures, co-optimization of algorithms and hardware (including sparsity) and use of advanced technologies (including memristors and optical computing). Includes labs involving modeling and analysis of hardware architectures, architecting deep learning inference systems, and an open-ended design project. Students taking graduate version complete additional assignments. V. Sze, J. Emer </div><div class="courseblock"> <h4 class="courseblocktitle">6.5940 TinyML and Efficient Deep Learning Computing</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> and <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> G (Fall) 3-0-9 units Introduces efficient deep learning computing techniques that enable powerful deep learning applications on resource-constrained devices. Topics include model compression, pruning, quantization, neural architecture search, distributed training, data/model parallellism, gradient compression, on-device fine-tuning. It also introduces application-specific acceleration techniques for video recognition, point cloud, and generative AI (diffusion model, LLM). Students will get hands-on experience accelerating deep learning applications with an open-ended design project. S. Han </div><div class="courseblock"> <h4 class="courseblocktitle">6.5950 Secure Hardware Design</h4> Subject meets with <a href="/search/?P=6.5951" title="6.5951" class="bubblelink code" onclick="return showCourse(this, '6.5951');">6.5951</a> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> G (Spring) 3-0-9 units Introduction聽to basic concepts, principles, and implementation issues in the designing of secure hardware systems. Through a mixture of lectures and paper discussions, covers state-of-the-art security attacks and defenses targeting the computer architecture, digital circuits, and physics layers of computer聽systems. Emphasizes both the conceptual and the practical aspects of security issues in modern hardware systems. Topics include microarchitectural timing side channels, speculative execution attacks, RowHammer, Trusted Execution Environment, physical attacks, hardware support for software security, and verification of digital systems. Students taking graduate version complete additional assignments. M. Yan </div><div class="courseblock"> <h4 class="courseblocktitle">6.5951 Secure Hardware Design</h4> Subject meets with <a href="/search/?P=6.5950" title="6.5950" class="bubblelink code" onclick="return showCourse(this, '6.5950');">6.5950</a> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> U (Spring) 3-0-9 units Introduction聽to basic concepts, principles, and implementation issues in the designing of secure hardware systems. Through a mixture of lectures and paper discussions, covers state-of-the-art security attacks and defenses targeting the computer architecture, digital circuits, and physics layers of computer聽systems. Emphasizes both the conceptual and the practical aspects of security issues in modern hardware systems. Topics include microarchitectural timing side channels, speculative execution attacks, RowHammer, Trusted Execution Environment, physical attacks, hardware support for software security, and verification of digital systems. Students taking graduate version complete additional assignments. M. Yan </div><h2 class="sectionhead">Circuits & Applications</h2><div class="courseblock"> <h4 class="courseblocktitle">6.2000 Electrical Circuits: Modeling and Design of Physical Systems</h4> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> U (Fall, Spring) 3-2-7 units. REST Fundamentals of linear systems, and abstraction modeling of multi-physics lumped and distributed systems using lumped electrical circuits. Linear networks involving independent and dependent sources, resistors, capacitors, and inductors. Extensions to include operational amplifiers and transducers. Dynamics of first- and second-order networks; analysis and design in the time and frequency domains; signal and energy processing applications. Design exercises. Weekly laboratory with microcontroller and transducers. J. H. Lang, T. Palacios, D. J. Perreault, J. Voldman </div><div class="courseblock"> <h4 class="courseblocktitle">6.2020[J] Electronics Project Laboratory</h4> Same subject as <a href="/search/?P=EC.120J" title="EC.120[J]" class="bubblelink code" onclick="return showCourse(this, 'EC.120J');">EC.120[J]</a> Prereq: None U (Fall, Spring) 1-2-3 units Intuition-based introduction to electronics, electronic components, and test equipment such as oscilloscopes, multimeters, and signal generators. Key components studied and used are op-amps, comparators, bi-polar transistors, and diodes (including LEDs). Students design, build, and debug small electronics projects (often featuring sound and light) to put their new knowledge into practice. Upon completing the class, students can take home a kit of components. Intended for students with little or no previous background in electronics. Enrollment may be limited. J. Bales </div><div class="courseblock"> <h4 class="courseblocktitle">6.2030 Electronics First Laboratory</h4> Prereq: None. Coreq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> U (Spring) 4-4-4 units Practical introduction to the design and construction of electronic circuits for information processing and control. Laboratory exercises include activities such as the construction of oscillators for a simple musical instrument, a laser audio communicator, a countdown timer, an audio amplifier, and a feedback-controlled solid-state lighting system for daylight energy conservation. Introduces basic electrical components including resistors, capacitors, and inductors; basic assembly techniques for electronics include breadboarding and soldering; and programmable system-on-chip electronics and C programming language. Enrollment limited. S. B. Leeb </div><div class="courseblock"> <h4 class="courseblocktitle">6.2040 Analog Electronics Laboratory</h4> Prereq: <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> U (Spring) 2-9-1 units. Institute LAB Experimental laboratory explores the design, construction, and debugging of analog electronic circuits. Lectures and laboratory projects in the first half of the course investigate the performance characteristics of semiconductor devices (diodes, BJTs, and MOSFETs) and functional analog building blocks, including single-stage amplifiers, op amps, small audio amplifier, filters, converters, sensor circuits, and medical electronics (ECG, pulse-oximetry). Projects involve design, implementation, and presentation in an environment similar to that of industry engineering design teams. Instruction and practice in written and oral communication provided. Opportunity to simulate real-world problems and solutions that involve tradeoffs and the use of engineering judgment. G. Hom, N. Reiskarimian </div><div class="courseblock"> <h4 class="courseblocktitle">6.2050 Digital Systems Laboratory</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> or permission of instructor U (Fall) 3-7-2 units. Institute LAB Lab-intensive subject that investigates digital systems with a focus on FPGAs. Lectures and labs cover logic, flip flops, counters, timing, synchronization, finite-state machines, digital signal processing, communication protocols, and modern sensors. Prepares students for the design and implementation of a large-scale final project of their choice: games, music, digital filters, wireless communications, video, or graphics. Extensive use of System/Verilog for describing and implementing and verifying digital logic designs. J. Steinmeyer, G. P. Hom, A. P. Chandrakasan </div><div class="courseblock"> <h4 class="courseblocktitle">6.2060 Microcomputer Project Laboratory</h4> Subject meets with <a href="/search/?P=6.2061" title="6.2061" class="bubblelink code" onclick="return showCourse(this, '6.2061');">6.2061</a> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a>, <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a>, or <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> U (Spring) 3-6-3 units. Institute LAB Introduces analysis and design of embedded systems. Microcontrollers provide adaptation, flexibility, and real-time control. Emphasizes construction of complete systems, including a five-axis robot arm, a fluorescent lamp ballast, a tomographic imaging station (e.g., a CAT scan), and a simple calculator. Presents a wide range of basic tools, including software and development tools, programmable system on chip, peripheral components such as A/D converters, communication schemes, signal processing techniques, closed-loop digital feedback control, interface and power electronics, and modeling of electromechanical systems. Includes a sequence of assigned projects, followed by a final project of the student's choice, emphasizing creativity and uniqueness. Provides instruction in written and oral communication. To satisfy the independent inquiry component of this subject, students expand the scope of their laboratory project. S. B. Leeb </div><div class="courseblock"> <h4 class="courseblocktitle">6.2061 Microcomputer Project Laboratory - Independent Inquiry</h4> Subject meets with <a href="/search/?P=6.2060" title="6.2060" class="bubblelink code" onclick="return showCourse(this, '6.2060');">6.2060</a> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a>, <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a>, or <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> U (Spring) 3-9-3 units Introduces analysis and design of embedded systems. Microcontrollers provide adaptation, flexibility, and real-time control. Emphasizes construction of complete systems, including a five-axis robot arm, a fluorescent lamp ballast, a tomographic imaging station (e.g., a CAT scan), and a simple calculator. Presents a wide range of basic tools, including software and development tools, programmable system on chip, peripheral components such as A/D converters, communication schemes, signal processing techniques, closed-loop digital feedback control, interface and power electronics, and modeling of electromechanical systems. Includes a sequence of assigned projects, followed by a final project of the student's choice, emphasizing creativity and uniqueness. Provides instruction in written and oral communication. Students taking independent inquiry version <a href="/search/?P=6.2061" title="6.2061" class="bubblelink code" onclick="return showCourse(this, '6.2061');">6.2061</a> expand the scope of their laboratory project. S. B. Leeb </div><div class="courseblock"> <h4 class="courseblocktitle">6.2080 Semiconductor Electronic Circuits</h4> Prereq: <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> U (Spring) 3-2-7 units Provides an introduction to basic circuit design, starting from basic semiconductor devices such as diodes and transistors, large and small signal models and analysis, to circuits such as basic amplifier and opamp circuits. Labs give students access to CAD/EDA tools to design, analyze, and layout analog circuits. At the end of the term, students have their chip design fabricated using a 22nm FinFET CMOS process. R. Han, N. Reiskarimian </div><div class="courseblock"> <h4 class="courseblocktitle">6.2090 Solid-State Circuits</h4> Subject meets with <a href="/search/?P=6.2092" title="6.2092" class="bubblelink code" onclick="return showCourse(this, '6.2092');">6.2092</a> Prereq: <a href="/search/?P=6.2040" title="6.2040" class="bubblelink code" onclick="return showCourse(this, '6.2040');">6.2040</a>, <a href="/search/?P=6.2080" title="6.2080" class="bubblelink code" onclick="return showCourse(this, '6.2080');">6.2080</a>, or permission of instructor U (Fall) 3-2-7 units Fosters deep understanding and intuition that is crucial in innovating analog circuits and optimizing the whole system in bipolar junction transistor (BJT) and metal oxide semiconductor (MOS) technologies. Covers both theory and real-world applications of basic amplifier structures, operational amplifiers, temperature sensors, bandgap references. Covers topics such as noise, linearity and stability. Homework and labs give students access to CAD/EDA tools to design and analyze analog circuits. Provides practical experience through lab exercises, including a broadband amplifier design and characterization. Students taking graduate version complete additional assignments. N. Reiskarimian, H.-S. Lee, R. Han </div><div class="courseblock"> <h4 class="courseblocktitle">6.2092 Solid-State Circuits</h4> Subject meets with <a href="/search/?P=6.2090" title="6.2090" class="bubblelink code" onclick="return showCourse(this, '6.2090');">6.2090</a> Prereq: <a href="/search/?P=6.2040" title="6.2040" class="bubblelink code" onclick="return showCourse(this, '6.2040');">6.2040</a>, <a href="/search/?P=6.2080" title="6.2080" class="bubblelink code" onclick="return showCourse(this, '6.2080');">6.2080</a>, or permission of instructor G (Fall) 3-2-7 units Fosters deep understanding and intuition that is crucial in innovating analog circuits and optimizing the whole system in bipolar junction transistor (BJT) and metal oxide semiconductor (MOS) technologies. Covers both theory and real-world applications of basic amplifier structures, operational amplifiers, temperature sensors, bandgap references. Covers topics such as noise, linearity and stability. Homework and labs give students access to CAD/EDA tools to design and analyze analog circuits. Provides practical experience through lab exercises, including a broadband amplifier design and characterization. Students taking graduate version complete additional assignments. N. Reiskarimian, H.-S. Lee, R. Han </div><div class="courseblock"> <h4 class="courseblocktitle">6.6000 CMOS Analog and Mixed-Signal Circuit Design</h4> Prereq: <a href="/search/?P=6.2090" title="6.2090" class="bubblelink code" onclick="return showCourse(this, '6.2090');">6.2090</a> G (Spring) 3-0-9 units A detailed exposition of the principles involved in designing and optimizing analog and mixed-signal circuits in CMOS technologies. Small-signal and large-signal models. Systemic methodology for device sizing and biasing. Basic circuit building blocks. Operational amplifier design. Principles of switched capacitor networks including switched-capacitor and continuous-time integrated filters. Basic and advanced A/D and D/A converters, delta-sigma modulators, RF and other signal processing circuits. Design projects on op amps and subsystems are a required part of the subject. H. S. Lee, R. Han </div><div class="courseblock"> <h4 class="courseblocktitle">6.6010 Analysis and Design of Digital Integrated Circuits</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a> and (<a href="/search/?P=6.2080" title="6.2080" class="bubblelink code" onclick="return showCourse(this, '6.2080');">6.2080</a> or <a href="/search/?P=6.2500" title="6.2500" class="bubblelink code" onclick="return showCourse(this, '6.2500');">6.2500</a>) G (Fall) 3-3-6 units Device and circuit level optimization of digital building blocks. Circuit design styles for logic, arithmetic, and sequential blocks. Estimation and minimization of energy consumption. Interconnect models and parasitics, device sizing and logical effort, timing issues (clock skew and jitter), and active clock distribution techniques. Memory architectures, circuits (sense amplifiers), and devices. Evaluation of how design choices affect tradeoffs across key metrics including energy consumption, speed, robustness, and cost. Extensive use of modern design flow and EDA/CAD tools for the analysis and design of digital building blocks and digital VLSI design for labs and design projects V. Sze, A. P. Chandrakasan </div><div class="courseblock"> <h4 class="courseblocktitle">6.6020 High-Frequency Integrated Circuits</h4> Prereq: <a href="/search/?P=6.2080" title="6.2080" class="bubblelink code" onclick="return showCourse(this, '6.2080');">6.2080</a> G (Fall) 3-3-6 units Principles and techniques of high-speed integrated circuits used in wireless/wireline data links and remote sensing. On-chip passive component design of inductors, capacitors, and antennas. Analysis of distributed effects, such as transmission line modeling, S-parameters, and Smith chart. Transceiver architectures and circuit blocks, which include low-noise amplifiers, mixers, voltage-controlled oscillators, power amplifiers, and frequency dividers. Involves IC/EM simulation and laboratory projects. R. Han </div><h2 class="sectionhead">Energy</h2><div class="courseblock"> <h4 class="courseblocktitle">6.2200 Electric Energy Systems</h4> Prereq: <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> U (Fall) 4-0-8 units Analysis and design of modern energy conversion and delivery systems. Develops a solid foundation in electromagnetic phenomena with a focus on electrical energy distribution, electro-mechanical energy conversion (motors and generators), and electrical-to-electrical energy conversion (DC-DC, DC-AC power conversion). Students apply the material covered to consider critical challenges associated with global energy systems, with particular examples related to the electrification of transport and decarbonization of the grid. R. Ram,聽J. H. Lang, M. Ilic,聽D. J. Perreault </div><div class="courseblock"> <h4 class="courseblocktitle">6.2210 Electromagnetic Fields, Forces and Motion</h4> Subject meets with <a href="/search/?P=6.6210" title="6.6210" class="bubblelink code" onclick="return showCourse(this, '6.6210');">6.6210</a> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> and <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> U (Fall) 4-0-8 units Study of electromagnetics and electromagnetic energy conversion leading to an understanding of devices, including electromagnetic sensors, actuators, motors and generators. Quasistatic Maxwell's equations and the Lorentz force law. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. Boundary conditions and multi-region boundary-value problems. Steady-state conduction, polarization, and magnetization. Charge conservation and relaxation, and magnetic induction and diffusion. Extension to moving materials. Electric and magnetic forces and force densities derived from energy, and stress tensors. Extensive use of engineering examples. Students taking graduate version complete additional assignments. J. H. Lang </div><div class="courseblock"> <h4 class="courseblocktitle">6.2220 Power Electronics Laboratory</h4> Subject meets with <a href="/search/?P=6.2221" title="6.2221" class="bubblelink code" onclick="return showCourse(this, '6.2221');">6.2221</a>, <a href="/search/?P=6.2222" title="6.2222" class="bubblelink code" onclick="return showCourse(this, '6.2222');">6.2222</a> Prereq: <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> or <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a> U (Fall) 3-6-3 units. Institute LAB Introduces the design and construction of power electronic circuits and motor drives. Laboratory exercises include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced include DC, induction, and permanent magnet motors, with drive considerations. Provides instruction in written and oral communication. Students taking independent inquiry version <a href="/search/?P=6.2221" title="6.2221" class="bubblelink code" onclick="return showCourse(this, '6.2221');">6.2221</a> expand the scope of their laboratory project. S. B. Leeb </div><div class="courseblock"> <h4 class="courseblocktitle">6.2221 Power Electronics Laboratory - Independent Inquiry</h4> Subject meets with <a href="/search/?P=6.2220" title="6.2220" class="bubblelink code" onclick="return showCourse(this, '6.2220');">6.2220</a>, <a href="/search/?P=6.2222" title="6.2222" class="bubblelink code" onclick="return showCourse(this, '6.2222');">6.2222</a> Prereq: <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> or <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> U (Fall) 3-9-3 units Introduces the design and construction of power electronic circuits and motor drives. Laboratory exercises include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced include DC, induction, and permanent magnet motors, with drive considerations. Provides instruction in written and oral communication. To satisfy the independent inquiry component of this subject, students expand the scope of their laboratory project. S. B. Leeb </div><div class="courseblock"> <h4 class="courseblocktitle">6.2222 Power Electronics Laboratory</h4> Subject meets with <a href="/search/?P=6.2220" title="6.2220" class="bubblelink code" onclick="return showCourse(this, '6.2220');">6.2220</a>, <a href="/search/?P=6.2221" title="6.2221" class="bubblelink code" onclick="return showCourse(this, '6.2221');">6.2221</a> Prereq: Permission of instructor G (Fall) 3-9-3 units 聽Hands-on introduction to the design and construction of power electronic circuits and motor drives. Laboratory exercises (shared with 6.131 and 6.1311) include the construction of drive circuitry for an electric go-cart, flash strobes, computer power supplies, three-phase inverters for AC motors, and resonant drives for lamp ballasts and induction heating. Basic electric machines introduced including DC, induction, and permanent magnet motors, with drive considerations. Students taking graduate version complete additional assignments and an extended final project. S. B. Leeb </div><div class="courseblock"> <h4 class="courseblocktitle">6.6210 Electromagnetic Fields, Forces and Motion</h4> Subject meets with <a href="/search/?P=6.2210" title="6.2210" class="bubblelink code" onclick="return showCourse(this, '6.2210');">6.2210</a> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> and <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> G (Fall) 4-0-8 units Study of electromagnetics and electromagnetic energy conversion leading to an understanding of devices, including electromagnetic sensors, actuators, motors and generators. Quasistatic Maxwell's equations and the Lorentz force law. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. Boundary conditions and multi-region boundary-value problems. Steady-state conduction, polarization, and magnetization. Charge conservation and relaxation, and magnetic induction and diffusion. Extension to moving materials. Electric and magnetic forces and force densities derived from energy, and stress tensors. Extensive use of engineering examples. Students taking graduate version complete additional assignments. J. H. Lang </div><div class="courseblock"> <h4 class="courseblocktitle">6.6220 Power Electronics</h4> Prereq: <a href="/search/?P=6.2500" title="6.2500" class="bubblelink code" onclick="return showCourse(this, '6.2500');">6.2500</a> G (Spring) 3-0-9 units The application of electronics to energy conversion and control. Modeling, analysis, and control techniques. Design of power circuits including inverters, rectifiers, and dc-dc converters. Analysis and design of magnetic components and filters. Characteristics of power semiconductor devices. Numerous application examples, such as motion control systems, power supplies, and radio-frequency power amplifiers. D. J. Perreault </div><div class="courseblock"> <h4 class="courseblocktitle">6.6280 Electric Machines</h4> Prereq: <a href="/search/?P=6.2200" title="6.2200" class="bubblelink code" onclick="return showCourse(this, '6.2200');">6.2200</a>, 6.690, or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Treatment of electromechanical transducers, rotating and linear electric machines. Lumped-parameter electromechanics. Power flow using Poynting's theorem, force estimation using the Maxwell stress tensor and Principle of virtual work. Development of analytical techniques for predicting device characteristics: energy conversion density, efficiency; and of system interaction characteristics: regulation, stability, controllability, and response. Use of electric machines in drive systems. Problems taken from current research. J. L. Kirtley, Jr. </div><h2 class="sectionhead">Electromagnetics, Photonics, and Quantum</h2><div class="courseblock"> <h4 class="courseblocktitle">6.2300 Electromagnetics Waves and Applications</h4> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> U (Spring) 3-5-4 units Analysis and design of modern applications that employ electromagnetic phenomena for signals and power transmission in RF, microwaves, optical and wireless communication systems. Fundamentals include dynamic solutions for Maxwell's equations; electromagnetic power and energy, waves in media, metallic and dielectric waveguides, radiation, and diffraction; resonance; filters; and acoustic analogs. Lab activities range from building to testing of devices and systems (e.g., antenna arrays, radars, dielectric waveguides). Students work in teams on self-proposed maker-style design projects with a focus on fostering creativity, teamwork, and debugging skills. <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> and <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> are recommended but not required. K. O'Brien, L. Daniel </div><div class="courseblock"> <h4 class="courseblocktitle">6.2370 Modern Optics Project Laboratory</h4> Subject meets with <a href="/search/?P=6.6370" title="6.6370" class="bubblelink code" onclick="return showCourse(this, '6.6370');">6.6370</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> U (Fall) 3-5-4 units. Institute LAB Lectures, laboratory exercises and projects on optical signal generation, transmission, detection, storage, processing and display. Topics include polarization properties of light; reflection and refraction; coherence and interference; Fraunhofer and Fresnel diffraction; holography; Fourier optics; coherent and incoherent imaging and signal processing systems; optical properties of materials; lasers and LEDs; electro-optic and acousto-optic light modulators; photorefractive and liquid-crystal light modulation; display technologies; optical waveguides and fiber-optic communication systems; photodetectors. Students may use this subject to find an advanced undergraduate project. Students engage in extensive oral and written communication exercises. Recommended prerequisite: <a href="/search/?P=8.03" title="8.03" class="bubblelink code" onclick="return showCourse(this, '8.03');">8.03</a>. C. Warde </div><div class="courseblock"> <h4 class="courseblocktitle">6.2400 Introduction to Quantum Systems Engineering</h4> Prereq: <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) U (Fall) 4-2-6 units Introduction to the quantum mechanics needed to engineer quantum systems for computation, communication, and sensing. Topics include: motivation for quantum engineering, qubits and quantum gates, rules of quantum mechanics, mathematical background, quantum electrical circuits and other physical quantum systems, harmonic and anharmonic oscillators, measurement, the Schr枚dinger equation, noise, entanglement, benchmarking, quantum communication, and quantum algorithms. No prior experience with quantum mechanics is assumed. K. Berggren, A. Natarajan, K. O'Brien </div><div class="courseblock"> <h4 class="courseblocktitle">6.2410 Quantum Engineering Platforms</h4> Prereq: <a href="/search/?P=6.2400" title="6.2400" class="bubblelink code" onclick="return showCourse(this, '6.2400');">6.2400</a>, <a href="/search/?P=6.6400" title="6.6400" class="bubblelink code" onclick="return showCourse(this, '6.6400');">6.6400</a>, <a href="/search/?P=18.435" title="18.435[J]" class="bubblelink code" onclick="return showCourse(this, '18.435');">18.435[J]</a>, or (<a href="/search/?P=8.04" title="8.04" class="bubblelink code" onclick="return showCourse(this, '8.04');">8.04</a> and <a href="/search/?P=8.05" title="8.05" class="bubblelink code" onclick="return showCourse(this, '8.05');">8.05</a>) U (Spring) 1-5-6 units Provides practical knowledge and quantum engineering experience with several physical platforms for quantum computation, communication, and sensing, including photonics, superconducting qubits, and trapped ions. Labs include both a hardware component -- to gain experience with challenges, design, and non-idealities -- and a cloud component to run algorithms on state of the art commercial systems. Use entangled photons to communicate securely (quantum key distribution). Run quantum algorithms on trapped ion and superconducting quantum computers. D. Englund </div><div class="courseblock"> <h4 class="courseblocktitle">6.6300 Electromagnetics</h4> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> and <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> G (Fall) 4-0-8 units Explores electromagnetic phenomena in modern applications, including wireless and optical communications, circuits, computer interconnects and peripherals, microwave communications and radar, antennas, sensors, micro-electromechanical systems, and power generation and transmission. Fundamentals include quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; modal expansions; resonance; acoustic analogs; and forces, power, and energy. Q. Hu, J. Notaros </div><div class="courseblock"> <h4 class="courseblocktitle">6.6310 Optics and Photonics</h4> Prereq: <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a> or <a href="/search/?P=8.03" title="8.03" class="bubblelink code" onclick="return showCourse(this, '8.03');">8.03</a> G (Fall) 3-0-9 units Introduction to fundamental concepts and techniques of optics, photonics, and fiber optics, aimed at developing skills for independent research. Topics include: Review of Maxwell's equations, light propagation, reflection and transmission, dielectric mirrors and filters. Scattering matrices, interferometers, and interferometric measurement. Fresnel and Fraunhoffer diffraction theory. Lenses, optical imaging systems, and software design tools. Gaussian beams, propagation and resonator design. Optical waveguides, optical fibers and photonic devices for encoding and detection. Discussion of research operations / funding and professional development topics. The course reviews and introduces mathematical methods and techniques, which are fundamental in optics and photonics, but also useful in many other engineering specialties. J. G. Fujimoto </div><div class="courseblock"> <h4 class="courseblocktitle">6.6330 Fundamentals of Photonics</h4> Subject meets with <a href="/search/?P=6.6331" title="6.6331" class="bubblelink code" onclick="return showCourse(this, '6.6331');">6.6331</a> Prereq: <a href="/search/?P=2.71" title="2.71" class="bubblelink code" onclick="return showCourse(this, '2.71');">2.71</a>, <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a>, or <a href="/search/?P=8.07" title="8.07" class="bubblelink code" onclick="return showCourse(this, '8.07');">8.07</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units Covers the fundamentals of optics and the interaction of light and matter, leading to devices such as light emitting diodes, optical amplifiers, and lasers. Topics include classical ray, wave, beam, and Fourier optics; Maxwell's electromagnetic waves; resonators; quantum theory of photons; light-matter interaction; laser amplification; lasers; and semiconductors optoelectronics. Students taking graduate version complete additional assignments. D. R. Englund </div><div class="courseblock"> <h4 class="courseblocktitle">6.6331 Fundamentals of Photonics</h4> Subject meets with <a href="/search/?P=6.6330" title="6.6330" class="bubblelink code" onclick="return showCourse(this, '6.6330');">6.6330</a> Prereq: <a href="/search/?P=2.71" title="2.71" class="bubblelink code" onclick="return showCourse(this, '2.71');">2.71</a>, <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a>, or <a href="/search/?P=8.07" title="8.07" class="bubblelink code" onclick="return showCourse(this, '8.07');">8.07</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Fall) 3-0-9 units Covers the fundamentals of optics and the interaction of light and matter, leading to devices such as light emitting diodes, optical amplifiers, and lasers. Topics include classical ray, wave, beam, and Fourier optics; Maxwell's electromagnetic waves; resonators; quantum theory of photons; light-matter interaction; laser amplification; lasers; and semiconductors optoelectronics. Students taking graduate version complete additional assignments. D. R. Englund </div><div class="courseblock"> <h4 class="courseblocktitle">6.6340[J] Nonlinear Optics</h4> Same subject as <a href="/search/?P=8.431J" title="8.431[J]" class="bubblelink code" onclick="return showCourse(this, '8.431J');">8.431[J]</a> Prereq: <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a> or <a href="/search/?P=8.03" title="8.03" class="bubblelink code" onclick="return showCourse(this, '8.03');">8.03</a> G (Spring) 3-0-9 units Techniques of nonlinear optics with emphasis on fundamentals for research in optics, photonics, spectroscopy, and ultrafast science. Topics include: electro-optic modulators and devices, sum and difference frequency generation, and parametric conversion. Nonlinear propagation effects in optical fibers including self-phase modulation, pulse compression, solitons, communication, and femtosecond fiber lasers. Review of quantum mechanics, interaction of light with matter, laser gain and operation, density matrix techniques, perturbation theory, diagrammatic methods, nonlinear spectroscopies, ultrafast lasers and measurements. Discussion of research operations and funding and professional development topics. Introduces fundamental methods and techniques needed for independent research in advanced optics and photonics, but useful in many other engineering and physics disciplines. J. G. Fujimoto </div><div class="courseblock"> <h4 class="courseblocktitle">6.6370 Optical Imaging Devices, and Systems</h4> Subject meets with <a href="/search/?P=6.2370" title="6.2370" class="bubblelink code" onclick="return showCourse(this, '6.2370');">6.2370</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> G (Fall) 3-0-9 units Principles of operation and applications of optical imaging devices and systems (includes optical signal generation, transmission, detection, storage, processing and display). Topics include review of the basic properties of electromagnetic waves; coherence and interference; diffraction and holography; Fourier optics; coherent and incoherent imaging and signal processing systems; optical properties of materials; lasers and LEDs; electro-optic and acousto-optic light modulators; photorefractive and liquid-crystal light modulation; spatial light modulators and displays; near-eye and projection displays, holographic and other 3-D display schemes, photodetectors; 2-D and 3-D optical storage technologies; adaptive optical systems; role of optics in next-generation computers. Requires a research paper on a specific contemporary optical imaging topic. Recommended prerequisite: <a href="/search/?P=8.03" title="8.03" class="bubblelink code" onclick="return showCourse(this, '8.03');">8.03</a>. C. Warde </div><div class="courseblock"> <h4 class="courseblocktitle">6.6400 Applied Quantum and Statistical Physics</h4> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Fall) 4-0-8 units Elementary quantum mechanics and statistical physics. Introduces applied quantum physics. Emphasizes experimental basis for quantum mechanics. Applies Schrodinger's equation to the free particle, tunneling, the harmonic oscillator, and hydrogen atom. Variational methods. Elementary statistical physics; Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions. Simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and more. Some familiarity with continuous time Fourier transforms recommended. P. L. Hagelstein </div><div class="courseblock"> <h4 class="courseblocktitle">6.6410[J] Quantum Computation</h4> Same subject as <a href="/search/?P=2.111J" title="2.111[J]" class="bubblelink code" onclick="return showCourse(this, '2.111J');">2.111[J]</a>, <a href="/search/?P=8.370J" title="8.370[J]" class="bubblelink code" onclick="return showCourse(this, '8.370J');">8.370[J]</a>, <a href="/search/?P=18.435J" title="18.435[J]" class="bubblelink code" onclick="return showCourse(this, '18.435J');">18.435[J]</a> Prereq: <a href="/search/?P=8.05" title="8.05" class="bubblelink code" onclick="return showCourse(this, '8.05');">8.05</a>, <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, <a href="/search/?P=18.700" title="18.700" class="bubblelink code" onclick="return showCourse(this, '18.700');">18.700</a>, <a href="/search/?P=18.701" title="18.701" class="bubblelink code" onclick="return showCourse(this, '18.701');">18.701</a>, or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a> G (Fall) 3-0-9 units See description under subject <a href="/search/?P=18.435J" title="18.435[J]" class="bubblelink code" onclick="return showCourse(this, '18.435J');">18.435[J]</a>. I. Chuang, A. Harrow, P. Shor </div><div class="courseblock"> <h4 class="courseblocktitle">6.6420[J] Quantum Information Science</h4> Same subject as <a href="/search/?P=8.371J" title="8.371[J]" class="bubblelink code" onclick="return showCourse(this, '8.371J');">8.371[J]</a>, <a href="/search/?P=18.436J" title="18.436[J]" class="bubblelink code" onclick="return showCourse(this, '18.436J');">18.436[J]</a> Prereq: <a href="/search/?P=18.435" title="18.435[J]" class="bubblelink code" onclick="return showCourse(this, '18.435');">18.435[J]</a> G (Spring) 3-0-9 units See description under subject <a href="/search/?P=8.371J" title="8.371[J]" class="bubblelink code" onclick="return showCourse(this, '8.371J');">8.371[J]</a>. I. Chuang, A. Harrow </div><h2 class="sectionhead">Nanoelectronics & Nanotechnology</h2><div class="courseblock"> <h4 class="courseblocktitle">6.2500 Nanoelectronics and Computing Systems</h4> Prereq: <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> U (Spring) 4-0-8 units Studies interaction between materials, semiconductor physics, electronic devices, and computing systems. Develops intuition of how transistors operate. Topics range from introductory semiconductor physics to modern state-of-the-art nano-scale devices. Considers how innovations in devices have driven historical progress in computing, and explores ideas for further improvements in devices and computing. Students apply material to understand how building improved computing systems requires knowledge of devices, and how making the correct device requires knowledge of computing systems. Includes a design project for practical application of concepts, and labs for experience building silicon transistors and devices. A. I. Akinwande, J. Kong, T. Palacios, M. Shulaker </div><div class="courseblock"> <h4 class="courseblocktitle">6.2530 Introduction to Nanoelectronics</h4> Subject meets with <a href="/search/?P=6.2532" title="6.2532" class="bubblelink code" onclick="return showCourse(this, '6.2532');">6.2532</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> U (Fall) Not offered regularly; consult department 4-0-8 units Transistors at the nanoscale. Quantization, wavefunctions, and Schrodinger's equation. Introduction to electronic properties of molecules, carbon nanotubes, and crystals. Energy band formation and the origin of metals, insulators and semiconductors. Ballistic transport, Ohm's law, ballistic versus traditional MOSFETs, fundamental limits to computation. M. A. Baldo </div><div class="courseblock"> <h4 class="courseblocktitle">6.2532 Nanoelectronics</h4> Subject meets with <a href="/search/?P=6.2530" title="6.2530" class="bubblelink code" onclick="return showCourse(this, '6.2530');">6.2530</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> G (Fall) Not offered regularly; consult department 4-0-8 units Meets with undergraduate subject <a href="/search/?P=6.2530" title="6.2530" class="bubblelink code" onclick="return showCourse(this, '6.2530');">6.2530</a>, but requires the completion of additional/different homework assignments and or projects. See subject description under <a href="/search/?P=6.2530" title="6.2530" class="bubblelink code" onclick="return showCourse(this, '6.2530');">6.2530</a>. M. A. Baldo </div><div class="courseblock"> <h4 class="courseblocktitle">6.2540 Nanotechnology: From Atoms to Systems</h4> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> U (Fall) 2-3-7 units Introduces the fundamentals of applied quantum mechanics, materials science, and fabrication skills needed to design, engineer, and build emerging nanodevices with diverse applications in energy, memory, display, communications, and sensing. Focuses on the application and outlines聽the聽full progression from the fundamentals to the implemented device and functional technology. Closely integrates聽lectures with design-oriented laboratory modules.聽 F. Niroui, R. Ram, L. Liu, T. Palacios聽 </div><div class="courseblock"> <h4 class="courseblocktitle">6.2600[J] Micro/Nano Processing Technology</h4> Same subject as <a href="/search/?P=3.155J" title="3.155[J]" class="bubblelink code" onclick="return showCourse(this, '3.155J');">3.155[J]</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a>, <a href="/search/?P=3.091|5.111|5.112" onclick="return showCourse(this, '3.091|5.111|5.112');">Chemistry (GIR)</a>, <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a>, or permission of instructor U (Spring) 3-4-5 units Introduces the theory and technology of micro/nano fabrication. Includes lectures and laboratory sessions on processing techniques: wet and dry etching, chemical and physical deposition, lithography, thermal processes, packaging, and device and materials characterization. Homework uses process simulation tools to build intuition about higher order effects. Emphasizes interrelationships between material properties and processing, device structure, and the electrical, mechanical, optical, chemical or biological behavior of devices. Students fabricate solar cells, and a choice of MEMS cantilevers or microfluidic mixers. Students formulate their own device idea, either based on cantilevers or mixers, then implement and test their designs in the lab. Students engage in extensive written and oral communication exercises. Course provides background for research work related to micro/nano fabrication. Enrollment limited. J. del Alamo, J. Michel, J. Scholvin </div><div class="courseblock"> <h4 class="courseblocktitle">6.6500[J] Integrated Microelectronic Devices</h4> Same subject as <a href="/search/?P=3.43J" title="3.43[J]" class="bubblelink code" onclick="return showCourse(this, '3.43J');">3.43[J]</a> Prereq: <a href="/search/?P=3.42" title="3.42" class="bubblelink code" onclick="return showCourse(this, '3.42');">3.42</a> or <a href="/search/?P=6.2500" title="6.2500" class="bubblelink code" onclick="return showCourse(this, '6.2500');">6.2500</a> G (Fall) 4-0-8 units Covers physics of microelectronic semiconductor devices for integrated circuit applications. Topics include semiconductor fundamentals, p-n junction, metal-oxide semiconductor structure, metal-semiconductor junction, MOS field-effect transistor, and bipolar junction transistor.聽 Emphasizes physical understanding of device operation through energy band diagrams and short-channel MOSFET device design and modern device scaling. Familiarity with MATLAB recommended. J. A. del Alamo, H. L. Tuller </div><div class="courseblock"> <h4 class="courseblocktitle">6.6510 Physics for Solid-State Applications</h4> Prereq: <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a> and <a href="/search/?P=6.6400" title="6.6400" class="bubblelink code" onclick="return showCourse(this, '6.6400');">6.6400</a> G (Spring) 5-0-7 units Classical and quantum models of electrons and lattice vibrations in solids, emphasizing physical models for elastic properties, electronic transport, and heat capacity. Crystal lattices, electronic energy band structures, phonon dispersion relations, effective mass theorem, semiclassical equations of motion, electron scattering and semiconductor optical properties. Band structure and transport properties of selected semiconductors. Connection of quantum theory of solids with quasi-Fermi levels and Boltzmann transport used in device modeling. Q. Hu, R. Ram </div><div class="courseblock"> <h4 class="courseblocktitle">6.6520 Semiconductor Optoelectronics: Theory and Design</h4> Prereq: <a href="/search/?P=6.2500" title="6.2500" class="bubblelink code" onclick="return showCourse(this, '6.2500');">6.2500</a> and <a href="/search/?P=6.6400" title="6.6400" class="bubblelink code" onclick="return showCourse(this, '6.6400');">6.6400</a> Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units Focuses on the physics of the interaction of photons with semiconductor materials. Uses the band theory of solids to calculate the absorption and gain of semiconductor media; and uses rate equation formalism to develop the concepts of laser threshold, population inversion, and modulation response. Presents theory and design for photodetectors, solar cells, modulators, amplifiers, and lasers. Introduces noise models for semiconductor devices, and applications of optoelectronic devices to fiber optic communications. R. J. Ram </div><div class="courseblock"> <h4 class="courseblocktitle">6.6530 Physics of Solids</h4> Prereq: <a href="/search/?P=6.6510" title="6.6510" class="bubblelink code" onclick="return showCourse(this, '6.6510');">6.6510</a> or <a href="/search/?P=8.231" title="8.231" class="bubblelink code" onclick="return showCourse(this, '8.231');">8.231</a> G (Fall) Not offered regularly; consult department 4-0-8 units Continuation of 6.730 emphasizing applications-related physical issues in solids. Topics include: electronic structure and energy band diagrams of semiconductors, metals, and insulators; Fermi surfaces; dynamics of electrons under electric and magnetic fields; classical diffusive transport phenomena such as electrical and thermal conduction and thermoelectric phenomena; quantum transport in tunneling and ballistic devices; optical properties of metals, semiconductors, and insulators; impurities and excitons; photon-lattice interactions; Kramers-Kronig relations; optoelectronic devices based on interband and intersubband transitions; magnetic properties of solids; exchange energy and magnetic ordering; magneto-oscillatory phenomena; quantum Hall effect; superconducting phenomena and simple models. Q. Hu </div><div class="courseblock"> <h4 class="courseblocktitle">6.6600[J] Nanostructure Fabrication</h4> Same subject as <a href="/search/?P=2.391J" title="2.391[J]" class="bubblelink code" onclick="return showCourse(this, '2.391J');">2.391[J]</a> Prereq: <a href="/search/?P=2.710" title="2.710" class="bubblelink code" onclick="return showCourse(this, '2.710');">2.710</a>, <a href="/search/?P=6.2370" title="6.2370" class="bubblelink code" onclick="return showCourse(this, '6.2370');">6.2370</a>, <a href="/search/?P=6.2600" title="6.2600[J]" class="bubblelink code" onclick="return showCourse(this, '6.2600');">6.2600[J]</a>, or permission of instructor G (Spring) 4-0-8 units Describes current techniques used to analyze and fabricate nanometer-length-scale structures and devices. Emphasizes imaging and patterning of nanostructures, including fundamentals of optical, electron (scanning, transmission, and tunneling), and atomic-force microscopy; optical, electron, ion, and nanoimprint lithography, templated self-assembly, and resist technology. Surveys substrate characterization and preparation, facilities, and metrology requirements for nanolithography. Addresses nanodevice processing methods, such as liquid and plasma etching, lift-off, electroplating, and ion-implant. Discusses applications in nanoelectronics, nanomaterials, and nanophotonics. K. K. Berggren </div><div class="courseblock"> <h4 class="courseblocktitle">6.6630[J] Control of Manufacturing Processes</h4> Same subject as <a href="/search/?P=2.830J" title="2.830[J]" class="bubblelink code" onclick="return showCourse(this, '2.830J');">2.830[J]</a> Prereq: <a href="/search/?P=2.008" title="2.008" class="bubblelink code" onclick="return showCourse(this, '2.008');">2.008</a>, <a href="/search/?P=6.2600" title="6.2600[J]" class="bubblelink code" onclick="return showCourse(this, '6.2600');">6.2600[J]</a>, or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> G (Fall) 3-0-9 units See description under subject <a href="/search/?P=2.830J" title="2.830[J]" class="bubblelink code" onclick="return showCourse(this, '2.830J');">2.830[J]</a>. D. E. Hardt, D. S. Boning </div><h2 class="sectionhead">Signal Processing</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3000 Signal Processing</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> U (Fall, Spring) 6-0-6 units. REST Fundamentals of signal processing, focusing on the use of Fourier methods to analyze and process signals such as sounds and images. Topics include Fourier series, Fourier transforms, the Discrete Fourier Transform, sampling, convolution, deconvolution, filtering, noise reduction, and compression. Applications draw broadly from areas of contemporary interest with emphasis on both analysis and design. D. M. Freeman, A. Hartz </div><div class="courseblock"> <h4 class="courseblocktitle">6.3010 Signals, Systems and Inference</h4> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>) U (Spring) 4-0-8 units Covers signals, systems and inference in communication, control and signal processing. Topics include input-output and state-space models of linear systems driven by deterministic and random signals; time- and transform-domain representations in discrete and continuous time; and group delay. State feedback and observers. Probabilistic models; stochastic processes, correlation functions, power spectra, spectral factorization. Least-mean square error estimation; Wiener filtering. Hypothesis testing; detection; matched filters. P. L. Hagelstein, G. C. Verghese </div><div class="courseblock"> <h4 class="courseblocktitle">6.3020[J] Fundamentals of Music Processing</h4> Same subject as <a href="/search/?P=21M.387J" title="21M.387[J]" class="bubblelink code" onclick="return showCourse(this, '21M.387J');">21M.387[J]</a> Subject meets with <a href="/search/?P=21M.587" title="21M.587" class="bubblelink code" onclick="return showCourse(this, '21M.587');">21M.587</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> and <a href="/search/?P=21M.051" title="21M.051" class="bubblelink code" onclick="return showCourse(this, '21M.051');">21M.051</a> U (Fall) 3-0-9 units. HASS-A See description under subject <a href="/search/?P=21M.387J" title="21M.387[J]" class="bubblelink code" onclick="return showCourse(this, '21M.387J');">21M.387[J]</a>. E. Egozy </div><div class="courseblock"> <h4 class="courseblocktitle">6.7000 Discrete-Time Signal Processing</h4> Prereq: <a href="/search/?P=6.3010" title="6.3010" class="bubblelink code" onclick="return showCourse(this, '6.3010');">6.3010</a> G (Fall) 4-0-8 units Representation, analysis, and design of discrete time signals and systems. Decimation, interpolation, and sampling rate conversion. Noise shaping. Flowgraph structures for DT systems. IIR and FIR filter design techniques. Parametric signal modeling, linear prediction, and聽lattice filters. Discrete Fourier transform, DFT computation,聽and FFT algorithms. Spectral analysis, time-frequency analysis,聽relation to filter banks. Multirate signal processing, perfect reconstruction filter banks, and connection to wavelets. A. V. Oppenheim, J. Ward </div><div class="courseblock"> <h4 class="courseblocktitle">6.7010 Digital Image Processing</h4> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> and <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> G (Spring) 3-0-9 units Introduces models, theories, and algorithms key to digital image processing. Core topics covered include models of image formation, image processing fundamentals, filtering in the spatial and frequency domains,聽image transforms, and feature extraction. Additional topics include image enhancement, image restoration and reconstruction, compression of images and videos, visual recognition, and the application of machine learning-based approaches to image processing. Includes student-driven term project. Y. Rachlin, J. S. Lim </div><div class="courseblock"> <h4 class="courseblocktitle">6.7020 Array Processing</h4> Prereq: <a href="/search/?P=6.7000" title="6.7000" class="bubblelink code" onclick="return showCourse(this, '6.7000');">6.7000</a> and (<a href="/search/?P=2.687" title="2.687" class="bubblelink code" onclick="return showCourse(this, '2.687');">2.687</a> or (<a href="/search/?P=6.3010" title="6.3010" class="bubblelink code" onclick="return showCourse(this, '6.3010');">6.3010</a> and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>)) Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-2-7 units Adaptive and non-adaptive processing of signals received at arrays of sensors. Deterministic beamforming, space-time random processes, optimal and adaptive algorithms, and the sensitivity of algorithm performance to modeling errors and limited data. Methods of improving the robustness of algorithms to modeling errors and limited data are derived. Advanced topics include an introduction to matched field processing and physics-based methods of estimating signal statistics. Homework exercises providing the opportunity to implement and analyze the performance of algorithms in processing data supplied during the course. J. Bonnel </div><h2 class="sectionhead">Control</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3100 Dynamical System Modeling and Control Design</h4> Subject meets with <a href="/search/?P=6.3102" title="6.3102" class="bubblelink code" onclick="return showCourse(this, '6.3102');">6.3102</a> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) U (Fall, Spring) 4-4-4 units. Institute LAB A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression, and identification). Concepts are introduced with lectures and online problems, and then mastered during weekly labs. In lab, students model, design, test, and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g., optimizing thrust-driven positioners or stabilizing magnetic levitators). Students taking graduate version complete additional problems and labs. K. Chen, J. K. White </div><div class="courseblock"> <h4 class="courseblocktitle">6.3102 Dynamical System Modeling and Control Design</h4> Subject meets with <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) G (Fall, Spring) 4-4-4 units A learn-by-design introduction to modeling and control of discrete- and continuous-time systems, from intuition-building analytical techniques to more computational and data-centric strategies. Topics include: linear difference/differential equations (natural frequencies, transfer functions); controller metrics (stability, tracking, disturbance rejection); analytical techniques (PID, root-loci, lead-lag, phase margin); computational strategies (state-space, eigen-placement, LQR); and data-centric approaches (state estimation, regression and identification). Concepts are introduced with lectures and on-line problems, and then mastered during weekly labs. In lab, students model, design, test and explain systems and controllers involving sensors, actuators, and a microcontroller (e.g. optimizing thrust-driven positioners or stabilizing magnetic levitators). Students in the graduate version complete additional problems and labs. K. Chen, J. K. White </div><div class="courseblock"> <h4 class="courseblocktitle">6.7100[J] Dynamic Systems and Control</h4> Same subject as <a href="/search/?P=16.338J" title="16.338[J]" class="bubblelink code" onclick="return showCourse(this, '16.338J');">16.338[J]</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Spring) 4-0-8 units Linear, discrete- and continuous-time, multi-input-output systems in control, related areas. Least squares and matrix perturbation problems. State-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, and minimality. Internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, and observer-based compensators. Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a>. M. A. Dahleh, A. Megretski </div><div class="courseblock"> <h4 class="courseblocktitle">6.7110 Multivariable Control Systems</h4> Prereq: <a href="/search/?P=6.7100" title="6.7100[J]" class="bubblelink code" onclick="return showCourse(this, '6.7100');">6.7100[J]</a> or <a href="/search/?P=16.31" title="16.31" class="bubblelink code" onclick="return showCourse(this, '16.31');">16.31</a> G (Fall) Not offered regularly; consult department 3-0-9 units Computer-aided design methodologies for synthesis of multivariable feedback control systems. Performance and robustness trade-offs. Model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; nonlinear effects. Computer-aided (MATLAB) design homework using models of physical processes. A. Megretski </div><div class="courseblock"> <h4 class="courseblocktitle">6.7120 Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems</h4> Subject meets with <a href="/search/?P=6.7121" title="6.7121" class="bubblelink code" onclick="return showCourse(this, '6.7121');">6.7121</a> Prereq: <a href="/search/?P=6.2200" title="6.2200" class="bubblelink code" onclick="return showCourse(this, '6.2200');">6.2200</a>, (<a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> and <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a>), or permission of instructor U (Fall) 4-0-8 units Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; data-enabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments. M. Ilic </div><div class="courseblock"> <h4 class="courseblocktitle">6.7121 Principles of Modeling, Computing and Control for Decarbonized Electric Energy Systems</h4> Subject meets with <a href="/search/?P=6.7120" title="6.7120" class="bubblelink code" onclick="return showCourse(this, '6.7120');">6.7120</a> Prereq: <a href="/search/?P=6.2200" title="6.2200" class="bubblelink code" onclick="return showCourse(this, '6.2200');">6.2200</a>, (<a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a> and <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a>), or permission of instructor G (Fall) 4-0-8 units Introduces fundamentals of electric energy systems as complex dynamical network systems. Topics include coordinated and distributed modeling and control methods for efficient and reliable power generation, delivery, and consumption; data-enabled algorithms for integrating clean intermittent resources, storage, and flexible demand, including electric vehicles; examples of network congestion management, frequency, and voltage control in electrical grids at various scales; and design and operation of supporting markets. Students taking graduate version complete additional assignments. M. Ilic </div><h2 class="sectionhead">Optimization & Engineering Mathematics</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3260[J] Networks</h4> Same subject as <a href="/search/?P=14.15J" title="14.15[J]" class="bubblelink code" onclick="return showCourse(this, '14.15J');">14.15[J]</a> Subject meets with <a href="/search/?P=14.150" title="14.150" class="bubblelink code" onclick="return showCourse(this, '14.150');">14.150</a> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or <a href="/search/?P=14.30" title="14.30" class="bubblelink code" onclick="return showCourse(this, '14.30');">14.30</a> U (Spring) 4-0-8 units. HASS-S See description under subject <a href="/search/?P=14.15J" title="14.15[J]" class="bubblelink code" onclick="return showCourse(this, '14.15J');">14.15[J]</a>. A. Wolitzky </div><div class="courseblock"> <h4 class="courseblocktitle">6.7210[J] Introduction to Mathematical Programming</h4> Same subject as <a href="/search/?P=15.081J" title="15.081[J]" class="bubblelink code" onclick="return showCourse(this, '15.081J');">15.081[J]</a> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Fall) 4-0-8 units Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; robust optimization;聽integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NP-completeness. D. Bertsimas, P. Jaillet </div><div class="courseblock"> <h4 class="courseblocktitle">6.7220[J] Nonlinear Optimization</h4> Same subject as <a href="/search/?P=15.084J" title="15.084[J]" class="bubblelink code" onclick="return showCourse(this, '15.084J');">15.084[J]</a> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> and (<a href="/search/?P=18.100A" title="18.100A" class="bubblelink code" onclick="return showCourse(this, '18.100A');">18.100A</a>, <a href="/search/?P=18.100B" title="18.100B" class="bubblelink code" onclick="return showCourse(this, '18.100B');">18.100B</a>, or <a href="/search/?P=18.100Q" title="18.100Q" class="bubblelink code" onclick="return showCourse(this, '18.100Q');">18.100Q</a>) G (Spring) 4-0-8 units Unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, sub-gradient and first-order methods. Constrained optimization methods include feasible directions, projection, interior point methods, and Lagrange multiplier methods. Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions and Lagrange multipliers. Geometric approach to duality theory. Applications drawn from control, communications, machine learning, and resource allocation problems. R. M. Freund, P. Parrilo, G. Perakis </div><div class="courseblock"> <h4 class="courseblocktitle">6.7230[J] Algebraic Techniques and Semidefinite Optimization</h4> Same subject as <a href="/search/?P=18.456J" title="18.456[J]" class="bubblelink code" onclick="return showCourse(this, '18.456J');">18.456[J]</a> Prereq: <a href="/search/?P=6.7210" title="6.7210[J]" class="bubblelink code" onclick="return showCourse(this, '6.7210');">6.7210[J]</a> or 15.093 Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units Theory and computational techniques for optimization problems involving polynomial equations and inequalities with particular, emphasis on the connections with semidefinite optimization. Develops algebraic and numerical approaches of general applicability, with a view towards methods that simultaneously incorporate both elements, stressing convexity-based ideas, complexity results, and efficient implementations. Examples from several engineering areas, in particular systems and control applications. Topics include semidefinite programming, resultants/discriminants, hyperbolic polynomials, Groebner bases, quantifier elimination, and sum of squares. P. Parrilo </div><div class="courseblock"> <h4 class="courseblocktitle">6.7240 Game Theory with Engineering Applications</h4> Prereq: <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a> G (Fall) Not offered regularly; consult department 4-0-8 units Introduction to fundamentals of game theory and mechanism design with motivations for each topic drawn from engineering applications (including distributed control of wireline/wireless communication networks, transportation networks, pricing). Emphasis on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notion in different environments. Topics include normal form games, supermodular games, dynamic games, repeated games, games with incomplete/imperfect information, mechanism design, cooperative game theory, and network games. A. Ozdaglar </div><div class="courseblock"> <h4 class="courseblocktitle">6.7250 Optimization for Machine Learning</h4> Prereq: <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Spring) Not offered regularly; consult department 3-0-9 units Optimization algorithms are central to all of machine learning. Covers a variety of topics in optimization, with a focus on non-convex optimization. Focuses on both classical and cutting-edge results, including foundational topics grounded in convexity, complexity theory of first-order methods, stochastic optimization, as well as recent progress in non-Euclidean optimization, deep learning, and beyond. Prepares students to appreciate a broad spectrum of ideas in OPTML, learning to be not only informed users but聽also gaining exposure to research questions in the area. S. Sra </div><div class="courseblock"> <h4 class="courseblocktitle">6.7260 Network Science and Models</h4> Prereq: <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a> and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Spring) 3-0-9 units Introduces the main mathematical models used to describe large networks and dynamical processes that evolve on networks. Static models of random graphs, preferential attachment, and other graph evolution models. Epidemic propagation, opinion dynamics, social learning, and inference in networks. Applications drawn from social, economic, natural, and infrastructure networks, as well as networked decision systems such as sensor networks. P. Jaillet </div><div class="courseblock"> <h4 class="courseblocktitle">6.7300[J] Introduction to Modeling and Simulation</h4> Same subject as <a href="/search/?P=2.096J" title="2.096[J]" class="bubblelink code" onclick="return showCourse(this, '2.096J');">2.096[J]</a>, <a href="/search/?P=16.910J" title="16.910[J]" class="bubblelink code" onclick="return showCourse(this, '16.910J');">16.910[J]</a> Prereq: <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> or <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Fall) 3-6-3 units Introduction to computational techniques for modeling and simulation of a variety of large and complex engineering, science, and socio-economical systems. Prepares students for practical use and development of computational engineering in their own research and future work. Topics include mathematical formulations (e.g., automatic assembly of constitutive and conservation principles); linear system solvers (sparse and iterative); nonlinear solvers (Newton and homotopy); ordinary, time-periodic and partial differential equation solvers; and model order reduction. Students develop their own models and simulators for self-proposed applications, with an emphasis on creativity, teamwork, and communication. Prior basic linear algebra required and at least one numerical programming language (e.g., MATLAB, Julia, Python, etc.) helpful. L. Daniel </div><div class="courseblock"> <h4 class="courseblocktitle">6.7310[J] Introduction to Numerical Methods</h4> Same subject as <a href="/search/?P=18.335J" title="18.335[J]" class="bubblelink code" onclick="return showCourse(this, '18.335J');">18.335[J]</a> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, <a href="/search/?P=18.700" title="18.700" class="bubblelink code" onclick="return showCourse(this, '18.700');">18.700</a>, or <a href="/search/?P=18.701" title="18.701" class="bubblelink code" onclick="return showCourse(this, '18.701');">18.701</a> Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units See description under subject <a href="/search/?P=18.335J" title="18.335[J]" class="bubblelink code" onclick="return showCourse(this, '18.335J');">18.335[J]</a>. A. J. Horning </div><div class="courseblock"> <h4 class="courseblocktitle">6.7320[J] Parallel Computing and Scientific Machine Learning</h4> Same subject as <a href="/search/?P=18.337J" title="18.337[J]" class="bubblelink code" onclick="return showCourse(this, '18.337J');">18.337[J]</a> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, <a href="/search/?P=18.700" title="18.700" class="bubblelink code" onclick="return showCourse(this, '18.700');">18.700</a>, or <a href="/search/?P=18.701" title="18.701" class="bubblelink code" onclick="return showCourse(this, '18.701');">18.701</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-9 units See description under subject <a href="/search/?P=18.337J" title="18.337[J]" class="bubblelink code" onclick="return showCourse(this, '18.337J');">18.337[J]</a>. A. Edelman </div><div class="courseblock"> <h4 class="courseblocktitle">6.7330[J] Numerical Methods for Partial Differential Equations</h4> Same subject as <a href="/search/?P=2.097J" title="2.097[J]" class="bubblelink code" onclick="return showCourse(this, '2.097J');">2.097[J]</a>, <a href="/search/?P=16.920J" title="16.920[J]" class="bubblelink code" onclick="return showCourse(this, '16.920J');">16.920[J]</a> Prereq: <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> or <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Fall) 3-0-9 units See description under subject <a href="/search/?P=16.920J" title="16.920[J]" class="bubblelink code" onclick="return showCourse(this, '16.920J');">16.920[J]</a>. J. Peraire </div><div class="courseblock"> <h4 class="courseblocktitle">6.7340[J] Fast Methods for Partial Differential and Integral Equations</h4> Same subject as <a href="/search/?P=18.336J" title="18.336[J]" class="bubblelink code" onclick="return showCourse(this, '18.336J');">18.336[J]</a> Prereq: <a href="/search/?P=6.7300" title="6.7300[J]" class="bubblelink code" onclick="return showCourse(this, '6.7300');">6.7300[J]</a>, <a href="/search/?P=16.920" title="16.920[J]" class="bubblelink code" onclick="return showCourse(this, '16.920');">16.920[J]</a>, <a href="/search/?P=18.085" title="18.085" class="bubblelink code" onclick="return showCourse(this, '18.085');">18.085</a>, <a href="/search/?P=18.335" title="18.335[J]" class="bubblelink code" onclick="return showCourse(this, '18.335');">18.335[J]</a>, or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall, Spring) 3-0-9 units See description under subject <a href="/search/?P=18.336J" title="18.336[J]" class="bubblelink code" onclick="return showCourse(this, '18.336J');">18.336[J]</a>. K. Burns </div><h2 class="sectionhead">Communications</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3400 Introduction to EECS via Communication Networks</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> U (Fall) Not offered regularly; consult department 4-4-4 units. Institute LAB Studies key concepts, systems, and algorithms to reliably communicate data in settings ranging from the cellular phone network and the Internet to deep space. Weekly laboratory experiments explore these areas in depth. Topics presented in three modules - bits, signals, and packets - spanning the multiple layers of a communication system. Bits module includes information, entropy, data compression algorithms, and error correction with block and convolutional codes. Signals module includes modeling physical channels and noise, signal design, filtering and detection, modulation, and frequency-division multiplexing. Packets module includes switching and queuing principles, media access control, routing protocols, and data transport protocols. K. LaCurts </div><div class="courseblock"> <h4 class="courseblocktitle">6.7410 Principles of Digital Communication</h4> Subject meets with <a href="/search/?P=6.7411" title="6.7411" class="bubblelink code" onclick="return showCourse(this, '6.7411');">6.7411</a> Prereq: (<a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> or <a href="/search/?P=6.3102" title="6.3102" class="bubblelink code" onclick="return showCourse(this, '6.3102');">6.3102</a>) and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>) G (Fall) Not offered regularly; consult department 3-0-9 units Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systems-level view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; in-class time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. M. Medard </div><div class="courseblock"> <h4 class="courseblocktitle">6.7411 Principles of Digital Communication</h4> Subject meets with <a href="/search/?P=6.7410" title="6.7410" class="bubblelink code" onclick="return showCourse(this, '6.7410');">6.7410</a> Prereq: (<a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a>, <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a>, or <a href="/search/?P=6.3400" title="6.3400" class="bubblelink code" onclick="return showCourse(this, '6.3400');">6.3400</a>) and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>) Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Fall) 3-0-9 units Covers communications by progressing through signal representation, sampling, quantization, compression, modulation, coding and decoding, medium access control, and queueing and principles of protocols. By providing simplified proofs, seeks to present an integrated, systems-level view of networking and communications while laying the foundations of analysis and design. Lectures are offered online; in-class time is dedicated to recitations, exercises, and weekly group labs. Homework exercises are based on theoretical derivation and software implementation. Students taking graduate version complete additional assignments. M. Medard </div><div class="courseblock"> <h4 class="courseblocktitle">6.7420 Heterogeneous Networks: Architecture, Transport, Proctocols, and Management</h4> Prereq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> G (Fall) Not offered regularly; consult department 4-0-8 units Introduction to modern heterogeneous networks and the provision of heterogeneous services. Architectural principles, analysis, algorithmic techniques, performance analysis, and existing designs are developed and applied to understand current problems in network design and architecture. Begins with basic principles of networking. Emphasizes development of mathematical and algorithmic tools; applies them to understanding network layer design from the performance and scalability viewpoint. Concludes with network management and control, including the architecture and performance analysis of interconnected heterogeneous networks. Provides background and insight to understand current network literature and to perform research on networks with the aid of network design projects. V. W. S. Chan, R. G. Gallager </div><div class="courseblock"> <h4 class="courseblocktitle">6.7430 Optical Networks</h4> Prereq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> G (Spring) Not offered regularly; consult department 3-0-9 units Introduces the fundamental and practical aspects of optical network technology, architecture, design and analysis tools and techniques. The treatment of optical networks are from the architecture and system design points of view. Optical hardware technologies are introduced and characterized as fundamental network building blocks on which optical transmission systems and network architectures are based. Beyond the Physical Layer, the higher network layers (Media Access Control, Network and Transport Layers) are treated together as integral parts of network design. Performance metrics, analysis and optimization techniques are developed to help guide the creation of high performance complex optical networks. V. W. S. Chan </div><div class="courseblock"> <h4 class="courseblocktitle">6.7440 Principles of Wireless Communication</h4> Prereq: <a href="/search/?P=6.7410" title="6.7410" class="bubblelink code" onclick="return showCourse(this, '6.7410');">6.7410</a> G (Fall) Not offered regularly; consult department 3-0-9 units Introduction to design, analysis, and fundamental limits of wireless transmission systems. Wireless channel and system models; fading and diversity; resource management and power control; multiple-antenna and MIMO systems; space-time codes and decoding algorithms; multiple-access techniques and multiuser detection; broadcast codes and precoding; cellular and ad-hoc network topologies; OFDM and ultrawideband systems; architectural issues. G. W. Wornell, L. Zheng </div><div class="courseblock"> <h4 class="courseblocktitle">6.7450[J] Data-Communication Networks</h4> Same subject as <a href="/search/?P=16.37J" title="16.37[J]" class="bubblelink code" onclick="return showCourse(this, '16.37J');">16.37[J]</a> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or <a href="/search/?P=18.204" title="18.204" class="bubblelink code" onclick="return showCourse(this, '18.204');">18.204</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units Provides an introduction to data networks with an analytic perspective, using wireless networks, satellite networks, optical networks, the internet and data centers as primary applications. Presents basic tools for modeling and performance analysis. Draws upon concepts from聽stochastic聽processes,聽queuing theory, and optimization. E. Modiano </div><div class="courseblock"> <h4 class="courseblocktitle">6.7460 Essential Coding Theory</h4> Prereq: <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a> and <a href="/search/?P=6.1400" title="6.1400[J]" class="bubblelink code" onclick="return showCourse(this, '6.1400');">6.1400[J]</a> G (Spring) Not offered regularly; consult department 3-0-9 units Introduces the theory of error-correcting codes. Focuses on the essential results in the area, taught from first principles. Special focus on results of asymptotic or algorithmic significance. Principal topics include construction and existence results for error-correcting codes; limitations on the combinatorial performance of error-correcting codes; decoding algorithms; and applications to other areas of mathematics and computer science. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.7470 Information Theory</h4> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units Credit cannot also be received for <a href="/search/?P=6.7480" title="6.7480" class="bubblelink code" onclick="return showCourse(this, '6.7480');">6.7480</a> Mathematical definitions of information measures, convexity, continuity, and variational properties. Lossless source coding; variable-length and block compression; Slepian-Wolf theorem; ergodic sources and Shannon-McMillan theorem. Hypothesis testing, large deviations and I-projection. Fundamental limits of block coding for noisy channels: capacity, dispersion, finite blocklength bounds. Coding with feedback. Joint source-channel problem. Rate-distortion theory, vector quantizers. Advanced topics include Gelfand-Pinsker problem, multiple access channels, broadcast channels (depending on available time). M. Medard, L. Zheng </div><div class="courseblock"> <h4 class="courseblocktitle">6.7480 Information Theory: From Coding to Learning (New)</h4> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a> Acad Year 2024-2025: G (Fall) Acad Year 2025-2026: Not offered 3-0-9 units Credit cannot also be received for <a href="/search/?P=6.7470" title="6.7470" class="bubblelink code" onclick="return showCourse(this, '6.7470');">6.7470</a> Introduces fundamentals of information theory and its applications to contemporary problems in statistics, machine learning, and computer science. A thorough study of information measures, including Fisher information, f-divergences, their convex duality, and variational characterizations. Covers information-theoretic treatment of inference, hypothesis testing and large deviations, universal compression, channel coding, lossy compression, and strong data-processing inequalities. Methods are applied to deriving PAC-Bayes bounds, GANs, and regret inequalities in machine learning, metric and non-parametric estimation in statistics, communication complexity, and computation with noisy gates in computer science. Fast-paced journey through a recent textbook with the same title. For a communication-focused version, consider <a href="/search/?P=6.7470" title="6.7470" class="bubblelink code" onclick="return showCourse(this, '6.7470');">6.7470</a>. Y. Polyanskiy </div><h2 class="sectionhead">Probability & Statistics</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3700 Introduction to Probability</h4> Subject meets with <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> U (Fall, Spring) 4-0-8 units. REST Credit cannot also be received for <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a> An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments. G. Bresler, P. Jaillet, J. N. Tsitsiklis </div><div class="courseblock"> <h4 class="courseblocktitle">6.3702 Introduction to Probability</h4> Subject meets with <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> G (Fall, Spring) 4-0-8 units Credit cannot also be received for <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a> An introduction to probability theory, the modeling and analysis of probabilistic systems, and elements of statistical inference. Probabilistic models, conditional probability. Discrete and continuous random variables. Expectation and conditional expectation, and further topics about random variables. Limit Theorems. Bayesian estimation and hypothesis testing. Elements of classical statistical inference. Bernoulli and Poisson processes. Markov chains. Students taking graduate version complete additional assignments. G. Bresler,聽P. Jaillet,聽J. N. Tsitsiklis </div><div class="courseblock"> <h4 class="courseblocktitle">6.3720 Introduction to Statistical Data Analysis</h4> Subject meets with <a href="/search/?P=6.3722" title="6.3722" class="bubblelink code" onclick="return showCourse(this, '6.3722');">6.3722</a> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a>) U (Spring) 4-0-8 units Introduction to the central concepts and methods of data science with an emphasis on statistical grounding and modern computational capabilities. Covers principles involved in extracting information from data for the purpose of making predictions or decisions, including data exploration, feature selection, model fitting, and performance assessment. Topics include learning of distributions, hypothesis testing (including multiple comparison procedures), linear and nonlinear regression and prediction, classification, time series, uncertainty quantification, model validation, causal inference, optimization, and decisions. Computational case studies and projects drawn from applications in finance, sports, engineering, and machine learning life sciences. Students taking graduate version complete additional assignments. Recommended prerequisite: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>. Y. Polyanskiy, D. Shah </div><div class="courseblock"> <h4 class="courseblocktitle">6.3722 Introduction to Statistical Data Analysis</h4> Subject meets with <a href="/search/?P=6.3720" title="6.3720" class="bubblelink code" onclick="return showCourse(this, '6.3720');">6.3720</a> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a>, or permission of instructor) G (Spring) 4-0-8 units Introduction to the central concepts and methods of data science with an emphasis on statistical grounding and modern computational capabilities. Covers principles involved in extracting information from data for the purpose of making predictions or decisions, including data exploration, feature selection, model fitting, and performance assessment. Topics include learning of distributions, hypothesis testing (including multiple comparison procedures), linear and nonlinear regression and prediction, classification, time series, uncertainty quantification, model validation, causal inference, optimization, and decisions. Computational case studies and projects drawn from applications in finance, sports, engineering, and machine learning life sciences. Students taking graduate version complete additional assignments. Recommended prerequisite: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>. Y. Polyanskiy, D. Shah </div><div class="courseblock"> <h4 class="courseblocktitle">6.3730[J] Statistics, Computation and Applications</h4> Same subject as <a href="/search/?P=IDS.012J" title="IDS.012[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.012J');">IDS.012[J]</a> Subject meets with <a href="/search/?P=6.3732J" title="6.3732[J]" class="bubblelink code" onclick="return showCourse(this, '6.3732J');">6.3732[J]</a>, <a href="/search/?P=IDS.131J" title="IDS.131[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.131J');">IDS.131[J]</a> Prereq: (<a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a>, (<a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>), and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, <a href="/search/?P=14.30" title="14.30" class="bubblelink code" onclick="return showCourse(this, '14.30');">14.30</a>, <a href="/search/?P=16.09" title="16.09" class="bubblelink code" onclick="return showCourse(this, '16.09');">16.09</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>)) or permission of instructor U (Spring) 3-1-8 units See description under subject <a href="/search/?P=IDS.012J" title="IDS.012[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.012J');">IDS.012[J]</a>. Enrollment limited; priority to Statistics and Data Science minors, and to juniors and seniors. C. Uhler, N. Azizan </div><div class="courseblock"> <h4 class="courseblocktitle">6.3732[J] Statistics, Computation and Applications</h4> Same subject as <a href="/search/?P=IDS.131J" title="IDS.131[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.131J');">IDS.131[J]</a> Subject meets with <a href="/search/?P=6.3730J" title="6.3730[J]" class="bubblelink code" onclick="return showCourse(this, '6.3730J');">6.3730[J]</a>, <a href="/search/?P=IDS.012J" title="IDS.012[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.012J');">IDS.012[J]</a> Prereq: (<a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a>, (<a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>), and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, <a href="/search/?P=14.30" title="14.30" class="bubblelink code" onclick="return showCourse(this, '14.30');">14.30</a>, <a href="/search/?P=16.09" title="16.09" class="bubblelink code" onclick="return showCourse(this, '16.09');">16.09</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>)) or permission of instructor G (Spring) 3-1-8 units See description under subject <a href="/search/?P=IDS.131J" title="IDS.131[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.131J');">IDS.131[J]</a>. Limited enrollment; priority to Statistics and Data Science minors and to juniors and seniors. C. Uhler, N. Azizan </div><div class="courseblock"> <h4 class="courseblocktitle">6.7700[J] Fundamentals of Probability</h4> Same subject as <a href="/search/?P=15.085J" title="15.085[J]" class="bubblelink code" onclick="return showCourse(this, '15.085J');">15.085[J]</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> G (Fall) 4-0-8 units Introduction to probability theory. Probability spaces and measures. Discrete and continuous random variables. Conditioning and independence. Multivariate normal distribution. Abstract integration, expectation, and related convergence results. Moment generating and characteristic functions. Bernoulli and Poisson process. Finite-state Markov chains. Convergence notions and their relations. Limit theorems. Familiarity with elementary probability and real analysis is desirable. T. Broderick, D. Gamarnik, Y. Polyanskiy </div><div class="courseblock"> <h4 class="courseblocktitle">6.7710 Discrete Stochastic Processes</h4> Prereq: <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a> or <a href="/search/?P=18.204" title="18.204" class="bubblelink code" onclick="return showCourse(this, '18.204');">18.204</a> Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 4-0-8 units Review of probability and laws of large numbers; Poisson counting process and renewal processes; Markov chains (including Markov decision theory), branching processes, birth-death processes, and semi-Markov processes; continuous-time Markov chains and reversibility; random walks, martingales, and large deviations; applications from queueing, communication, control, and operations research. R. G. Gallager, V. W. S. Chan </div><div class="courseblock"> <h4 class="courseblocktitle">6.7720[J] Discrete Probability and Stochastic Processes</h4> Same subject as <a href="/search/?P=15.070J" title="15.070[J]" class="bubblelink code" onclick="return showCourse(this, '15.070J');">15.070[J]</a>, <a href="/search/?P=18.619J" title="18.619[J]" class="bubblelink code" onclick="return showCourse(this, '18.619J');">18.619[J]</a> Prereq: <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a>, <a href="/search/?P=6.7700" title="6.7700[J]" class="bubblelink code" onclick="return showCourse(this, '6.7700');">6.7700[J]</a>, <a href="/search/?P=18.100A" title="18.100A" class="bubblelink code" onclick="return showCourse(this, '18.100A');">18.100A</a>, <a href="/search/?P=18.100B" title="18.100B" class="bubblelink code" onclick="return showCourse(this, '18.100B');">18.100B</a>, or <a href="/search/?P=18.100Q" title="18.100Q" class="bubblelink code" onclick="return showCourse(this, '18.100Q');">18.100Q</a> G (Spring) 3-0-9 units See description under subject <a href="/search/?P=15.070J" title="15.070[J]" class="bubblelink code" onclick="return showCourse(this, '15.070J');">15.070[J]</a>. G. Bresler, D. Gamarnik, E. Mossel,聽Y. Polyanskiy </div><h2 class="sectionhead">Inference</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3800 Introduction to Inference</h4> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> or permission of instructor U (Fall) 4-4-4 units. Institute LAB Introduces聽probabilistic modeling for problems of inference and machine learning from data, emphasizing analytical and computational aspects. Distributions, marginalization, conditioning, and structure, including graphical and neural network representations. Belief propagation, decision-making, classification, estimation, and prediction. Sampling methods and analysis.聽Introduces asymptotic analysis and information measures. Computational laboratory component explores the concepts introduced in class in the context of contemporary applications. Students design inference algorithms, investigate their behavior on real data, and discuss experimental results. P. Golland, G. W. Wornell </div><div class="courseblock"> <h4 class="courseblocktitle">6.7800 Inference and Information</h4> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=6.7700" title="6.7700[J]" class="bubblelink code" onclick="return showCourse(this, '6.7700');">6.7700[J]</a> G (Spring) 4-0-8 units Introduction to principles of Bayesian and non-Bayesian statistical inference. Hypothesis testing and parameter estimation, sufficient statistics; exponential families. EM agorithm. Log-loss inference criterion, entropy and model capacity. Kullback-Leibler distance and information geometry. Asymptotic analysis and large deviations theory. Model order estimation; nonparametric statistics. Computational issues and approximation techniques; Monte Carlo methods. Selected topics such as universal inference and learning, and universal features and neural networks. P. Golland, G. W. Wornell </div><div class="courseblock"> <h4 class="courseblocktitle">6.7810 Algorithms for Inference</h4> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=6.7700" title="6.7700[J]" class="bubblelink code" onclick="return showCourse(this, '6.7700');">6.7700[J]</a>) G (Fall) 4-0-8 units Introduction to computational aspects of statistical inference via probabilistic graphical models. Directed and undirected graphical models, and factor graphs, over discrete and Gaussian distributions; hidden Markov models, linear dynamical systems. Sum-product and junction tree algorithms; forward-backward algorithm, Kalman filtering and smoothing. Min-sum and Viterbi algorithms. Variational methods, mean-field theory, and loopy belief propagation. Sampling methods; Glauber dynamics and mixing time analysis. Parameter structure learning for graphical models; Baum-Welch and Chow-Liu algorithms. Selected topics such as causal inference, particle filtering, restricted Boltzmann machines, and graph neural networks. G. Bresler, D. Shah, G. W. Wornell </div><div class="courseblock"> <h4 class="courseblocktitle">6.7820[J] Graphical Models: A Geometric, Algebraic, and Combinatorial Perspective</h4> Same subject as <a href="/search/?P=IDS.136J" title="IDS.136[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.136J');">IDS.136[J]</a> Prereq: <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a> and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Fall) Not offered regularly; consult department 3-0-9 units See description under subject <a href="/search/?P=IDS.136J" title="IDS.136[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.136J');">IDS.136[J]</a>. C. Uhler </div><div class="courseblock"> <h4 class="courseblocktitle">6.7830 Bayesian Modeling and Inference</h4> Prereq: <a href="/search/?P=6.7700" title="6.7700[J]" class="bubblelink code" onclick="return showCourse(this, '6.7700');">6.7700[J]</a> and <a href="/search/?P=6.7900" title="6.7900" class="bubblelink code" onclick="return showCourse(this, '6.7900');">6.7900</a> G (Spring) 3-0-9 units Covers聽Bayesian modeling and inference at an advanced graduate level. Topics include de Finetti's theorem, decision theory, approximate inference (modern approaches and analysis of Monte Carlo, variational inference, etc.), hierarchical modeling, (continuous and discrete) nonparametric Bayesian approaches, sensitivity and robustness, and evaluation. T. Broderick </div><h2 class="sectionhead">Machine Learning</h2><div class="courseblock"> <h4 class="courseblocktitle">6.3900 Introduction to Machine Learning</h4> Prereq: (<a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> or <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>) and (<a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, <a href="/search/?P=18.700" title="18.700" class="bubblelink code" onclick="return showCourse(this, '18.700');">18.700</a>, or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) U (Fall, Spring) 4-0-8 units Introduction to the principles and algorithms of machine learning from an optimization perspective. Topics include linear and non-linear models for supervised, unsupervised, and reinforcement learning, with a focus on gradient-based methods and neural-network architectures. Previous experience with algorithms may be helpful. V. Monardo, S. Shen </div><div class="courseblock"> <h4 class="courseblocktitle">6.3950 AI, Decision Making, and Society</h4> Subject meets with <a href="/search/?P=6.3952" title="6.3952" class="bubblelink code" onclick="return showCourse(this, '6.3952');">6.3952</a> Prereq: None. Coreq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a>, <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>, or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a> U (Fall) 4-0-8 units Introduction to fundamentals of modern data-driven decision-making frameworks, such as causal inference and hypothesis testing in statistics as well as supervised and reinforcement learning in machine learning. Explores how these frameworks are being applied in various societal contexts, including criminal justice, healthcare, finance, and social media. Emphasis on pinpointing the non-obvious interactions, undesirable feedback loops, and unintended consequences that arise in such settings. Enables students to develop their own principled perspective on the interface of data-driven decision making and society. Students taking graduate version complete additional assignments. A. Ozdaglar, A. Madry, A. Wilson </div><div class="courseblock"> <h4 class="courseblocktitle">6.3952 AI, Decision Making, and Society</h4> Subject meets with <a href="/search/?P=6.3950" title="6.3950" class="bubblelink code" onclick="return showCourse(this, '6.3950');">6.3950</a> Prereq: None. Coreq: <a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a>, <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a> G (Fall) 4-0-8 units Introduction to fundamentals of modern data-driven decision-making frameworks, such as causal inference and hypothesis testing in statistics as well as supervised and reinforcement learning in machine learning. Explores how these frameworks are being applied in various societal contexts, including criminal justice, healthcare, finance, and social media. Emphasis on pinpointing the non-obvious interactions, undesirable feedback loops, and unintended consequences that arise in such settings. Enables students to develop their own principled perspective on the interface of data-driven decision making and society. Students taking graduate version complete additional assignments. A. Ozdaglar, A. Madry, A. Wilson </div><div class="courseblock"> <h4 class="courseblocktitle">6.7900 Machine Learning</h4> Prereq: <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a>) G (Fall) 3-0-9 units Principles, techniques, and algorithms in machine learning from the point of view of statistical inference; representation, generalization, and model selection; and methods such as linear/additive models, active learning, boosting, support vector machines, non-parametric Bayesian methods, hidden Markov models, Bayesian networks, and convolutional and recurrent neural networks. Recommended prerequisite: <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> or other previous experience in machine learning. Enrollment may be limited. C. Daskalakis, T. Jaakkola </div><div class="courseblock"> <h4 class="courseblocktitle">6.7910[J] Statistical Learning Theory and Applications</h4> Same subject as <a href="/search/?P=9.520J" title="9.520[J]" class="bubblelink code" onclick="return showCourse(this, '9.520J');">9.520[J]</a> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.7900" title="6.7900" class="bubblelink code" onclick="return showCourse(this, '6.7900');">6.7900</a>, <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, or permission of instructor G (Fall) 3-0-9 units See description under subject <a href="/search/?P=9.520J" title="9.520[J]" class="bubblelink code" onclick="return showCourse(this, '9.520J');">9.520[J]</a>. T. Poggio, L. Rosasco </div><div class="courseblock"> <h4 class="courseblocktitle">6.7920[J] Reinforcement Learning: Foundations and Methods</h4> Same subject as <a href="/search/?P=1.127J" title="1.127[J]" class="bubblelink code" onclick="return showCourse(this, '1.127J');">1.127[J]</a>, <a href="/search/?P=IDS.140J" title="IDS.140[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.140J');">IDS.140[J]</a> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or permission of instructor G (Fall) 4-0-8 units Examines reinforcement learning (RL) as a methodology for approximately solving sequential decision-making under uncertainty, with foundations in optimal control and machine learning. Provides a mathematical introduction to RL, including dynamic programming, statistical, and empirical perspectives, and special topics. Core topics include: dynamic programming, special structures, finite and infinite horizon Markov Decision Processes, value and policy iteration, Monte Carlo methods, temporal differences, Q-learning, stochastic approximation, and bandits. Also covers approximate dynamic programming, including value-based methods and policy space methods. Applications and examples drawn from diverse domains. Focus is mathematical, but is supplemented with computational exercises. An analysis prerequisite is suggested but not required; mathematical maturity is necessary. C. Wu, M. Dahleh </div><div class="courseblock"> <h4 class="courseblocktitle">6.7930[J] Machine Learning for Healthcare</h4> Same subject as <a href="/search/?P=HST.956J" title="HST.956[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.956J');">HST.956[J]</a> Prereq: <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>, <a href="/search/?P=6.4100" title="6.4100" class="bubblelink code" onclick="return showCourse(this, '6.4100');">6.4100</a>, <a href="/search/?P=6.7810" title="6.7810" class="bubblelink code" onclick="return showCourse(this, '6.7810');">6.7810</a>, <a href="/search/?P=6.7900" title="6.7900" class="bubblelink code" onclick="return showCourse(this, '6.7900');">6.7900</a>, <a href="/search/?P=6.8611" title="6.8611" class="bubblelink code" onclick="return showCourse(this, '6.8611');">6.8611</a>, or <a href="/search/?P=9.520" title="9.520[J]" class="bubblelink code" onclick="return showCourse(this, '9.520');">9.520[J]</a> G (Spring) 4-0-8 units Introduces students to machine learning in healthcare, including the nature of clinical data and the use of machine learning for risk stratification, disease progression modeling, precision medicine, diagnosis, subtype discovery, and improving clinical workflows. Topics include causality, interpretability, algorithmic fairness, time-series analysis, graphical models, deep learning and transfer learning. Guest lectures by clinicians from the Boston area, and projects with real clinical data, emphasize subtleties of working with clinical data and translating machine learning into clinical practice. Limited to 55. D. Sontag, P. Szolovits </div><div class="courseblock"> <h4 class="courseblocktitle">6.7940 Dynamic Programming and Reinforcement Learning</h4> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a> G (Spring) Not offered regularly; consult department 4-0-8 units Dynamic programming as a unifying framework for sequential decision-making under uncertainty, Markov decision problems, and stochastic control. Perfect and imperfect state information models. Finite horizon and infinite horizon problems, including discounted and average cost formulations. Value and policy iteration. Suboptimal methods. Approximate dynamic programming for large-scale problems, and reinforcement learning. Applications and examples drawn from diverse domains. While an analysis prerequisite is not required, mathematical maturity is necessary. J. N. Tsitsiklis </div><div class="courseblock"> <h4 class="courseblocktitle">6.7950 Advanced Topics in Control</h4> Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Advanced study of topics in control. Specific focus varies from year to year. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.7960 Deep Learning (New)</h4> Prereq: <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a> and (<a href="/search/?P=6.3720" title="6.3720" class="bubblelink code" onclick="return showCourse(this, '6.3720');">6.3720</a>, <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>, or <a href="/search/?P=6.C01" title="6.C01" class="bubblelink code" onclick="return showCourse(this, '6.C01');">6.C01</a>) G (Fall) 3-0-9 units Fundamentals of deep learning, including both theory and applications. Topics include neural net architectures (MLPs, CNNs, RNNs, graph nets, transformers), geometry and invariances in deep learning, backpropagation and automatic differentiation, learning theory and generalization in high-dimensions, and applications to computer vision, natural language processing, and robotics. P. Isola, S. Jegelka, S. Beery </div><h2 class="sectionhead">Artificial Intelligence</h2><div class="courseblock"> <h4 class="courseblocktitle">6.4100 Artificial Intelligence</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> U (Fall) Not offered regularly; consult department 4-3-5 units Introduces representations, methods, and architectures used to build applications and to account for human intelligence from a computational point of view. Covers applications of rule chaining, constraint propagation, constrained search, inheritance, statistical inference, and other problem-solving paradigms. Also addresses applications of identification trees, neural nets, genetic algorithms, support-vector machines, boosting, and other learning paradigms. Considers what separates human intelligence from that of other animals. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.4102 Artificial Intelligence</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> G (Fall) Not offered regularly; consult department 4-3-5 units Introduces representations, methods, and architectures used to build applications and to account for human intelligence from a computational point of view. Covers applications of rule chaining, constraint propagation, constrained search, inheritance, statistical inference, and other problem-solving paradigms. Also addresses applications of identification trees, neural nets, genetic algorithms, support-vector machines, boosting, and other learning paradigms. Considers what separates human intelligence from that of other animals. Students taking聽 graduate version complete additional assignments. K. Koile </div><div class="courseblock"> <h4 class="courseblocktitle">6.4110 Representation, Inference, and Reasoning in AI</h4> Subject meets with <a href="/search/?P=16.420" title="16.420" class="bubblelink code" onclick="return showCourse(this, '16.420');">16.420</a> Prereq: (<a href="/search/?P=16.09" title="16.09" class="bubblelink code" onclick="return showCourse(this, '16.09');">16.09</a> and <a href="/search/?P=16.410" title="16.410[J]" class="bubblelink code" onclick="return showCourse(this, '16.410');">16.410[J]</a>) or (<a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a>, <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>, and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>)) U (Spring) 3-0-9 units An introduction to representations and algorithms for artificial intelligence. Topics covered include: constraint satisfaction in discrete and continuous problems, logical representation and inference, Monte Carlo tree search, probabilistic graphical models and inference, planning in discrete and continuous deterministic and probabilistic models including MDPs and POMDPs. L. P. Kaelbling, T. Lozano-Perez, N. Roy </div><div class="courseblock"> <h4 class="courseblocktitle">6.4120[J] Computational Cognitive Science</h4> Same subject as <a href="/search/?P=9.66J" title="9.66[J]" class="bubblelink code" onclick="return showCourse(this, '9.66J');">9.66[J]</a> Subject meets with <a href="/search/?P=9.660" title="9.660" class="bubblelink code" onclick="return showCourse(this, '9.660');">9.660</a> Prereq: <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, <a href="/search/?P=6.3800" title="6.3800" class="bubblelink code" onclick="return showCourse(this, '6.3800');">6.3800</a>, <a href="/search/?P=9.40" title="9.40" class="bubblelink code" onclick="return showCourse(this, '9.40');">9.40</a>, <a href="/search/?P=18.05" title="18.05" class="bubblelink code" onclick="return showCourse(this, '18.05');">18.05</a>, <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>, or permission of instructor U (Fall) 3-0-9 units See description under subject <a href="/search/?P=9.66J" title="9.66[J]" class="bubblelink code" onclick="return showCourse(this, '9.66J');">9.66[J]</a>. J. Tenenbaum </div><div class="courseblock"> <h4 class="courseblocktitle">6.4130[J] Principles of Autonomy and Decision Making</h4> Same subject as <a href="/search/?P=16.410J" title="16.410[J]" class="bubblelink code" onclick="return showCourse(this, '16.410J');">16.410[J]</a> Subject meets with <a href="/search/?P=6.4132J" title="6.4132[J]" class="bubblelink code" onclick="return showCourse(this, '6.4132J');">6.4132[J]</a>, <a href="/search/?P=16.413J" title="16.413[J]" class="bubblelink code" onclick="return showCourse(this, '16.413J');">16.413[J]</a> Prereq: <a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a>, <a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a>, <a href="/search/?P=6.9080" title="6.9080" class="bubblelink code" onclick="return showCourse(this, '6.9080');">6.9080</a>, or permission of instructor U (Fall) 4-0-8 units See description under subject <a href="/search/?P=16.410J" title="16.410[J]" class="bubblelink code" onclick="return showCourse(this, '16.410J');">16.410[J]</a>. B. C. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.4132[J] Principles of Autonomy and Decision Making</h4> Same subject as <a href="/search/?P=16.413J" title="16.413[J]" class="bubblelink code" onclick="return showCourse(this, '16.413J');">16.413[J]</a> Subject meets with <a href="/search/?P=6.4130J" title="6.4130[J]" class="bubblelink code" onclick="return showCourse(this, '6.4130J');">6.4130[J]</a>, <a href="/search/?P=16.410J" title="16.410[J]" class="bubblelink code" onclick="return showCourse(this, '16.410J');">16.410[J]</a> Prereq: <a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a>, <a href="/search/?P=6.9080" title="6.9080" class="bubblelink code" onclick="return showCourse(this, '6.9080');">6.9080</a>, or permission of instructor G (Fall) 3-0-9 units See description under subject <a href="/search/?P=16.413J" title="16.413[J]" class="bubblelink code" onclick="return showCourse(this, '16.413J');">16.413[J]</a>. B. C. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.4150[J] Artificial Intelligence for Business</h4> Same subject as <a href="/search/?P=15.563J" title="15.563[J]" class="bubblelink code" onclick="return showCourse(this, '15.563J');">15.563[J]</a> Prereq: None Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-0-6 units See description under subject <a href="/search/?P=15.563J" title="15.563[J]" class="bubblelink code" onclick="return showCourse(this, '15.563J');">15.563[J]</a>. M. 聽Raghavan </div><div class="courseblock"> <h4 class="courseblocktitle">6.8110[J] Cognitive Robotics</h4> Same subject as <a href="/search/?P=16.412J" title="16.412[J]" class="bubblelink code" onclick="return showCourse(this, '16.412J');">16.412[J]</a> Prereq: (<a href="/search/?P=6.4100" title="6.4100" class="bubblelink code" onclick="return showCourse(this, '6.4100');">6.4100</a> or <a href="/search/?P=16.413" title="16.413[J]" class="bubblelink code" onclick="return showCourse(this, '16.413');">16.413[J]</a>) and (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a>, <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>, or <a href="/search/?P=16.09" title="16.09" class="bubblelink code" onclick="return showCourse(this, '16.09');">16.09</a>) G (Spring) 3-0-9 units See description under subject <a href="/search/?P=16.412J" title="16.412[J]" class="bubblelink code" onclick="return showCourse(this, '16.412J');">16.412[J]</a>. Enrollment may be limited. B. C. Williams </div><h2 class="sectionhead">Robotics</h2><div class="courseblock"> <h4 class="courseblocktitle">6.4200[J] Robotics: Science and Systems</h4> Same subject as <a href="/search/?P=2.124J" title="2.124[J]" class="bubblelink code" onclick="return showCourse(this, '2.124J');">2.124[J]</a>, <a href="/search/?P=16.405J" title="16.405[J]" class="bubblelink code" onclick="return showCourse(this, '16.405J');">16.405[J]</a> Prereq: ((<a href="/search/?P=1.00" title="1.00" class="bubblelink code" onclick="return showCourse(this, '1.00');">1.00</a> or <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>) and (<a href="/search/?P=2.003" title="2.003[J]" class="bubblelink code" onclick="return showCourse(this, '2.003');">2.003[J]</a>, <a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a>, <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>, or <a href="/search/?P=16.06" title="16.06" class="bubblelink code" onclick="return showCourse(this, '16.06');">16.06</a>)) or permission of instructor U (Spring) 2-6-4 units. Institute LAB Presents concepts, principles, and algorithmic foundations for robots and autonomous vehicles operating in the physical world. Topics include sensing, kinematics and dynamics, state estimation, computer vision, perception, learning, control, motion planning, and embedded system development. Students design and implement advanced algorithms on complex robotic platforms capable of agile autonomous navigation and real-time interaction with the physical word. Students engage in extensive written and oral communication exercises. Enrollment limited. L. Carlone, S. Karaman, D. Hadfield-Manell, J. Leonard </div><div class="courseblock"> <h4 class="courseblocktitle">6.4210 Robotic Manipulation</h4> Subject meets with <a href="/search/?P=6.4212" title="6.4212" class="bubblelink code" onclick="return showCourse(this, '6.4212');">6.4212</a> Prereq: (<a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>) or permission of instructor U (Fall) 4-2-9 units Introduces the fundamental algorithmic approaches for creating robot systems that can autonomously manipulate physical objects in unstructured environments such as homes and restaurants. Topics include perception (including approaches based on deep learning and approaches based on 3D geometry), planning (robot kinematics and trajectory generation, collision-free motion planning, task-and-motion planning, and planning under uncertainty), as well as dynamics and control (both model-based and learning-based). Students taking graduate version complete additional assignments. Students engage in extensive written and oral communication exercises. R. Tedrake </div><div class="courseblock"> <h4 class="courseblocktitle">6.4212 Robotic Manipulation</h4> Subject meets with <a href="/search/?P=6.4210" title="6.4210" class="bubblelink code" onclick="return showCourse(this, '6.4210');">6.4210</a> Prereq: (<a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a>) or permission of instructor G (Fall) 3-0-9 units Introduces the fundamental algorithmic approaches for creating robot systems that can autonomously manipulate physical objects in unstructured environments such as homes and restaurants. Topics include perception (including approaches based on deep learning and approaches based on 3D geometry), planning (robot kinematics and trajectory generation, collision-free motion planning, task-and-motion planning, and planning under uncertainty), as well as dynamics and control (both model-based and learning-based. Students taking graduate version complete additional assignments. T. P. Lozano-Perez, R. Tedrake </div><div class="courseblock"> <h4 class="courseblocktitle">6.8200 Sensorimotor Learning</h4> Prereq: <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> or <a href="/search/?P=6.7900" title="6.7900" class="bubblelink code" onclick="return showCourse(this, '6.7900');">6.7900</a> G (Spring) 3-0-9 units Provides an in-depth view of the state-of-the-art learning methods for control and the know-how of applying these techniques. Topics span reinforcement learning, self-supervised learning, imitation learning, model-based learning, and advanced deep learning architectures, and specific machine learning challenges unique to building sensorimotor systems. Discusses how to identify if learning-based control can help solve a particular problem, how to formulate the problem in the learning framework, and what algorithm to use. Applications of algorithms in robotics, logistics, recommendation systems, playing games, and other control domains covered. Instruction involves two lectures a week, practical experience through exercises, discussion of current research directions, and a group project. P. Agrawal </div><div class="courseblock"> <h4 class="courseblocktitle">6.8210 Underactuated Robotics</h4> Prereq: <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> G (Spring) 3-0-9 units Covers nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on computational methods. Topics include the nonlinear dynamics of robotic manipulators, applied optimal and robust control and motion planning. Discussions include examples from biology and applications to legged locomotion, compliant manipulation, underwater robots, and flying machines. R. Tedrake </div><h2 class="sectionhead">Graphics</h2><div class="courseblock"> <h4 class="courseblocktitle">6.4400 Computer Graphics</h4> Prereq: <a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Fall) 3-0-9 units Introduction to computer graphics algorithms, software and hardware. Topics include ray tracing, the graphics pipeline, transformations, texture mapping, shadows, sampling, global illumination, splines, animation and color. F. P. Durand, M. Konakovic-Lukovic, W. Matusik, J. Solomon </div><div class="courseblock"> <h4 class="courseblocktitle">6.4420[J] Computational Design and Fabrication</h4> Same subject as <a href="/search/?P=2.0911J" title="2.0911[J]" class="bubblelink code" onclick="return showCourse(this, '2.0911J');">2.0911[J]</a> Subject meets with <a href="/search/?P=6.8420" title="6.8420" class="bubblelink code" onclick="return showCourse(this, '6.8420');">6.8420</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and (<a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> or permission of instructor) U (Spring) 3-0-9 units Introduces computational aspects of computer-aided design and manufacturing. Explores relevant methods in the context of additive manufacturing (e.g., 3D printing). Topics include computer graphics (geometry modeling, solid modeling, procedural modeling), physically-based simulation (kinematics, finite element method), 3D scanning/geometry processing, and an overview of 3D fabrication methods. Exposes students to the latest research in computational fabrication. Students taking the graduate version complete additional assignments. W. Matusik </div><div class="courseblock"> <h4 class="courseblocktitle">6.8410 Shape Analysis</h4> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a>, <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, and (<a href="/search/?P=6.8300" title="6.8300" class="bubblelink code" onclick="return showCourse(this, '6.8300');">6.8300</a> or <a href="/search/?P=6.4400" title="6.4400" class="bubblelink code" onclick="return showCourse(this, '6.4400');">6.4400</a>) Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units Introduces mathematical, algorithmic, and statistical tools needed to analyze geometric data and to apply geometric techniques to data analysis, with applications to fields such as computer graphics, machine learning, computer vision, medical imaging, and architecture. Potential topics include applied introduction to differential geometry, discrete notions of curvature, metric embedding, geometric PDE via the finite element method (FEM) and discrete exterior calculus (DEC),; computational spectral geometry and relationship to graph-based learning, correspondence and mapping, level set method, descriptor, shape collections, optimal transport, and vector field design. J. Solomon </div><div class="courseblock"> <h4 class="courseblocktitle">6.8420 Computational Design and Fabrication</h4> Subject meets with <a href="/search/?P=2.0911J" title="2.0911[J]" class="bubblelink code" onclick="return showCourse(this, '2.0911J');">2.0911[J]</a>, <a href="/search/?P=6.4420J" title="6.4420[J]" class="bubblelink code" onclick="return showCourse(this, '6.4420J');">6.4420[J]</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and (<a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> or permission of instructor) G (Spring) 3-0-9 units Introduces computational aspects of computer-aided design and manufacturing. Explores relevant methods in the context of additive manufacturing (e.g., 3D printing). Topics include computer graphics (geometry modeling, solid modeling, procedural modeling), physically-based simulation (kinematics, finite element method), 3D scanning/geometry processing, and an overview of 3D fabrication methods. Exposes students to the latest research in computational fabrication. Students taking graduate version complete additional assignments. W. Matusik </div><h2 class="sectionhead">Human-Computer Interaction & Society</h2><div class="courseblock"> <h4 class="courseblocktitle">6.4510 Engineering Interactive Technologies</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a>, <a href="/search/?P=6.2050" title="6.2050" class="bubblelink code" onclick="return showCourse(this, '6.2050');">6.2050</a>, <a href="/search/?P=6.2060" title="6.2060" class="bubblelink code" onclick="return showCourse(this, '6.2060');">6.2060</a>, <a href="/search/?P=6.9010" title="6.9010" class="bubblelink code" onclick="return showCourse(this, '6.9010');">6.9010</a>, or permission of instructor U (Fall) Not offered regularly; consult department 1-5-6 units Provides instruction in building cutting-edge interactive technologies, explains the underlying engineering concepts, and shows how those technologies evolved over time. Students use a studio format (i.e., extended periods of time) for constructing software and hardware prototypes. Topics include interactive technologies, such as multi-touch, augmented reality, haptics, wearables, and shape-changing聽interfaces. In a group project, students build their own interactive hardware/software prototypes and present them in a live demo at the end of term. Enrollment may be limited. S. Mueller </div><div class="courseblock"> <h4 class="courseblocktitle">6.4530[J] Principles and Practice of Assistive Technology</h4> Same subject as <a href="/search/?P=2.78J" title="2.78[J]" class="bubblelink code" onclick="return showCourse(this, '2.78J');">2.78[J]</a>, <a href="/search/?P=HST.420J" title="HST.420[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.420J');">HST.420[J]</a> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department 2-4-6 units Students work closely with people with disabilities to develop assistive and adaptive technologies that help them live more independently. Covers design methods and problem-solving strategies; human factors; human-machine interfaces; community perspectives; social and ethical aspects; and assistive technology for motor, cognitive, perceptual, and age-related impairments. Prior knowledge of one or more of the following areas useful: software; electronics; human-computer interaction; cognitive science; mechanical engineering; control; or MIT hobby shop, MIT PSC, or other relevant independent project experience. Enrollment may be limited. R. C. Miller, J. E. Greenberg, J. J. Leonard </div><div class="courseblock"> <h4 class="courseblocktitle">6.4550[J] Interactive Music Systems</h4> Same subject as <a href="/search/?P=21M.385J" title="21M.385[J]" class="bubblelink code" onclick="return showCourse(this, '21M.385J');">21M.385[J]</a> Subject meets with <a href="/search/?P=21M.585" title="21M.585" class="bubblelink code" onclick="return showCourse(this, '21M.585');">21M.585</a> Prereq: (<a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> and <a href="/search/?P=21M.301" title="21M.301" class="bubblelink code" onclick="return showCourse(this, '21M.301');">21M.301</a>) or permission of instructor U (Fall, Spring) 3-0-9 units. HASS-A See description under subject <a href="/search/?P=21M.385J" title="21M.385[J]" class="bubblelink code" onclick="return showCourse(this, '21M.385J');">21M.385[J]</a>. Limited to 36. E. Egozy, L. Kaelbling </div><div class="courseblock"> <h4 class="courseblocktitle">6.4570[J] Creating Video Games</h4> Same subject as <a href="/search/?P=CMS.611J" title="CMS.611[J]" class="bubblelink code" onclick="return showCourse(this, 'CMS.611J');">CMS.611[J]</a> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> or <a href="/search/?P=CMS.301" title="CMS.301" class="bubblelink code" onclick="return showCourse(this, 'CMS.301');">CMS.301</a> U (Fall) 3-3-6 units. HASS-A See description under subject <a href="/search/?P=CMS.611J" title="CMS.611[J]" class="bubblelink code" onclick="return showCourse(this, 'CMS.611J');">CMS.611[J]</a>. Limited to 36. P. Tan, S. Verrilli, R. Eberhardt </div><div class="courseblock"> <h4 class="courseblocktitle">6.4590[J] Foundations of Information Policy</h4> Same subject as <a href="/search/?P=STS.085J" title="STS.085[J]" class="bubblelink code" onclick="return showCourse(this, 'STS.085J');">STS.085[J]</a> Subject meets with <a href="/search/?P=STS.487" title="STS.487" class="bubblelink code" onclick="return showCourse(this, 'STS.487');">STS.487</a> Prereq: Permission of instructor Acad Year 2024-2025: U (Fall) Acad Year 2025-2026: Not offered 3-0-9 units. HASS-S Studies the growth of computer and communications technology and the new legal and ethical challenges that reflect tensions between individual rights and societal needs. Topics include computer crime; intellectual property restrictions on software; encryption, privacy, and national security; academic freedom and free speech. Students meet and question technologists, activists, law enforcement agents, journalists, and legal experts. Instruction and practice in oral and written communication provided. Students taking graduate version complete additional assignments. Enrollment limited. H. Abelson, M. Fischer, D. Weitzner </div><div class="courseblock"> <h4 class="courseblocktitle">6.8510 Intelligent Multimodal User Interfaces</h4> Prereq: (<a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> and <a href="/search/?P=6.4100" title="6.4100" class="bubblelink code" onclick="return showCourse(this, '6.4100');">6.4100</a>) or permission of instructor G (Spring) 3-0-9 units Implementation and evaluation of intelligent multi-modal user interfaces, taught from a combination of hands-on exercises and papers from the original literature. Topics include basic technologies for handling speech, vision, pen-based interaction, and other modalities, as well as various techniques for combining modalities. Substantial readings and a term project, where students build a program that illustrates one or more of the themes of the course. R. Davis </div><div class="courseblock"> <h4 class="courseblocktitle">6.8530 Interactive Data Visualization</h4> Prereq: <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> G (Spring) Not offered regularly; consult department 3-0-9 units Credit cannot also be received for <a href="/search/?P=6.C35" title="6.C35[J]" class="bubblelink code" onclick="return showCourse(this, '6.C35');">6.C35[J]</a>, <a href="/search/?P=6.C85" title="6.C85[J]" class="bubblelink code" onclick="return showCourse(this, '6.C85');">6.C85[J]</a>, <a href="/search/?P=11.154" title="11.154" class="bubblelink code" onclick="return showCourse(this, '11.154');">11.154</a>, <a href="/search/?P=11.454" title="11.454" class="bubblelink code" onclick="return showCourse(this, '11.454');">11.454</a>, <a href="/search/?P=11.C35" title="11.C35[J]" class="bubblelink code" onclick="return showCourse(this, '11.C35');">11.C35[J]</a>, <a href="/search/?P=11.C85" title="11.C85[J]" class="bubblelink code" onclick="return showCourse(this, '11.C85');">11.C85[J]</a> Interactive visualization provides a means of making sense of a world awash in data. Covers the techniques and algorithms for creating effective visualizations, using principles from graphic design, perceptual psychology, and cognitive science. Short assignments build familiarity with the data analysis and visualization design process, and a final project provides experience designing, implementing, and deploying an explanatory narrative visualization or visual analysis tool to address a concrete challenge. A. Satyanarayan </div><h2 class="sectionhead">Computational Biology</h2><div class="courseblock"> <h4 class="courseblocktitle">6.4710[J] Evolutionary Biology: Concepts, Models and Computation</h4> Same subject as <a href="/search/?P=7.33J" title="7.33[J]" class="bubblelink code" onclick="return showCourse(this, '7.33J');">7.33[J]</a> Prereq: (<a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> and <a href="/search/?P=7.03" title="7.03" class="bubblelink code" onclick="return showCourse(this, '7.03');">7.03</a>) or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Spring) 3-0-9 units See description under subject <a href="/search/?P=7.33J" title="7.33[J]" class="bubblelink code" onclick="return showCourse(this, '7.33J');">7.33[J]</a>. R. Berwick, D. Bartel </div><div class="courseblock"> <h4 class="courseblocktitle">6.8700[J] Advanced Computational Biology: Genomes, Networks, Evolution</h4> Same subject as <a href="/search/?P=HST.507J" title="HST.507[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.507J');">HST.507[J]</a> Subject meets with <a href="/search/?P=6.8701" title="6.8701" class="bubblelink code" onclick="return showCourse(this, '6.8701');">6.8701</a> Prereq: (<a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a>, <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>, and <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>) or permission of instructor G (Fall) 4-0-8 units See description for <a href="/search/?P=6.8701" title="6.8701" class="bubblelink code" onclick="return showCourse(this, '6.8701');">6.8701</a>. Additionally examines recent publications in the areas covered, with research-style assignments. A more substantial final project is expected, which can lead to a thesis and publication. M. Kellis </div><div class="courseblock"> <h4 class="courseblocktitle">6.8701 Computational Biology: Genomes, Networks, Evolution</h4> Subject meets with <a href="/search/?P=6.8700J" title="6.8700[J]" class="bubblelink code" onclick="return showCourse(this, '6.8700J');">6.8700[J]</a>, <a href="/search/?P=HST.507J" title="HST.507[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.507J');">HST.507[J]</a> Prereq: (<a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a>, <a href="/search/?P=6.1210" title="6.1210" class="bubblelink code" onclick="return showCourse(this, '6.1210');">6.1210</a>, and <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>) or permission of instructor U (Fall) 3-0-9 units Covers the algorithmic and machine learning foundations of computational biology, combining theory with practice. Principles of algorithm design, influential problems and techniques, and analysis of large-scale biological datasets. Topics include (a) genomes: sequence analysis, gene finding, RNA folding, genome alignment and assembly, database search; (b) networks: gene expression analysis, regulatory motifs, biological network analysis; (c) evolution: comparative genomics, phylogenetics, genome duplication, genome rearrangements, evolutionary theory. These are coupled with fundamental algorithmic techniques including: dynamic programming, hashing, Gibbs sampling, expectation maximization, hidden Markov models, stochastic context-free grammars, graph clustering, dimensionality reduction, Bayesian networks. M. Kellis </div><div class="courseblock"> <h4 class="courseblocktitle">6.8710[J] Computational Systems Biology: Deep Learning in the Life Sciences</h4> Same subject as <a href="/search/?P=HST.506J" title="HST.506[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.506J');">HST.506[J]</a> Subject meets with <a href="/search/?P=6.8711J" title="6.8711[J]" class="bubblelink code" onclick="return showCourse(this, '6.8711J');">6.8711[J]</a>, <a href="/search/?P=20.390J" title="20.390[J]" class="bubblelink code" onclick="return showCourse(this, '20.390J');">20.390[J]</a>, <a href="/search/?P=20.490" title="20.490" class="bubblelink code" onclick="return showCourse(this, '20.490');">20.490</a> Prereq: <a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or <a href="/search/?P=18.600" title="18.600" class="bubblelink code" onclick="return showCourse(this, '18.600');">18.600</a>) Acad Year 2024-2025: G (Spring) Acad Year 2025-2026: Not offered 3-0-9 units Presents innovative approaches to computational problems in the life sciences, focusing on deep learning-based approaches with comparisons to conventional methods. Topics include protein-DNA interaction, chromatin accessibility, regulatory variant interpretation, medical image understanding, medical record understanding, therapeutic design, and experiment design (the choice and interpretation of interventions). Focuses on machine learning model selection, robustness, and interpretation. Teams complete a multidisciplinary final research project using TensorFlow or other framework. Provides a comprehensive introduction to each life sciences problem, but relies upon students understanding probabilistic problem formulations. Students taking graduate version complete additional assignments. D. K. Gifford </div><div class="courseblock"> <h4 class="courseblocktitle">6.8711[J] Computational Systems Biology: Deep Learning in the Life Sciences</h4> Same subject as <a href="/search/?P=20.390J" title="20.390[J]" class="bubblelink code" onclick="return showCourse(this, '20.390J');">20.390[J]</a> Subject meets with <a href="/search/?P=6.8710J" title="6.8710[J]" class="bubblelink code" onclick="return showCourse(this, '6.8710J');">6.8710[J]</a>, <a href="/search/?P=20.490" title="20.490" class="bubblelink code" onclick="return showCourse(this, '20.490');">20.490</a>, <a href="/search/?P=HST.506J" title="HST.506[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.506J');">HST.506[J]</a> Prereq: (<a href="/search/?P=6.100B" title="6.100B" class="bubblelink code" onclick="return showCourse(this, '6.100B');">6.100B</a> and <a href="/search/?P=7.05" title="7.05" class="bubblelink code" onclick="return showCourse(this, '7.05');">7.05</a>) or permission of instructor Acad Year 2024-2025: U (Spring) Acad Year 2025-2026: Not offered 3-0-9 units Presents innovative approaches to computational problems in the life sciences, focusing on deep learning-based approaches with comparisons to conventional methods. Topics include protein-DNA interaction, chromatin accessibility, regulatory variant interpretation, medical image understanding, medical record understanding, therapeutic design, and experiment design (the choice and interpretation of interventions). Focuses on machine learning model selection, robustness, and interpretation. Teams complete a multidisciplinary final research project using TensorFlow or other framework. Provides a comprehensive introduction to each life sciences problem, but relies upon students understanding probabilistic problem formulations. Students taking graduate version complete additional assignments. D. K. Gifford </div><div class="courseblock"> <h4 class="courseblocktitle">6.8720[J] Principles of Synthetic Biology</h4> Same subject as <a href="/search/?P=20.405J" title="20.405[J]" class="bubblelink code" onclick="return showCourse(this, '20.405J');">20.405[J]</a> Subject meets with <a href="/search/?P=6.8721J" title="6.8721[J]" class="bubblelink code" onclick="return showCourse(this, '6.8721J');">6.8721[J]</a>, <a href="/search/?P=20.305J" title="20.305[J]" class="bubblelink code" onclick="return showCourse(this, '20.305J');">20.305[J]</a> Prereq: None G (Fall) 3-0-9 units See description under subject <a href="/search/?P=20.405J" title="20.405[J]" class="bubblelink code" onclick="return showCourse(this, '20.405J');">20.405[J]</a>. R. Weiss </div><div class="courseblock"> <h4 class="courseblocktitle">6.8721[J] Principles of Synthetic Biology</h4> Same subject as <a href="/search/?P=20.305J" title="20.305[J]" class="bubblelink code" onclick="return showCourse(this, '20.305J');">20.305[J]</a> Subject meets with <a href="/search/?P=6.8720J" title="6.8720[J]" class="bubblelink code" onclick="return showCourse(this, '6.8720J');">6.8720[J]</a>, <a href="/search/?P=20.405J" title="20.405[J]" class="bubblelink code" onclick="return showCourse(this, '20.405J');">20.405[J]</a> Prereq: None U (Fall) 3-0-9 units See description under subject <a href="/search/?P=20.305J" title="20.305[J]" class="bubblelink code" onclick="return showCourse(this, '20.305J');">20.305[J]</a>. R. Weiss </div><h2 class="sectionhead">Biomedical & Health</h2><div class="courseblock"> <h4 class="courseblocktitle">6.4800[J] Biomedical Systems: Modeling and Inference</h4> Same subject as <a href="/search/?P=22.54J" title="22.54[J]" class="bubblelink code" onclick="return showCourse(this, '22.54J');">22.54[J]</a> Prereq: (<a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>)) or permission of instructor Acad Year 2024-2025: Not offered Acad Year 2025-2026: U (Fall) 4-4-4 units Medically motivated examples of problems in human health that engage students in systems modeling, signal analysis and inference, and design. Content draws on two domains, first by establishing a model of the human cardiovascular system with signal analysis and inference applications of electrocardiograms in health and disease. In a second topic, medical imaging by MRI is motivated by examples of common clinical decision making, followed by laboratory work with technology and instrumentation with the functionality of commercial diagnostic scanners. Students apply concepts from lectures in labs for data collection for image reconstruction, image analysis, and inference by their own design. Labs further include kits for interactive and portable low-cost devices that can be assembled by the students to demonstrate fundamental building blocks of an MRI system. E. Adalsteinsson, T. Heldt, C. M. Stultz, J. K. White </div><div class="courseblock"> <h4 class="courseblocktitle">6.4810[J] Cellular Neurophysiology and Computing</h4> Same subject as <a href="/search/?P=2.791J" title="2.791[J]" class="bubblelink code" onclick="return showCourse(this, '2.791J');">2.791[J]</a>, <a href="/search/?P=9.21J" title="9.21[J]" class="bubblelink code" onclick="return showCourse(this, '9.21J');">9.21[J]</a>, <a href="/search/?P=20.370J" title="20.370[J]" class="bubblelink code" onclick="return showCourse(this, '20.370J');">20.370[J]</a> Subject meets with <a href="/search/?P=2.794J" title="2.794[J]" class="bubblelink code" onclick="return showCourse(this, '2.794J');">2.794[J]</a>, <a href="/search/?P=6.4812J" title="6.4812[J]" class="bubblelink code" onclick="return showCourse(this, '6.4812J');">6.4812[J]</a>, <a href="/search/?P=9.021J" title="9.021[J]" class="bubblelink code" onclick="return showCourse(this, '9.021J');">9.021[J]</a>, <a href="/search/?P=20.470J" title="20.470[J]" class="bubblelink code" onclick="return showCourse(this, '20.470J');">20.470[J]</a>, <a href="/search/?P=HST.541J" title="HST.541[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.541J');">HST.541[J]</a> Prereq: (<a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a>, <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, and (<a href="/search/?P=2.005" title="2.005" class="bubblelink code" onclick="return showCourse(this, '2.005');">2.005</a>, <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a>, <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a>, <a href="/search/?P=10.301" title="10.301" class="bubblelink code" onclick="return showCourse(this, '10.301');">10.301</a>, or <a href="/search/?P=20.110" title="20.110[J]" class="bubblelink code" onclick="return showCourse(this, '20.110');">20.110[J]</a>)) or permission of instructor U (Spring) 5-2-5 units Integrated overview of the biophysics of cells from prokaryotes to neurons, with a focus on mass transport and electrical signal generation across cell membrane. First third of course focuses on mass transport through membranes: diffusion, osmosis, chemically mediated, and active transport. Second third focuses on electrical properties of cells: ion transport to action potential generation and propagation in electrically excitable cells. Synaptic transmission. Electrical properties interpreted via kinetic and molecular properties of single voltage-gated ion channels. Final third focuses on biophysics of synaptic transmission and introduction to neural computing. Laboratory and computer exercises illustrate the concepts. Students taking graduate version complete different assignments. Preference to juniors and seniors. J. Han, T. Heldt </div><div class="courseblock"> <h4 class="courseblocktitle">6.4812[J] Cellular Neurophysiology and Computing</h4> Same subject as <a href="/search/?P=2.794J" title="2.794[J]" class="bubblelink code" onclick="return showCourse(this, '2.794J');">2.794[J]</a>, <a href="/search/?P=9.021J" title="9.021[J]" class="bubblelink code" onclick="return showCourse(this, '9.021J');">9.021[J]</a>, <a href="/search/?P=20.470J" title="20.470[J]" class="bubblelink code" onclick="return showCourse(this, '20.470J');">20.470[J]</a>, <a href="/search/?P=HST.541J" title="HST.541[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.541J');">HST.541[J]</a> Subject meets with <a href="/search/?P=2.791J" title="2.791[J]" class="bubblelink code" onclick="return showCourse(this, '2.791J');">2.791[J]</a>, <a href="/search/?P=6.4810J" title="6.4810[J]" class="bubblelink code" onclick="return showCourse(this, '6.4810J');">6.4810[J]</a>, <a href="/search/?P=9.21J" title="9.21[J]" class="bubblelink code" onclick="return showCourse(this, '9.21J');">9.21[J]</a>, <a href="/search/?P=20.370J" title="20.370[J]" class="bubblelink code" onclick="return showCourse(this, '20.370J');">20.370[J]</a> Prereq: (<a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a>, <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, and (<a href="/search/?P=2.005" title="2.005" class="bubblelink code" onclick="return showCourse(this, '2.005');">2.005</a>, <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a>, <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a>, <a href="/search/?P=10.301" title="10.301" class="bubblelink code" onclick="return showCourse(this, '10.301');">10.301</a>, or <a href="/search/?P=20.110" title="20.110[J]" class="bubblelink code" onclick="return showCourse(this, '20.110');">20.110[J]</a>)) or permission of instructor G (Spring) 5-2-5 units Integrated overview of the biophysics of cells from prokaryotes to neurons, with a focus on mass transport and electrical signal generation across cell membrane. First third of course focuses on mass transport through membranes: diffusion, osmosis, chemically mediated, and active transport. Second third focuses on electrical properties of cells: ion transport to action potential generation and propagation in electrically excitable cells. Synaptic transmission. Electrical properties interpreted via kinetic and molecular properties of single voltage-gated ion channels. Final third focuses on biophysics of synaptic transmission and introduction to neural computing. Laboratory and computer exercises illustrate the concepts. Students taking graduate version complete different assignments. J. Han, T. Heldt </div><div class="courseblock"> <h4 class="courseblocktitle">6.4820[J] Quantitative and Clinical Physiology</h4> Same subject as <a href="/search/?P=2.792J" title="2.792[J]" class="bubblelink code" onclick="return showCourse(this, '2.792J');">2.792[J]</a>, <a href="/search/?P=HST.542J" title="HST.542[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.542J');">HST.542[J]</a> Subject meets with <a href="/search/?P=2.796J" title="2.796[J]" class="bubblelink code" onclick="return showCourse(this, '2.796J');">2.796[J]</a>, <a href="/search/?P=6.4822J" title="6.4822[J]" class="bubblelink code" onclick="return showCourse(this, '6.4822J');">6.4822[J]</a>, <a href="/search/?P=16.426J" title="16.426[J]" class="bubblelink code" onclick="return showCourse(this, '16.426J');">16.426[J]</a> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a>, <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, or permission of instructor U (Fall) 4-2-6 units Application of the principles of energy and mass flow to major human organ systems. Anatomical, physiological and clinical features of the cardiovascular, respiratory and renal systems. Mechanisms of regulation and homeostasis. Systems, features and devices that are most illuminated by the methods of physical sciences and engineering models. Required laboratory work includes animal studies. Students taking graduate version complete additional assignments. T. Heldt, R. G. Mark </div><div class="courseblock"> <h4 class="courseblocktitle">6.4822[J] Quantitative and Clinical Physiology</h4> Same subject as <a href="/search/?P=2.796J" title="2.796[J]" class="bubblelink code" onclick="return showCourse(this, '2.796J');">2.796[J]</a>, <a href="/search/?P=16.426J" title="16.426[J]" class="bubblelink code" onclick="return showCourse(this, '16.426J');">16.426[J]</a> Subject meets with <a href="/search/?P=2.792J" title="2.792[J]" class="bubblelink code" onclick="return showCourse(this, '2.792J');">2.792[J]</a>, <a href="/search/?P=6.4820J" title="6.4820[J]" class="bubblelink code" onclick="return showCourse(this, '6.4820J');">6.4820[J]</a>, <a href="/search/?P=HST.542J" title="HST.542[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.542J');">HST.542[J]</a> Prereq: <a href="/search/?P=6.4810" title="6.4810[J]" class="bubblelink code" onclick="return showCourse(this, '6.4810');">6.4810[J]</a> and (<a href="/search/?P=2.006" title="2.006" class="bubblelink code" onclick="return showCourse(this, '2.006');">2.006</a> or <a href="/search/?P=6.2300" title="6.2300" class="bubblelink code" onclick="return showCourse(this, '6.2300');">6.2300</a>) G (Fall) 4-2-6 units Application of the principles of energy and mass flow to major human organ systems. Anatomical, physiological and clinical features of the cardiovascular, respiratory and renal systems. Mechanisms of regulation and homeostasis. Systems, features and devices that are most illuminated by the methods of physical sciences and engineering models. Required laboratory work includes animal studies. Students taking graduate version complete additional assignments. T. Heldt, R. G. Mark, L. G. Petersen </div><div class="courseblock"> <h4 class="courseblocktitle">6.4830[J] Fields, Forces and Flows in Biological Systems</h4> Same subject as <a href="/search/?P=2.793J" title="2.793[J]" class="bubblelink code" onclick="return showCourse(this, '2.793J');">2.793[J]</a>, <a href="/search/?P=20.330J" title="20.330[J]" class="bubblelink code" onclick="return showCourse(this, '20.330J');">20.330[J]</a> Prereq: <a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a>, <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a>, and <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> U (Spring) 4-0-8 units See description under subject <a href="/search/?P=20.330J" title="20.330[J]" class="bubblelink code" onclick="return showCourse(this, '20.330J');">20.330[J]</a>. J. Han, S. Manalis </div><div class="courseblock"> <h4 class="courseblocktitle">6.4832[J] Fields, Forces, and Flows in Biological Systems</h4> Same subject as <a href="/search/?P=2.795J" title="2.795[J]" class="bubblelink code" onclick="return showCourse(this, '2.795J');">2.795[J]</a>, <a href="/search/?P=10.539J" title="10.539[J]" class="bubblelink code" onclick="return showCourse(this, '10.539J');">10.539[J]</a>, <a href="/search/?P=20.430J" title="20.430[J]" class="bubblelink code" onclick="return showCourse(this, '20.430J');">20.430[J]</a> Prereq: Permission of instructor G (Fall) 3-0-9 units See description under subject <a href="/search/?P=20.430J" title="20.430[J]" class="bubblelink code" onclick="return showCourse(this, '20.430J');">20.430[J]</a>. M. Bathe, A. J. Grodzinsky </div><div class="courseblock"> <h4 class="courseblocktitle">6.4840[J] Molecular, Cellular, and Tissue Biomechanics</h4> Same subject as <a href="/search/?P=2.797J" title="2.797[J]" class="bubblelink code" onclick="return showCourse(this, '2.797J');">2.797[J]</a>, <a href="/search/?P=3.053J" title="3.053[J]" class="bubblelink code" onclick="return showCourse(this, '3.053J');">3.053[J]</a>, <a href="/search/?P=20.310J" title="20.310[J]" class="bubblelink code" onclick="return showCourse(this, '20.310J');">20.310[J]</a> Subject meets with <a href="/search/?P=2.798J" title="2.798[J]" class="bubblelink code" onclick="return showCourse(this, '2.798J');">2.798[J]</a>, <a href="/search/?P=3.971J" title="3.971[J]" class="bubblelink code" onclick="return showCourse(this, '3.971J');">3.971[J]</a>, <a href="/search/?P=6.4842J" title="6.4842[J]" class="bubblelink code" onclick="return showCourse(this, '6.4842J');">6.4842[J]</a>, <a href="/search/?P=10.537J" title="10.537[J]" class="bubblelink code" onclick="return showCourse(this, '10.537J');">10.537[J]</a>, <a href="/search/?P=20.410J" title="20.410[J]" class="bubblelink code" onclick="return showCourse(this, '20.410J');">20.410[J]</a> Prereq: <a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a> and <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> U (Spring) 4-0-8 units See description under subject <a href="/search/?P=20.310J" title="20.310[J]" class="bubblelink code" onclick="return showCourse(this, '20.310J');">20.310[J]</a>. M. Bathe, K. Ribbeck, P. T. So </div><div class="courseblock"> <h4 class="courseblocktitle">6.4842[J] Molecular, Cellular, and Tissue Biomechanics</h4> Same subject as <a href="/search/?P=2.798J" title="2.798[J]" class="bubblelink code" onclick="return showCourse(this, '2.798J');">2.798[J]</a>, <a href="/search/?P=3.971J" title="3.971[J]" class="bubblelink code" onclick="return showCourse(this, '3.971J');">3.971[J]</a>, <a href="/search/?P=10.537J" title="10.537[J]" class="bubblelink code" onclick="return showCourse(this, '10.537J');">10.537[J]</a>, <a href="/search/?P=20.410J" title="20.410[J]" class="bubblelink code" onclick="return showCourse(this, '20.410J');">20.410[J]</a> Subject meets with <a href="/search/?P=2.797J" title="2.797[J]" class="bubblelink code" onclick="return showCourse(this, '2.797J');">2.797[J]</a>, <a href="/search/?P=3.053J" title="3.053[J]" class="bubblelink code" onclick="return showCourse(this, '3.053J');">3.053[J]</a>, <a href="/search/?P=6.4840J" title="6.4840[J]" class="bubblelink code" onclick="return showCourse(this, '6.4840J');">6.4840[J]</a>, <a href="/search/?P=20.310J" title="20.310[J]" class="bubblelink code" onclick="return showCourse(this, '20.310J');">20.310[J]</a> Prereq: <a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a> and <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a> G (Spring) 3-0-9 units See description under subject <a href="/search/?P=20.410J" title="20.410[J]" class="bubblelink code" onclick="return showCourse(this, '20.410J');">20.410[J]</a>. M. Bathe, K. Ribbeck, P. T. So </div><div class="courseblock"> <h4 class="courseblocktitle">6.4860[J] Medical Device Design</h4> Same subject as <a href="/search/?P=2.750J" title="2.750[J]" class="bubblelink code" onclick="return showCourse(this, '2.750J');">2.750[J]</a> Subject meets with <a href="/search/?P=2.75J" title="2.75[J]" class="bubblelink code" onclick="return showCourse(this, '2.75J');">2.75[J]</a>, <a href="/search/?P=6.4861J" title="6.4861[J]" class="bubblelink code" onclick="return showCourse(this, '6.4861J');">6.4861[J]</a>, <a href="/search/?P=HST.552J" title="HST.552[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.552J');">HST.552[J]</a> Prereq: <a href="/search/?P=2.008" title="2.008" class="bubblelink code" onclick="return showCourse(this, '2.008');">2.008</a>, <a href="/search/?P=6.2040" title="6.2040" class="bubblelink code" onclick="return showCourse(this, '6.2040');">6.2040</a>, <a href="/search/?P=6.2050" title="6.2050" class="bubblelink code" onclick="return showCourse(this, '6.2050');">6.2050</a>, <a href="/search/?P=6.2060" title="6.2060" class="bubblelink code" onclick="return showCourse(this, '6.2060');">6.2060</a>, <a href="/search/?P=22.071" title="22.071" class="bubblelink code" onclick="return showCourse(this, '22.071');">22.071</a>, or permission of instructor U (Spring) 3-3-6 units See description under subject <a href="/search/?P=2.750J" title="2.750[J]" class="bubblelink code" onclick="return showCourse(this, '2.750J');">2.750[J]</a>. Enrollment limited. A. H. Slocum, E. Roche, N. C. Hanumara,聽G. Traverso, A. Pennes </div><div class="courseblock"> <h4 class="courseblocktitle">6.4861[J] Medical Device Design</h4> Same subject as <a href="/search/?P=2.75J" title="2.75[J]" class="bubblelink code" onclick="return showCourse(this, '2.75J');">2.75[J]</a>, <a href="/search/?P=HST.552J" title="HST.552[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.552J');">HST.552[J]</a> Subject meets with <a href="/search/?P=2.750J" title="2.750[J]" class="bubblelink code" onclick="return showCourse(this, '2.750J');">2.750[J]</a>, <a href="/search/?P=6.4860J" title="6.4860[J]" class="bubblelink code" onclick="return showCourse(this, '6.4860J');">6.4860[J]</a> Prereq: <a href="/search/?P=2.008" title="2.008" class="bubblelink code" onclick="return showCourse(this, '2.008');">2.008</a>, <a href="/search/?P=6.2040" title="6.2040" class="bubblelink code" onclick="return showCourse(this, '6.2040');">6.2040</a>, <a href="/search/?P=6.2050" title="6.2050" class="bubblelink code" onclick="return showCourse(this, '6.2050');">6.2050</a>, <a href="/search/?P=6.2060" title="6.2060" class="bubblelink code" onclick="return showCourse(this, '6.2060');">6.2060</a>, <a href="/search/?P=22.071" title="22.071" class="bubblelink code" onclick="return showCourse(this, '22.071');">22.071</a>, or permission of instructor G (Spring) 3-3-6 units See description under subject <a href="/search/?P=2.75J" title="2.75[J]" class="bubblelink code" onclick="return showCourse(this, '2.75J');">2.75[J]</a>. Enrollment limited. A. H. Slocum, E. Roche, N. C. Hanumara,聽G. Traverso,聽A. Pennes </div><div class="courseblock"> <h4 class="courseblocktitle">6.4880[J] Biological Circuit Engineering Laboratory</h4> Same subject as <a href="/search/?P=20.129J" title="20.129[J]" class="bubblelink code" onclick="return showCourse(this, '20.129J');">20.129[J]</a> Prereq: <a href="/search/?P=7.012|7.013|7.014|7.015|7.016" onclick="return showCourse(this, '7.012|7.013|7.014|7.015|7.016');">Biology (GIR)</a> and <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> U (Spring) 2-8-2 units. Institute LAB See description under subject <a href="/search/?P=20.129J" title="20.129[J]" class="bubblelink code" onclick="return showCourse(this, '20.129J');">20.129[J]</a>. Enrollment limited. T. Lu, R. Weiss </div><div class="courseblock"> <h4 class="courseblocktitle">6.4900 Introduction to EECS via Medical Technology</h4> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> U (Spring) Not offered regularly; consult department 4-4-4 units. Institute LAB Explores biomedical signals generated from electrocardiograms, glucose detectors or ultrasound images, and magnetic resonance images. Topics include physical characterization and modeling of systems in the time and frequency domains; analog and digital signals and noise; basic machine learning including decision trees, clustering, and classification; and introductory machine vision. Labs designed to strengthen background in signal processing and machine learning. Students design and run structured experiments, and develop and test procedures through further experimentation. C. M. Stultz, E. Adalsteinsson </div><div class="courseblock"> <h4 class="courseblocktitle">6.8800[J] Biomedical Signal and Image Processing</h4> Same subject as <a href="/search/?P=16.456J" title="16.456[J]" class="bubblelink code" onclick="return showCourse(this, '16.456J');">16.456[J]</a>, <a href="/search/?P=HST.582J" title="HST.582[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.582J');">HST.582[J]</a> Subject meets with <a href="/search/?P=6.8801J" title="6.8801[J]" class="bubblelink code" onclick="return showCourse(this, '6.8801J');">6.8801[J]</a>, <a href="/search/?P=HST.482J" title="HST.482[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.482J');">HST.482[J]</a> Prereq: (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> and (<a href="/search/?P=2.004" title="2.004" class="bubblelink code" onclick="return showCourse(this, '2.004');">2.004</a>, <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a>, <a href="/search/?P=16.002" title="16.002" class="bubblelink code" onclick="return showCourse(this, '16.002');">16.002</a>, or <a href="/search/?P=18.085" title="18.085" class="bubblelink code" onclick="return showCourse(this, '18.085');">18.085</a>)) or permission of instructor G (Spring) 3-1-8 units Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine. Basic principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. Lab projects, performed in MATLAB, provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs. Students taking graduate version complete additional assignments. J. Greenberg, E. Adalsteinsson, W. Wells </div><div class="courseblock"> <h4 class="courseblocktitle">6.8801[J] Biomedical Signal and Image Processing</h4> Same subject as <a href="/search/?P=HST.482J" title="HST.482[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.482J');">HST.482[J]</a> Subject meets with <a href="/search/?P=6.8800J" title="6.8800[J]" class="bubblelink code" onclick="return showCourse(this, '6.8800J');">6.8800[J]</a>, <a href="/search/?P=16.456J" title="16.456[J]" class="bubblelink code" onclick="return showCourse(this, '16.456J');">16.456[J]</a>, <a href="/search/?P=HST.582J" title="HST.582[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.582J');">HST.582[J]</a> Prereq: (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or permission of instructor) and (<a href="/search/?P=2.004" title="2.004" class="bubblelink code" onclick="return showCourse(this, '2.004');">2.004</a>, <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a>, <a href="/search/?P=16.002" title="16.002" class="bubblelink code" onclick="return showCourse(this, '16.002');">16.002</a>, or <a href="/search/?P=18.085" title="18.085" class="bubblelink code" onclick="return showCourse(this, '18.085');">18.085</a>) U (Spring) 3-1-8 units Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine. Basic principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. Lab projects, performed in MATLAB, provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs. Students taking graduate version complete additional assignments. J. Greenberg, E. Adalsteinsson, W. Wells </div><div class="courseblock"> <h4 class="courseblocktitle">6.8810[J] Data Acquisition and Image Reconstruction in MRI</h4> Same subject as <a href="/search/?P=HST.580J" title="HST.580[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.580J');">HST.580[J]</a> Prereq: <a href="/search/?P=6.3010" title="6.3010" class="bubblelink code" onclick="return showCourse(this, '6.3010');">6.3010</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Fall) 3-0-9 units Applies analysis of signals and noise in linear systems, sampling, and Fourier properties to magnetic resonance (MR) imaging acquisition and reconstruction. Provides adequate foundation for MR physics to enable study of RF excitation design, efficient Fourier sampling, parallel encoding, reconstruction of non-uniformly sampled data, and the impact of hardware imperfections on reconstruction performance. Surveys active areas of MR research. Assignments include Matlab-based work with real data. Includes visit to a scan site for human MR studies. E. Adalsteinsson </div><div class="courseblock"> <h4 class="courseblocktitle">6.8830[J] Signal Processing by the Auditory System: Perception</h4> Same subject as <a href="/search/?P=HST.716J" title="HST.716[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.716J');">HST.716[J]</a> Prereq: (<a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> and (<a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a> or <a href="/search/?P=6.3702" title="6.3702" class="bubblelink code" onclick="return showCourse(this, '6.3702');">6.3702</a>)) or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Studies information processing performance of the human auditory system in relation to current physiological knowledge. Examines mathematical models for the quantification of auditory-based behavior and the relation between behavior and peripheral physiology, reflecting the tono-topic organization and stochastic responses of the auditory system. Mathematical models of psychophysical relations, incorporating quantitative knowledge of physiological transformations by the peripheral auditory system. L. D. Braida </div><div class="courseblock"> <h4 class="courseblocktitle">6.8850[J] Clinical Data Learning, Visualization, and Deployments (New)</h4> Same subject as <a href="/search/?P=HST.953J" title="HST.953[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.953J');">HST.953[J]</a> Prereq: (<a href="/search/?P=6.7900" title="6.7900" class="bubblelink code" onclick="return showCourse(this, '6.7900');">6.7900</a> and <a href="/search/?P=6.7930" title="6.7930[J]" class="bubblelink code" onclick="return showCourse(this, '6.7930');">6.7930[J]</a>) or permission of instructor G (Fall) 3-0-9 units See description under subject <a href="/search/?P=HST.953J" title="HST.953[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.953J');">HST.953[J]</a>. M. Ghassemi, L. A. Celi,聽N. McCague and E. Gottlieb </div><h2 class="sectionhead">Vision</h2><div class="courseblock"> <h4 class="courseblocktitle">6.8300 Advances in Computer Vision</h4> Subject meets with <a href="/search/?P=6.8301" title="6.8301" class="bubblelink code" onclick="return showCourse(this, '6.8301');">6.8301</a> Prereq: (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>) and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) G (Spring) 3-0-9 units Advanced topics in computer vision with a focus on the use of machine learning techniques and applications in graphics and human-computer interface. Covers image representations, texture models, structure-from-motion algorithms, Bayesian techniques, object and scene recognition, tracking, shape modeling, and image databases. Applications may include face recognition, multimodal interaction, interactive systems, cinematic special effects, and photorealistic rendering. Covers topics complementary to 6.8390. Students taking graduate version complete additional assignments. W. T. Freeman, M. Konakovic Lukovic, V. Sitzmann </div><div class="courseblock"> <h4 class="courseblocktitle">6.8301 Advances in Computer Vision</h4> Subject meets with <a href="/search/?P=6.8300" title="6.8300" class="bubblelink code" onclick="return showCourse(this, '6.8300');">6.8300</a> Prereq: (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>) and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) U (Spring) Not offered regularly; consult department 4-0-11 units Advanced topics in computer vision with a focus on the use of machine learning techniques and applications in graphics and human-computer interface. Covers image representations, texture models, structure-from-motion algorithms, Bayesian techniques, object and scene recognition, tracking, shape modeling, and image databases. Applications may include face recognition, multimodal interaction, interactive systems, cinematic special effects, and photorealistic rendering. Includes instruction and practice in written and oral communication. Students taking graduate version complete additional assignments. W. T. Freeman, M. Konakovic Lukovic, V. Sitzmann </div><div class="courseblock"> <h4 class="courseblocktitle">6.8320 Advanced Topics in Computer Vision</h4> Prereq: 6.801, <a href="/search/?P=6.8300" title="6.8300" class="bubblelink code" onclick="return showCourse(this, '6.8300');">6.8300</a>, or permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Seminar exploring advanced research topics in the field of computer vision; focus varies with lecturer. Typically structured around discussion of assigned research papers and presentations by students. Example research areas explored in this seminar include learning in vision, computational imaging techniques, multimodal human-computer interaction, biomedical imaging, representation and estimation methods used in modern computer vision. W. T. Freeman, B. K. P. Horn, A. Torralba </div><div class="courseblock"> <h4 class="courseblocktitle">6.8370 Advanced Computational Photography</h4> Subject meets with <a href="/search/?P=6.8371" title="6.8371" class="bubblelink code" onclick="return showCourse(this, '6.8371');">6.8371</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and <a href="/search/?P=6.1020" title="6.1020" class="bubblelink code" onclick="return showCourse(this, '6.1020');">6.1020</a> G (Fall) 3-0-9 units Presents fundamentals and applications of hardware and software techniques used in digital and computational photography, with an emphasis on software methods. Provides sufficient background to implement solutions to photographic challenges and opportunities. Topics include cameras and image formation, image processing and image representations, high-dynamic-range imaging, human visual perception and color, single view 3-D model reconstruction, morphing, data-rich photography, super-resolution, and image-based rendering. Students taking graduate version complete additional assignments. F. P. Durand </div><div class="courseblock"> <h4 class="courseblocktitle">6.8371 Digital and Computational Photography</h4> Subject meets with <a href="/search/?P=6.8370" title="6.8370" class="bubblelink code" onclick="return showCourse(this, '6.8370');">6.8370</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and <a href="/search/?P=6.1010" title="6.1010" class="bubblelink code" onclick="return showCourse(this, '6.1010');">6.1010</a> U (Fall) 3-0-9 units Presents fundamentals and applications of hardware and software techniques used in digital and computational photography, with an emphasis on software methods. Provides sufficient background to implement solutions to photographic challenges and opportunities. Topics include cameras and image formation, image processing and image representations, high-dynamic-range imaging, human visual perception and color, single view 3-D model reconstruction, morphing, data-rich photography, super-resolution, and image-based rendering. Students taking graduate version complete additional assignments. F. P. Durand </div><h2 class="sectionhead">Natural Language Processing & Speech</h2><div class="courseblock"> <h4 class="courseblocktitle">6.8610 Quantitative Methods for Natural Language Processing</h4> Subject meets with <a href="/search/?P=6.8611" title="6.8611" class="bubblelink code" onclick="return showCourse(this, '6.8611');">6.8611</a> Prereq: <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) G (Fall) 3-0-9 units Introduces the study of human language from a computational perspective, including syntactic, semantic and discourse processing models. Emphasizes machine learning methods and algorithms. Uses these methods and models in applications such as syntactic parsing, information extraction, statistical machine translation, dialogue systems. Students taking graduate version complete additional assignments. J. Andreas, J. Glass </div><div class="courseblock"> <h4 class="courseblocktitle">6.8611 Quantitative Methods for Natural Language Processing</h4> Subject meets with <a href="/search/?P=6.8610" title="6.8610" class="bubblelink code" onclick="return showCourse(this, '6.8610');">6.8610</a> Prereq: <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) U (Fall) 4-0-11 units Introduces the study of human language from a computational perspective, including syntactic, semantic and discourse processing models. Emphasizes machine learning methods and algorithms. Uses these methods and models in applications such as syntactic parsing, information extraction, statistical machine translation, dialogue systems. Instruction and practice in oral and written communication provided. Students taking graduate version complete additional assignments. J. Andreas, J. Glass </div><div class="courseblock"> <h4 class="courseblocktitle">6.8620[J] Spoken Language Processing</h4> Same subject as <a href="/search/?P=HST.728J" title="HST.728[J]" class="bubblelink code" onclick="return showCourse(this, 'HST.728J');">HST.728[J]</a> Prereq: <a href="/search/?P=6.3000" title="6.3000" class="bubblelink code" onclick="return showCourse(this, '6.3000');">6.3000</a> and <a href="/search/?P=6.3900" title="6.3900" class="bubblelink code" onclick="return showCourse(this, '6.3900');">6.3900</a> Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring) 3-1-8 units Introduces the rapidly developing field of spoken language processing including automatic speech recognition. Topics include acoustic theory of speech production, acoustic-phonetics, signal representation, acoustic and language modeling, search, hidden Markov modeling, neural networks models, end-to-end deep learning models, and other machine learning techniques applied to speech and language processing topics. Lecture material intersperses theory with practice. Includes problem sets, laboratory exercises, and open-ended term project. J. R. Glass </div><div class="courseblock"> <h4 class="courseblocktitle">6.8630[J] Natural Language and the Computer Representation of Knowledge</h4> Same subject as <a href="/search/?P=9.611J" title="9.611[J]" class="bubblelink code" onclick="return showCourse(this, '9.611J');">9.611[J]</a>, <a href="/search/?P=24.984J" title="24.984[J]" class="bubblelink code" onclick="return showCourse(this, '24.984J');">24.984[J]</a> Prereq: <a href="/search/?P=6.4100" title="6.4100" class="bubblelink code" onclick="return showCourse(this, '6.4100');">6.4100</a> or permission of instructor G (Spring) 3-3-6 units Explores the relationship between the computer representation and acquisition of knowledge and the structure of human language, its acquisition, and hypotheses about its differentiating uniqueness. Emphasizes development of analytical skills necessary to judge the computational implications of grammatical formalisms and their role in connecting human intelligence to computational intelligence. Uses concrete examples to illustrate particular computational issues in this area. R. C. Berwick </div><h2 class="sectionhead">Cross-cutting EECS Subjects</h2><div class="courseblock"> <h4 class="courseblocktitle">6.9000 Engineering for Impact</h4> Prereq: <a href="/search/?P=6.1910" title="6.1910" class="bubblelink code" onclick="return showCourse(this, '6.1910');">6.1910</a>, <a href="/search/?P=6.2000" title="6.2000" class="bubblelink code" onclick="return showCourse(this, '6.2000');">6.2000</a>, and <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a> U (Spring) 2-3-7 units Students work in large teams to engineer hardware/software systems that solve important problems in society. Topics include requirements, specifications, system design and partitioning, detailed engineering design, prototyping and implementation, test and verification, and the ethical implications of these choices. Explores case studies of existing hardware/software systems to understand implications of different system design choices. Teams design and build functional prototypes of useful systems. Grading is based on individual- and team-based elements. Enrollment may be limited due to staffing and space requirements. J. Voldman </div><div class="courseblock"> <h4 class="courseblocktitle">6.9010 Introduction to EECS via Interconnected Embedded Systems</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>; Coreq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> U (Spring) Not offered regularly; consult department 1-5-6 units. Institute LAB Introduction to embedded systems in the context of connected devices, wearables, and the "Internet of Things" (IoT). Topics include microcontrollers, energy utilization, algorithmic efficiency, interfacing with sensors, networking, cryptography, and local versus distributed computation. Students design, make, and program an Internet-connected wearable or handheld device. In the final project, student teams design and demo their own server-connected IoT system. Enrollment limited; preference to first- and second-year students. S. Mueller,聽J. D. Steinmeyer, J. Voldman </div><div class="courseblock"> <h4 class="courseblocktitle">6.9020[J] How to Make (Almost) Anything</h4> Same subject as <a href="/search/?P=4.140J" title="4.140[J]" class="bubblelink code" onclick="return showCourse(this, '4.140J');">4.140[J]</a>, <a href="/search/?P=MAS.863J" title="MAS.863[J]" class="bubblelink code" onclick="return showCourse(this, 'MAS.863J');">MAS.863[J]</a> Prereq: Permission of instructor G (Fall) 3-9-6 units See description under subject <a href="/search/?P=MAS.863J" title="MAS.863[J]" class="bubblelink code" onclick="return showCourse(this, 'MAS.863J');">MAS.863[J]</a>. N. Gershenfeld, J. DiFrancesco, J. Lavallee, G. Darcey </div><div class="courseblock"> <h4 class="courseblocktitle">6.9030 Strobe Project Laboratory</h4> Prereq: <a href="/search/?P=8.02|8.021|8.022" onclick="return showCourse(this, '8.02|8.021|8.022');">Physics II (GIR)</a> or permission of instructor U (Fall, Spring) 2-8-2 units. Institute LAB Application of electronic flash sources to measurement and photography. First half covers fundamentals of photography and electronic flashes, including experiments on application of electronic flash to photography, stroboscopy, motion analysis, and high-speed videography. Students write four extensive lab reports. In the second half, students work in small groups to select, design, and execute independent projects in measurement or photography that apply learned techniques. Project planning and execution skills are discussed and developed over the term. Students engage in extensive written and oral communication exercises. Enrollment limited. J. K. Vandiver, J. W. Bales </div><div class="courseblock"> <h4 class="courseblocktitle">6.9080 Introduction to EECS via Robotics</h4> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a> or permission of instructor U (Spring) Not offered regularly; consult department 2-4-6 units. Institute LAB An integrated introduction to electrical engineering and computer science, taught using substantial laboratory experiments with mobile robots. Key issues in the design of engineered artifacts operating in the natural world: measuring and modeling system behaviors; assessing errors in sensors and effectors; specifying tasks; designing solutions based on analytical and computational models; planning, executing, and evaluating experimental tests of performance; refining models and designs. Issues addressed in the context of computer programs, control systems, probabilistic inference problems, circuits and transducers, which all play important roles in achieving robust operation of a large variety of engineered systems. D. M. Freeman, A. Hartz, L. P. Kaelbling, T. Lozano-Perez </div><div class="courseblock"> <h4 class="courseblocktitle">6.UAR Seminar in Undergraduate Advanced Research</h4> Prereq: Permission of instructor U (Fall, Spring) 2-0-4 units Can be repeated for credit. Instruction in effective undergraduate research, including choosing and developing a research topic, surveying previous work and publications, research topics in EECS and the School of Engineering, industry best practices, design for robustness, technical presentation, authorship and collaboration, and ethics. Students engage in extensive written and oral communication exercises, in the context of an approved advanced research project. A total of 12 units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult EECS SuperUROP website for more information. D. Katabi, A. P. Chandrakasan </div><div class="courseblock"> <h4 class="courseblocktitle">6.UAT Oral Communication</h4> Prereq: None U (Fall, Spring) 3-0-6 units Provides instruction in aspects of effective technical oral presentations and exposure to communication skills useful in a workplace setting. Students create, give and revise a number of presentations of varying length targeting a range of different audiences. Enrollment may be limited. T. L. Eng </div><h2 class="sectionhead">Gordon Engineering Leadership Program</h2><div class="courseblock"> <h4 class="courseblocktitle">6.9101[J] Introduction to Design Thinking and Innovation in Engineering</h4> Same subject as <a href="/search/?P=2.7231J" title="2.7231[J]" class="bubblelink code" onclick="return showCourse(this, '2.7231J');">2.7231[J]</a>, <a href="/search/?P=16.6621J" title="16.6621[J]" class="bubblelink code" onclick="return showCourse(this, '16.6621J');">16.6621[J]</a> Prereq: None U (Fall, Spring; partial term) 2-0-1 units Introduces students to concepts of design thinking and innovation that can be applied to any engineering discipline. Focuses on introducing an iterative design process, a systems-thinking approach for stakeholder analysis, methods for articulating design concepts, methods for concept selection, and techniques for testing with users. Provides an opportunity for first-year students to explore product or system design and development, and to build their understanding of what it means to lead and coordinate projects in engineering design. Subject can count toward the 6-unit discovery-focused credit limit for first-year students. Enrollment limited to 25; priority to first-year students. B. Kotelly </div><div class="courseblock"> <h4 class="courseblocktitle">6.910A Design Thinking and Innovation Leadership for Engineers</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=2.723A" title="2.723A" class="bubblelink code" onclick="return showCourse(this, '2.723A');">2.723A</a>, <a href="/search/?P=6.910A" title="6.910A" class="bubblelink code" onclick="return showCourse(this, '6.910A');">6.910A</a>, <a href="/search/?P=16.662A" title="16.662A" class="bubblelink code" onclick="return showCourse(this, '16.662A');">16.662A</a> Prereq: None U (Fall, Spring; partial term) 2-0-1 units Introductory subject in design聽thinking and innovation. Develops students' ability to conceive, implement, and evaluate successful projects in any engineering discipline. Lessons focus on an iterative聽design process, a systems-thinking approach for stakeholder analysis, methods for articulating聽design concepts, methods for concept selection, and techniques for testing with users. B. Kotelly </div><div class="courseblock"> <h4 class="courseblocktitle">6.910B Design Thinking and Innovation Project</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=2.723B" title="2.723B" class="bubblelink code" onclick="return showCourse(this, '2.723B');">2.723B</a>, <a href="/search/?P=6.910B" title="6.910B" class="bubblelink code" onclick="return showCourse(this, '6.910B');">6.910B</a>, <a href="/search/?P=16.662B" title="16.662B" class="bubblelink code" onclick="return showCourse(this, '16.662B');">16.662B</a> Prereq: <a href="/search/?P=6.910A" title="6.910A" class="bubblelink code" onclick="return showCourse(this, '6.910A');">6.910A</a> U (Fall, Spring; partial term) 2-0-1 units Project-based subject. Students employ design-thinking techniques learned in 6.902A to develop a robust speech-recognition application using a web-based platform. Students practice in leadership and teamwork skills as they collaboratively conceive, implement, and iteratively refine their designs based on user feedback. Topics covered include techniques for leading the creative process in teams, the ethics of engineering systems, methods for articulating designs with group collaboration, identifying and reconciling paradoxes of engineering designs, and communicating solution concepts with impact. Students present oral presentations and receive feedback to sharpen their communication skills. B. Kotelly </div><div class="courseblock"> <h4 class="courseblocktitle">6.9110 Engineering Leadership Lab</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=6.9110" title="6.9110" class="bubblelink code" onclick="return showCourse(this, '6.9110');">6.9110</a>, <a href="/search/?P=16.650" title="16.650" class="bubblelink code" onclick="return showCourse(this, '16.650');">16.650</a> Subject meets with <a href="/search/?P=6.9130J" title="6.9130[J]" class="bubblelink code" onclick="return showCourse(this, '6.9130J');">6.9130[J]</a>, <a href="/search/?P=16.667J" title="16.667[J]" class="bubblelink code" onclick="return showCourse(this, '16.667J');">16.667[J]</a> Prereq: None. Coreq: <a href="/search/?P=6.9120" title="6.9120" class="bubblelink code" onclick="return showCourse(this, '6.9120');">6.9120</a>; or permission of instructor U (Fall, Spring) 0-2-1 units Can be repeated for credit. See description under subject <a href="/search/?P=6.9130" title="6.9130" class="bubblelink code" onclick="return showCourse(this, '6.9130');">6.9130</a>. Preference to students enrolled in the Bernard M. Gordon-MIT Engineering Leadership Program. L. McGonagle, J. Feiler </div><div class="courseblock"> <h4 class="courseblocktitle">6.9120 Engineering Leadership</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=6.9120" title="6.9120" class="bubblelink code" onclick="return showCourse(this, '6.9120');">6.9120</a>, <a href="/search/?P=16.651" title="16.651" class="bubblelink code" onclick="return showCourse(this, '16.651');">16.651</a> Prereq: None. Coreq: <a href="/search/?P=6.9110" title="6.9110" class="bubblelink code" onclick="return showCourse(this, '6.9110');">6.9110</a>; or permission of instructor U (Fall, Spring) 1-0-2 units Can be repeated for credit. Exposes students to the models and methods of engineering leadership within the contexts of conceiving, designing, implementing and operating products, processes and systems. Introduces the Capabilities of Effective Engineering Leaders, and models and theories related to the capabilities. Discusses the appropriate times and reasons to use particular models to deliver engineering success. Includes occasional guest speakers or panel discussions. May be repeated for credit once with permission of instructor. Preference to first-year students in the Gordon Engineering Leadership Program. J. Magarian </div><div class="courseblock"> <h4 class="courseblocktitle">6.9130 Engineering Leadership Lab</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=6.9130" title="6.9130" class="bubblelink code" onclick="return showCourse(this, '6.9130');">6.9130</a>, <a href="/search/?P=16.667" title="16.667" class="bubblelink code" onclick="return showCourse(this, '16.667');">16.667</a> Subject meets with <a href="/search/?P=6.9110J" title="6.9110[J]" class="bubblelink code" onclick="return showCourse(this, '6.9110J');">6.9110[J]</a>, <a href="/search/?P=16.650J" title="16.650[J]" class="bubblelink code" onclick="return showCourse(this, '16.650J');">16.650[J]</a> Prereq: <a href="/search/?P=6.910A" title="6.910A" class="bubblelink code" onclick="return showCourse(this, '6.910A');">6.910A</a>, <a href="/search/?P=6.9110" title="6.9110" class="bubblelink code" onclick="return showCourse(this, '6.9110');">6.9110</a>, <a href="/search/?P=6.9120" title="6.9120" class="bubblelink code" onclick="return showCourse(this, '6.9120');">6.9120</a>, or permission of instructor U (Fall, Spring) 0-2-4 units Can be repeated for credit. Advances students' leadership, teamwork, and communication skills through further exposure to leadership frameworks, models, and cases within an engineering context in an interactive, practice-based environment. Students coach others, assess performance, and lead guided reflections on individual and team successes, while discovering opportunities for improvement. Students assist with programmatic planning and implementation of role-play simulations, small group discussions, and performance and peer assessments by and of other students and by instructors. Includes frequent engineering industry-guest participation and involvement. Content is frequently student-led. Second year Gordon Engineering Leadership Program (GEL) Program students register for <a href="/search/?P=6.9130" title="6.9130" class="bubblelink code" onclick="return showCourse(this, '6.9130');">6.9130</a>. Preference to students enrolled in the second year of the Gordon-MIT Engineering Leadership Program. L. McGonagle, J. Feiler </div><div class="courseblock"> <h4 class="courseblocktitle">6.9140 Project Engineering</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=6.9140" title="6.9140" class="bubblelink code" onclick="return showCourse(this, '6.9140');">6.9140</a>, <a href="/search/?P=16.669" title="16.669" class="bubblelink code" onclick="return showCourse(this, '16.669');">16.669</a> Prereq: (<a href="/search/?P=6.910A" title="6.910A" class="bubblelink code" onclick="return showCourse(this, '6.910A');">6.910A</a> and (<a href="/search/?P=6.9110" title="6.9110" class="bubblelink code" onclick="return showCourse(this, '6.9110');">6.9110</a> or <a href="/search/?P=6.9120" title="6.9120" class="bubblelink code" onclick="return showCourse(this, '6.9120');">6.9120</a>)) or permission of instructor U (IAP) 4-0-0 units Students attend and participate in a four-day off-site workshop covering an introduction to basic principles, methods, and tools for project management in a realistic context. In teams, students create a plan for a project of their choice in one of several areas, including: aircraft modification, factory automation, flood prevention engineering, solar farm engineering, small-business digital transformation/modernization, and disaster response, among others. Develops skills applicable to the planning and management of complex engineering projects. Topics include cost-benefit analysis, resource and cost estimation, and project control and delivery which are practiced during an experiential, team-based activity. Case studies highlight projects in both hardware/software and consumer packaged goods. Preference to students in the Bernard M. Gordon-MIT Engineering Leadership Program. O. de Weck, J. Feiler, L. McGonagle, R. Rahaman </div><div class="courseblock"> <h4 class="courseblocktitle">6.9150[J] Leading Innovation in Teams</h4> Same subject as <a href="/search/?P=16.671J" title="16.671[J]" class="bubblelink code" onclick="return showCourse(this, '16.671J');">16.671[J]</a> Prereq: None U (Spring) Not offered regularly; consult department 3-0-6 units Empowers future innovators in engineering and technology with a foundation of leadership and teamwork skills. Grounded in research but practical in focus, equips students with leadership competencies such as building self-awareness, motivating and developing others, influencing without authority, managing conflict, and communicating effectively. Teamwork skills include how to convene, launch, and develop various types of teams, including project teams. Reviews recent advances in implementing innovations and building personal capacity for lifelong learning as a leading innovator. Enrollment limited to seating capacity of classroom. Admittance may be controlled by lottery. D. Nino, J. Schindall </div><div class="courseblock"> <h4 class="courseblocktitle">6.9160[J] Engineering Innovation: Global Security Systems</h4> Same subject as <a href="/search/?P=15.359J" title="15.359[J]" class="bubblelink code" onclick="return showCourse(this, '15.359J');">15.359[J]</a> Prereq: None U (Spring) 3-3-6 units See description under subject <a href="/search/?P=15.359J" title="15.359[J]" class="bubblelink code" onclick="return showCourse(this, '15.359J');">15.359[J]</a>. G. Keselman </div><div class="courseblock"> <h4 class="courseblocktitle">6.9260 Multistakeholder Negotiation for Technical Experts</h4> Prereq: None G (Spring) 2-0-4 units Presents strategies and proven techniques for improving communications, relationships, and decision-making in groups using simulations, role-plays, case studies, and video analysis. Aims to provide the skill set needed to effectively negotiate with both internal and external stakeholders to align efforts and overcome differences. No prior experience in negotiation required. Satisfies the requirements for the Graduate Certificate in Technical Leadership. S. Dinnar </div><div class="courseblock"> <h4 class="courseblocktitle">6.9270 Negotiation and Influence Skills for Technical Leaders</h4> Prereq: None G (Fall) 2-0-4 units Focuses around the premise that the abilities to negotiate with, and influence others, are essential to being an effective leader in technology rich environments. Provides graduate students with underlying principles and a repertoire of negotiation and influence skills that apply to interpersonal situations, particularly those where an engineer or project leader lacks formal authority over others in delivering results. Utilizes research-based approaches through the application of multiple learning methods, including experiential role plays, case studies, assessments, feedback, and personal reflections. Concepts such as the zone of possible agreements, best alternative to negotiated agreements, and sources of influence are put into practice. Satisfies the requirements for the Graduate Certificate in Technical Leadership. R. M. Best </div><div class="courseblock"> <h4 class="courseblocktitle">6.9280[J] Leading Creative Teams</h4> Same subject as <a href="/search/?P=15.674J" title="15.674[J]" class="bubblelink code" onclick="return showCourse(this, '15.674J');">15.674[J]</a>, <a href="/search/?P=16.990J" title="16.990[J]" class="bubblelink code" onclick="return showCourse(this, '16.990J');">16.990[J]</a> Prereq: Permission of instructor G (Fall, Spring) 3-0-6 units Prepares students to lead teams charged with developing creative solutions in engineering and technical environments. Grounded in research but practical in focus, equips students with leadership competencies such as building self-awareness, motivating and developing others, creative problem solving, influencing without authority, managing conflict, and communicating effectively. Teamwork skills include how to convene, launch, and develop various types of teams, including project teams. Learning methods emphasize personalized and experiential skill development. Enrollment limited. D. Nino </div><div class="courseblock"> <h4 class="courseblocktitle">6.EPE UPOP Engineering Practice Experience</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=1.EPE" title="1.EPE" class="bubblelink code" onclick="return showCourse(this, '1.EPE');">1.EPE</a>, <a href="/search/?P=2.EPE" title="2.EPE" class="bubblelink code" onclick="return showCourse(this, '2.EPE');">2.EPE</a>, <a href="/search/?P=3.EPE" title="3.EPE" class="bubblelink code" onclick="return showCourse(this, '3.EPE');">3.EPE</a>, <a href="/search/?P=6.EPE" title="6.EPE" class="bubblelink code" onclick="return showCourse(this, '6.EPE');">6.EPE</a>, <a href="/search/?P=8.EPE" title="8.EPE" class="bubblelink code" onclick="return showCourse(this, '8.EPE');">8.EPE</a>, <a href="/search/?P=10.EPE" title="10.EPE" class="bubblelink code" onclick="return showCourse(this, '10.EPE');">10.EPE</a>, <a href="/search/?P=15.EPE" title="15.EPE" class="bubblelink code" onclick="return showCourse(this, '15.EPE');">15.EPE</a>, <a href="/search/?P=16.EPE" title="16.EPE" class="bubblelink code" onclick="return showCourse(this, '16.EPE');">16.EPE</a>, <a href="/search/?P=20.EPE" title="20.EPE" class="bubblelink code" onclick="return showCourse(this, '20.EPE');">20.EPE</a>, <a href="/search/?P=22.EPE" title="22.EPE" class="bubblelink code" onclick="return showCourse(this, '22.EPE');">22.EPE</a> Prereq: None U (Fall, Spring) 0-0-1 units Can be repeated for credit. See description under subject <a href="/search/?P=2.EPE" title="2.EPE" class="bubblelink code" onclick="return showCourse(this, '2.EPE');">2.EPE</a>. Application required; consult UPOP website for more information. K. Tan-Tiongco, D. Fordell </div><div class="courseblock"> <h4 class="courseblocktitle">6.EPW UPOP Engineering Practice Workshop</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=1.EPW" title="1.EPW" class="bubblelink code" onclick="return showCourse(this, '1.EPW');">1.EPW</a>, <a href="/search/?P=2.EPW" title="2.EPW" class="bubblelink code" onclick="return showCourse(this, '2.EPW');">2.EPW</a>, <a href="/search/?P=3.EPW" title="3.EPW" class="bubblelink code" onclick="return showCourse(this, '3.EPW');">3.EPW</a>, <a href="/search/?P=6.EPW" title="6.EPW" class="bubblelink code" onclick="return showCourse(this, '6.EPW');">6.EPW</a>, <a href="/search/?P=10.EPW" title="10.EPW" class="bubblelink code" onclick="return showCourse(this, '10.EPW');">10.EPW</a>, <a href="/search/?P=16.EPW" title="16.EPW" class="bubblelink code" onclick="return showCourse(this, '16.EPW');">16.EPW</a>, <a href="/search/?P=20.EPW" title="20.EPW" class="bubblelink code" onclick="return showCourse(this, '20.EPW');">20.EPW</a>, <a href="/search/?P=22.EPW" title="22.EPW" class="bubblelink code" onclick="return showCourse(this, '22.EPW');">22.EPW</a> Prereq: <a href="/search/?P=2.EPE" title="2.EPE" class="bubblelink code" onclick="return showCourse(this, '2.EPE');">2.EPE</a> U (Fall, IAP, Spring) 1-0-0 units See description under subject <a href="/search/?P=2.EPW" title="2.EPW" class="bubblelink code" onclick="return showCourse(this, '2.EPW');">2.EPW</a>. Enrollment limited to those in the UPOP program. K. Tan-Tiongco, D. Fordell </div><h2 class="sectionhead">EECS & Beyond</h2><div class="courseblock"> <h4 class="courseblocktitle">6.9302[J] StartMIT: Exploring Entrepreneurship and Innovation</h4> Same subject as <a href="/search/?P=15.352J" title="15.352[J]" class="bubblelink code" onclick="return showCourse(this, '15.352J');">15.352[J]</a> Prereq: None G (IAP) 4-0-2 units Designed for students who are interested in entrepreneurship. Introduces practices for building a successful company, such as idea creation and validation, defining a value proposition, building a team, marketing, customer traction, and possible funding models. S. Neal, D. Ruiz Massieu </div><div class="courseblock"> <h4 class="courseblocktitle">6.9310 Patents, Copyrights, and the Law of Intellectual Property</h4> Prereq: None U (Fall) Not offered regularly; consult department 2-0-4 units Intensive introduction to the law, focusing on intellectual property, patents, copyrights, trademarks, and trade secrets. Covers the process of drafting and filing patent applications, enforcement of patents in the courts,聽the differences between US and international IP laws and enforcement mechanisms, and the inventor's ability to monetize and protect his/her innovations. Highlights current legal issues and trends relating to聽the technology,聽and life sciences industries. Readings include judicial opinions and statutory material. Class聽projects include patent drafting, patent searching, and聽patentability opinions, and courtroom presentation. S. M. Bauer </div><div class="courseblock"> <h4 class="courseblocktitle">6.9320 Ethics for Engineers</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=1.082" title="1.082" class="bubblelink code" onclick="return showCourse(this, '1.082');">1.082</a>, <a href="/search/?P=2.900" title="2.900" class="bubblelink code" onclick="return showCourse(this, '2.900');">2.900</a>, <a href="/search/?P=6.9320" title="6.9320" class="bubblelink code" onclick="return showCourse(this, '6.9320');">6.9320</a>, <a href="/search/?P=10.01" title="10.01" class="bubblelink code" onclick="return showCourse(this, '10.01');">10.01</a>, <a href="/search/?P=16.676" title="16.676" class="bubblelink code" onclick="return showCourse(this, '16.676');">16.676</a> Subject meets with <a href="/search/?P=6.9321" title="6.9321" class="bubblelink code" onclick="return showCourse(this, '6.9321');">6.9321</a>, <a href="/search/?P=20.005" title="20.005" class="bubblelink code" onclick="return showCourse(this, '20.005');">20.005</a> Prereq: None U (Fall, Spring) 2-0-4 units See description under subject <a href="/search/?P=10.01" title="10.01" class="bubblelink code" onclick="return showCourse(this, '10.01');">10.01</a>. D. A. Lauffenburger, B. L. Trout </div><div class="courseblock"> <h4 class="courseblocktitle">6.9321 Ethics for Engineers - Independent Inquiry</h4> Subject meets with <a href="/search/?P=1.082J" title="1.082[J]" class="bubblelink code" onclick="return showCourse(this, '1.082J');">1.082[J]</a>, <a href="/search/?P=2.900J" title="2.900[J]" class="bubblelink code" onclick="return showCourse(this, '2.900J');">2.900[J]</a>, <a href="/search/?P=6.9320J" title="6.9320[J]" class="bubblelink code" onclick="return showCourse(this, '6.9320J');">6.9320[J]</a>, <a href="/search/?P=10.01J" title="10.01[J]" class="bubblelink code" onclick="return showCourse(this, '10.01J');">10.01[J]</a>, <a href="/search/?P=16.676J" title="16.676[J]" class="bubblelink code" onclick="return showCourse(this, '16.676J');">16.676[J]</a>, <a href="/search/?P=20.005" title="20.005" class="bubblelink code" onclick="return showCourse(this, '20.005');">20.005</a> Prereq: None U (Fall) Not offered regularly; consult department 2-0-10 units Explores the ethical principles by which an engineer ought to be guided. Integrates foundational texts in ethics with case studies illustrating ethical problems arising in the practice of engineering. Readings from classic sources including Aristotle, Kant, Machiavelli, Hobbes, Locke, Rousseau, Franklin, Tocqueville, Arendt, and King. Case studies include articles and films that address engineering disasters, safety, biotechnology, the internet and AI, and the ultimate scope and aims of engineering. Different sections may focus on themes, such as AI or biotechnology. To satisfy the independent inquiry component of this subject, students expand the scope of their term project. Students taking <a href="/search/?P=20.005" title="20.005" class="bubblelink code" onclick="return showCourse(this, '20.005');">20.005</a> focus their term project on a problem in biological engineering in which there are intertwined ethical and technical issues. D. A. Lauffenburger, B. L. Trout </div><div class="courseblock"> <h4 class="courseblocktitle">6.9350[J] Financial Market Dynamics and Human Behavior</h4> Same subject as <a href="/search/?P=15.481J" title="15.481[J]" class="bubblelink code" onclick="return showCourse(this, '15.481J');">15.481[J]</a> Prereq: <a href="/search/?P=15.401" title="15.401" class="bubblelink code" onclick="return showCourse(this, '15.401');">15.401</a>, <a href="/search/?P=15.414" title="15.414" class="bubblelink code" onclick="return showCourse(this, '15.414');">15.414</a>, or <a href="/search/?P=15.415" title="15.415" class="bubblelink code" onclick="return showCourse(this, '15.415');">15.415</a> G (Spring) 4-0-5 units See description under subject <a href="/search/?P=15.481J" title="15.481[J]" class="bubblelink code" onclick="return showCourse(this, '15.481J');">15.481[J]</a>. Enrollment may be limited; preference to Sloan graduate students. A. Lo </div><div class="courseblock"> <h4 class="courseblocktitle">6.9360 Management in Engineering</h4> Engineering School-Wide Elective Subject. Offered under: <a href="/search/?P=2.96" title="2.96" class="bubblelink code" onclick="return showCourse(this, '2.96');">2.96</a>, <a href="/search/?P=6.9360" title="6.9360" class="bubblelink code" onclick="return showCourse(this, '6.9360');">6.9360</a>, <a href="/search/?P=10.806" title="10.806" class="bubblelink code" onclick="return showCourse(this, '10.806');">10.806</a>, <a href="/search/?P=16.653" title="16.653" class="bubblelink code" onclick="return showCourse(this, '16.653');">16.653</a> Prereq: None U (Fall) 3-1-8 units See description under subject <a href="/search/?P=2.96" title="2.96" class="bubblelink code" onclick="return showCourse(this, '2.96');">2.96</a>. Restricted to juniors and seniors. H. S. Marcus, J.-H. Chun </div><h2 class="sectionhead">Independent Activities Period</h2><div class="courseblock"> <h4 class="courseblocktitle">6.9500 Introduction to MATLAB</h4> Prereq: None U (IAP) Not offered regularly; consult department 1-0-2 units Accelerated introduction to MATLAB and its popular toolboxes. Lectures are interactive, with students conducting sample MATLAB problems in real time. Includes problem-based MATLAB assignments. Students must provide their own laptop and software. Enrollment limited. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9510 Introduction to Signals and Systems, and Feedback Control</h4> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> or permission of instructor U (IAP) Not offered regularly; consult department 2-2-2 units Introduces fundamental concepts for 6.003, including Fourier and Laplace transforms, convolution, sampling, filters, feedback control, stability, and Bode plots. Students engage in problem solving, using Mathematica and MATLAB software extensively to help visualize processing in the time frequency domains. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9520 Introduction to Electrical Engineering Lab Skills</h4> Prereq: None U (IAP) Not offered regularly; consult department 1-3-2 units Introduces basic electrical engineering concepts, components, and laboratory techniques. Covers analog integrated circuits, power supplies, and digital circuits. Lab exercises provide practical experience in constructing projects using multi-meters, oscilloscopes, logic analyzers, and other tools. Includes a project in which students build a circuit to display their own EKG. Enrollment limited. G. P. Hom </div><div class="courseblock"> <h4 class="courseblocktitle">6.9550 Structure and Interpretation of Computer Programs</h4> Prereq: None U (IAP) Not offered regularly; consult department 1-0-5 units Studies the structure and interpretation of computer programs which transcend specific programming languages. Demonstrates thought patterns for computer science using Scheme. Includes weekly programming projects. Enrollment may be limited. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9560 Introduction to Software Engineering in Java</h4> Prereq: None U (IAP) Not offered regularly; consult department 1-1-4 units Covers the fundamentals of Java, helping students develop intuition about object-oriented programming. Focuses on developing working software that solves real problems. Designed for students with little or no programming experience. Concepts covered useful to <a href="/search/?P=6.3100" title="6.3100" class="bubblelink code" onclick="return showCourse(this, '6.3100');">6.3100</a>. Enrollment limited. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9570 Introduction to C and C++</h4> Prereq: None U (IAP) Not offered regularly; consult department 3-3-0 units Fast-paced introduction to the C and C++ programming languages. Intended for those with experience in other languages who have never used C or C++. Students complete daily assignments, a small-scale individual project, and a mandatory online diagnostic test. Enrollment limited. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9600 Mobile Autonomous Systems Laboratory: MASLAB</h4> Prereq: None U (IAP) 2-2-2 units Can be repeated for credit. Autonomous robotics contest emphasizing technical AI, vision, mapping and navigation from a robot-mounted camera. Few restrictions are placed on materials, sensors, and/or actuators enabling teams to build robots very creatively. Teams should have members with varying engineering, programming and mechanical backgrounds. Culminates with a robot competition at the end of IAP. Enrollment limited. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9610 The Battlecode Programming Competition</h4> Prereq: None U (IAP) 2-0-4 units Can be repeated for credit. Artificial Intelligence programming contest in Java. Student teams program virtual robots to play Battlecode, a real-time strategy game. Competition culminates in a live BattleCode tournament. Assumes basic knowledge of programming. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9620 Web Lab: A Web Programming Class and Competition</h4> Prereq: None U (IAP) 1-0-5 units Can be repeated for credit. Student teams learn to build a functional and user-friendly website. Topics include version control, HTML, CSS, JavaScript, ReactJS, and nodejs. All teams are eligible to enter a competition where sites are judged by industry experts. Beginners and experienced web programmers welcome, but some previous programming experience is recommended. Registration on subject website required. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.9630 Pokerbots Competition</h4> Prereq: None U (IAP) 1-0-5 units Can be repeated for credit. Build autonomous poker players and aquire the knowledge of the game of poker. Showcase decision making skills, apply concepts in mathematics, computer science and economics. Provides instruction in programming, game theory, probability and statistics and machine learning. Concludes with a final competition and prizes. Enrollment limited. Staff </div><h2 class="sectionhead">Non-classroom & Career</h2><div class="courseblock"> <h4 class="courseblocktitle">6.9700 Studies in Artificial Intelligence and Decision Making</h4> Prereq: Permission of department G (Fall) Not offered regularly; consult department 0-0-48 units Introduction to artificial intelligence and decision making in a series of online subjects followed by a comprehensive examination. Probability: distributions and probabilistic calculations, inference methods, laws of large numbers, and random processes. Statistical data analysis: linear regression, parameter estimation, hypothesis testing, model selection, and causal inference. Machine learning: linear classification, fundamentals of supervised machine learning, deep learning, unsupervised learning, and generative models. Online decision making: online optimization, online learning, Markov decision processes and reinforcement learning, elements of control theory, and fundamentals of game theory.聽 Computer vision: fundamentals of image and signal processing, introduction to machine learning for vision, generative models and representation learning, and elements of scene understanding. Restricted to Artificial Intelligence and Decision Making MicroMasters Credential holders in the AI+D Blended Master's program. A. Madry, P. Parrilo </div><div class="courseblock"> <h4 class="courseblocktitle">6.9710 Internship in Artificial Intelligence and Decision Making</h4> Prereq: Permission of department G (Spring, Summer) Units arranged [P/D/F] Provides an opportunity for students to synthesize their coursework and聽to聽apply the knowledge gained in the program towards a project with a host organization. All internship placements are subject to approval by program director. Each student must write a capstone project report. Restricted to students in the AI+D blended master's program. A. Madry, P. Parrilo </div><div class="courseblock"> <h4 class="courseblocktitle">6.9720 Research in Artificial Intelligence and Decision Making</h4> Prereq: Permission of department Acad Year 2024-2025: Not offered Acad Year 2025-2026: G (Spring, Summer) 0-0-12 units Individual research project arranged with appropriate faculty member or approved advisor. A final paper summarizing research is required. Restricted to students in the AI+D blended SM program. A. Madry, P. Parrilo </div><div class="courseblock"> <h4 class="courseblocktitle">6.9800 Independent Study in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit. Opportunity for independent study at the undergraduate level under regular supervision by a faculty member.聽Study plans聽require prior approval. Consult Department Undergraduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9820 Practical Internship Experience</h4> Prereq: None U (Fall, IAP, Spring, Summer) 0-1-0 units Can be repeated for credit. For Course 6 students participating in curriculum-related off-campus internship experiences in electrical engineering or computer science. Before enrolling, students must have an employment offer from a company or organization and must find an EECS advisor. Upon completion of the internship the student must submit a letter from the employer evaluating the work accomplished, a substantive final report from the student, approved by the MIT advisor. Subject to departmental approval. Consult Department Undergraduate Office for details on procedures and restrictions. Consult Department Undergraduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9830 Professional Perspective Internship</h4> Prereq: None G (Fall, IAP, Spring, Summer) 0-1-0 units Required for Course 6 MEng students to gain professional experience in electrical engineering or computer science through an internship (industry, government, or academic) of 4 or more weeks in IAP or summer. This can be completed as MEng students or as undergrads, through previous employment completed while deferring MEng entry or by attending a series of three colloquia, seminars, or technical talks related to their field. For internships/work experience, a letter from the employer confirming dates of employment is required. All students are required to write responses to short essay prompts about their professional experience. International students must consult ISO and the EECS Undergraduate Office on work authorization and allowable employment dates. Consult Department Undergraduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9840 Practical Experience in EECS</h4> Prereq: None G (Fall, IAP, Spring, Summer) 0-1-0 units Can be repeated for credit. For Course 6 students in the MEng program who seek practical off-campus research experiences or internships in electrical engineering or computer science. Before enrolling, students must have an offer of employment from a company or organization and secure an advisor within EECS. Employers must document the work accomplished. Proposals subject to departmental approval. For students who begin the MEng program in the summer only, the experience or internship cannot exceed 20 hours per week and must begin no earlier than the first day of the Summer Session, but may end as late as the last business day before the Fall Term. Consult Department Undergraduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9850 6-A Internship</h4> Prereq: None U (Fall, Spring, Summer) 0-12-0 units Provides academic credit for the first assignment of 6-A undergraduate students at companies affiliated with the department's 6-A internship program. Limited to students participating in the 6-A internship program. T. Palacios </div><div class="courseblock"> <h4 class="courseblocktitle">6.9860 Advanced 6-A Internship</h4> Prereq: <a href="/search/?P=6.9850" title="6.9850" class="bubblelink code" onclick="return showCourse(this, '6.9850');">6.9850</a> U (Fall, Spring, Summer) 0-12-0 units Provides academic credit for the second assignment of 6-A undergraduate students at companies affiliated with the department's 6-A internship program. Limited to students participating in the 6-A internship program. T. Palacios </div><div class="courseblock"> <h4 class="courseblocktitle">6.9870 Graduate 6-A Internship</h4> Prereq: <a href="/search/?P=6.9850" title="6.9850" class="bubblelink code" onclick="return showCourse(this, '6.9850');">6.9850</a> or <a href="/search/?P=6.9860" title="6.9860" class="bubblelink code" onclick="return showCourse(this, '6.9860');">6.9860</a> G (Fall, Spring, Summer) 0-12-0 units Provides academic credit for a graduate assignment of graduate 6-A students at companies affiliated with the department's 6-A internship program. Limited to graduate students participating in the 6-A internship program. T. Palacios </div><div class="courseblock"> <h4 class="courseblocktitle">6.9880 Graduate 6-A Internship</h4> Prereq: <a href="/search/?P=6.9870" title="6.9870" class="bubblelink code" onclick="return showCourse(this, '6.9870');">6.9870</a> G (Fall, Spring, Summer) 0-12-0 units Provides academic credit for graduate students in the second half of their 6-A MEng industry internship. Limited to graduate students participating in the 6-A internship program. T. Palacios </div><div class="courseblock"> <h4 class="courseblocktitle">6.9900 Teaching Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, Spring) Units arranged [P/D/F] Can be repeated for credit. For Teaching Assistants in Electrical Engineering and Computer Science, in cases where teaching assignment is approved for academic credit by the department. E. Adalsteinsson, D. M. Freeman, L. P. Kaelbling,聽R. C. Miller </div><div class="courseblock"> <h4 class="courseblocktitle">6.9910 Research in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit. For EECS MEng students who are Research Assistants in Electrical Engineering and Computer Science, in cases where the assigned research is approved for academic credit by the department. Hours arranged with research advisor. Consult Department Undergraduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9920 Introductory Research in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit. Enrollment restricted to first-year graduate students in Electrical Engineering and Computer Science who are doing introductory research leading to an SM, EE, ECS, PhD, or ScD thesis. Opportunity to become involved in graduate research, under guidance of a staff member, on a problem of mutual interest to student and advisor. Individual programs subject to approval of professor in charge. L. A. Kolodziejski </div><div class="courseblock"> <h4 class="courseblocktitle">6.9930 Networking Seminars in EECS</h4> Prereq: None G (Fall) Units arranged [P/D/F] For first year Course 6 students in the SM/PhD track, who seek weekly engagement with departmental faculty and staff, to discuss topics related to the graduate student experience, and to promote a successful start to graduate school. J. Fischer </div><div class="courseblock"> <h4 class="courseblocktitle">6.9932 Introduction to Research in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall, Spring, Summer) 3-0-0 units Seminar on topics related to research leading to an SM, EE, ECS, PhD, or ScD thesis. Limited to first-year regular graduate students in EECS with a fellowship or teaching assistantship. L. A. Kolodziejski </div><div class="courseblock"> <h4 class="courseblocktitle">6.9940 Professional Perspective I</h4> Prereq: None G (Fall, IAP, Spring, Summer) 0-0-1 units Can be repeated for credit. Required for Course 6 students in the doctoral program to gain professional perspective in research experiences, academic experiences, and internships in electrical engineering and computer science. Professional perspective options include: internships (with industry, government or academia), industrial colloquia or seminars, research collaboration with industry or government, and professional development for entry into academia or entrepreneurial engagement. For an internship experience, an offer of employment from a company or organization is required prior to enrollment; employers must document work accomplished. A written report is required upon completion of a minimum of 4 weeks of off-campus experiences. Proposals subject to departmental approval. Consult Department Graduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9950 Professional Perspective II</h4> Prereq: <a href="/search/?P=6.9940" title="6.9940" class="bubblelink code" onclick="return showCourse(this, '6.9940');">6.9940</a> G (Fall, IAP, Spring, Summer) 0-0-1 units Can be repeated for credit. Required for Course 6 students in the doctoral program to gain professional perspective in research experiences, academic experiences, and internships in electrical engineering and computer science. Professional perspective options include: internships (with industry, government or academia), industrial colloquia or seminars, research collaboration with industry or government, and professional development for entry into academia or entrepreneurial engagement. For an internship experience, an offer of employment from a company or organization is required prior to enrollment; employers must document work accomplished. A written report is required upon completion of a minimum of 4 weeks of off-campus experiences. Proposals subject to departmental approval. Consult Department Graduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.9960 Experience in Technical Communication</h4> Prereq: Permission of instructor G (Fall, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit. Provides training and practice in technical communication. Includes communication coaching, workshop facilitation, and other communication-related projects under supervision of Communication Lab staff. Students selected by interview. Enrollment limited by availability of suitable assignments. Enrollment could be limited if there isn't enough student participation. D. Chien, D. Montgomery </div><div class="courseblock"> <h4 class="courseblocktitle">6.9970 Academic Job Search</h4> Prereq: Permission of instructor G (Fall) 2-0-4 units Interactive workshops and homework assignments provide guidance for the faculty application process, including CV; cover letter; research, teaching, and diversity statements; interview and job talk preparation; and post-offer negotiations. Includes perspectives of junior faculty, search committee members, and department leadership at MIT and other institutions. Academic Career Day provides opportunity for students to participate in one-on-one pre-interviews with external faculty. Preference to EECS senior PhD students and postdocs. S. Amarasinghe, D. Montgomery </div><div class="courseblock"> <h4 class="courseblocktitle">6.9990 Independent Study in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit. Opportunity for independent study under regular supervision by a faculty member. Projects require prior approval. L. A. Kolodziejski </div><div class="courseblock"> <h4 class="courseblocktitle">6.THG Graduate Thesis</h4> Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit. Program of research leading to the writing of an SM, EE, ECS, PhD, or ScD thesis; to be arranged by the student and an appropriate MIT faculty member. L. A. Kolodziejski </div><div class="courseblock"> <h4 class="courseblocktitle">6.THM Master of Engineering Program Thesis</h4> Prereq: None G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit. Program of research leading to the writing of an MEng thesis; to be arranged by the student and an appropriate MIT faculty member. Restricted to MEng graduate students. Consult Department Undergraduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.UR Undergraduate Research in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall, IAP, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit. Individual research project arranged with appropriate faculty member or approved advisor. Forms and instructions for the聽final report are available in the EECS Undergraduate Office. Consult Department Undergraduate Office </div><h2 class="sectionhead">Special Subjects</h2><div class="courseblock"> <h4 class="courseblocktitle">6.S040 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S041 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S042 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S043 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S044 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall, Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S045 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S046 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) 3-0-9 units Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S047 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S050 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S051 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S052 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) 3-0-3 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S053 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S054 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S055 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S056 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S057 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S058 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S059 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) Units arranged Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S060 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Basic undergraduate subjects not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S061 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Basic undergraduate subjects not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S062 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S063 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None U (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S076 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S077 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Spring; first half of term) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S078 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S079 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S080 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S081 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S082 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S083 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S084 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S085 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S086 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S087 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S088 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S089 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S090 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Summer) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. D. M. Freeman </div><div class="courseblock"> <h4 class="courseblocktitle">6.S091 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S092 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S093 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. D. M. Freeman </div><div class="courseblock"> <h4 class="courseblocktitle">6.S094 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S095 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S096 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S097 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S098 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S099 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S183 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S184 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S185 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. D. M. Freeman </div><div class="courseblock"> <h4 class="courseblocktitle">6.S186 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S187 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.S188 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. D. M. Freeman </div><div class="courseblock"> <h4 class="courseblocktitle">6.S189 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. D. M. Freeman </div><div class="courseblock"> <h4 class="courseblocktitle">6.S190 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. D. M. Freeman </div><div class="courseblock"> <h4 class="courseblocktitle">6.S191 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S192 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S193 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S197 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Not offered regularly; consult department Units arranged Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S193-6.S198 Special Laboratory Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Laboratory subject that covers content not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S630 Special Subject in Engineering Leadership</h4> Prereq: None G (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult the Gordon Engineering Leadership Program or Riccio Graduate Engineering Leadership Program to learn of offerings for a particular term. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.S640 Special Subject in Engineering Leadership</h4> Prereq: None G (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult the Gordon Engineering Leadership Program or Riccio Graduate Engineering Leadership Program to learn of offerings for a particular term. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.S650 Special Subject in Engineering Leadership</h4> Prereq: None G (Fall) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult the Gordon Engineering Leadership Program or Riccio Graduate Engineering Leadership Program to learn of offerings for a particular term. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.S660 Special Subject in Engineering Leadership</h4> Prereq: None G (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult the Gordon Engineering Leadership Program or Riccio Graduate Engineering Leadership Program to learn of offerings for a particular term. Staff </div><div class="courseblock"> <h4 class="courseblocktitle">6.S890 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S891 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S892 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S893 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S894 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S895 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S896 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S897 Special Subject in Computer Science</h4> Prereq: Permission of instructor G (Spring; first half of term) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S898 Special Subject in Computer Science</h4> Prereq: Permission of instructor G (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S899 Special Subject in Computer Science</h4> Prereq: Permission of instructor G (Fall) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S911 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S912 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S913 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S914 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S915 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S916 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S917 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S918 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (IAP) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S919 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor U (Fall, IAP, Spring) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S950 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring; first half of term) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S951 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S952 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) 3-0-3 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S953 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S954 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S955 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S956 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, Spring, Summer) Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S960 Special Studies: Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Opportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. Consult Department Graduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.S961 Special Studies: Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Opportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. Consult Department Graduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.S962 Special Studies: Electrical Engineering and Computer Science</h4> Prereq: None G (Fall, Spring) Not offered regularly; consult department Units arranged Can be repeated for credit. Opportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. Consult Department Graduate Office </div><div class="courseblock"> <h4 class="courseblocktitle">6.S963-6.S967 Special Studies: EECS</h4> Prereq: None G (Fall) Units arranged Can be repeated for credit. Opportunity for study of graduate-level topics related to electrical engineering and computer science but not included elsewhere in the curriculum. Registration under this subject normally used for situations involving small study groups. Normal registration is for 12 units. Registration subject to approval of professor in charge. Consult the department for details. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S974 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S975 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Not offered regularly; consult department Units arranged [P/D/F] Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S976 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Spring) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S977 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S978 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall) Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S979 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall) Not offered regularly; consult department Units arranged Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S980 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S981 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S982 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: Permission of instructor G (Fall) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S983 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S984 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S985 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) Not offered regularly; consult department 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S986 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S987 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><div class="courseblock"> <h4 class="courseblocktitle">6.S988 Special Subject in Electrical Engineering and Computer Science</h4> Prereq: None G (Spring) 3-0-9 units Can be repeated for credit. Covers subject matter not offered in the regular curriculum. Consult department to learn of offerings for a particular term. Consult Department </div><h2 class="sectionhead">Common Ground for Computing Education</h2><div class="courseblock"> <h4 class="courseblocktitle">6.C01 Modeling with Machine Learning: from Algorithms to Applications</h4> Subject meets with <a href="/search/?P=6.C51" title="6.C51" class="bubblelink code" onclick="return showCourse(this, '6.C51');">6.C51</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>; Coreq: <a href="/search/?P=1.C01" title="1.C01" class="bubblelink code" onclick="return showCourse(this, '1.C01');">1.C01</a>, <a href="/search/?P=2.C01" title="2.C01" class="bubblelink code" onclick="return showCourse(this, '2.C01');">2.C01</a>, <a href="/search/?P=3.C01" title="3.C01[J]" class="bubblelink code" onclick="return showCourse(this, '3.C01');">3.C01[J]</a>, <a href="/search/?P=6.C011" title="6.C011" class="bubblelink code" onclick="return showCourse(this, '6.C011');">6.C011</a>, <a href="/search/?P=7.C01" title="7.C01" class="bubblelink code" onclick="return showCourse(this, '7.C01');">7.C01</a>, or <a href="/search/?P=22.C01" title="22.C01" class="bubblelink code" onclick="return showCourse(this, '22.C01');">22.C01</a> U (Spring; first half of term) 2-0-4 units Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited. R. Barzilay, T. Jaakkola </div><div class="courseblock"> <h4 class="courseblocktitle">6.C011 Modeling with Machine Learning for Computer Science (New)</h4> Subject meets with <a href="/search/?P=6.C511" title="6.C511" class="bubblelink code" onclick="return showCourse(this, '6.C511');">6.C511</a> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>, <a href="/search/?P=6.C01" title="6.C01" class="bubblelink code" onclick="return showCourse(this, '6.C01');">6.C01</a>, (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>), and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) U (Spring; second half of term) 3-0-3 units Focuses on in-depth modeling of engineering tasks as machine learning problems. Emphasizes聽framing, method design, and interpretation of results. In comparison to broader prerequisite聽<a href="/search/?P=6.C01" title="6.C01" class="bubblelink code" onclick="return showCourse(this, '6.C01');">6.C01</a>, this project-oriented subject consists of deep dives into select technical areas or聽engineering tasks involving both supervised and exploratory uses of machine learning. Explores technical areas such robustness, interpretability, fairness and engineering tasks such as recommender systems, performance optimization, and automated聽design. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of the core subject <a href="/search/?P=6.C01" title="6.C01" class="bubblelink code" onclick="return showCourse(this, '6.C01');">6.C01</a>. Enrollment may be limited. T. Jaakkola </div><div class="courseblock"> <h4 class="courseblocktitle">6.C06[J] Linear Algebra and Optimization</h4> Same subject as <a href="/search/?P=18.C06J" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06J');">18.C06[J]</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> U (Fall) 5-0-7 units. REST Credit cannot also be received for <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a>, <a href="/search/?P=18.700" title="18.700" class="bubblelink code" onclick="return showCourse(this, '18.700');">18.700</a>, <a href="/search/?P=ES.1806" title="ES.1806" class="bubblelink code" onclick="return showCourse(this, 'ES.1806');">ES.1806</a> See description under subject <a href="/search/?P=18.C06J" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06J');">18.C06[J]</a>. A. Moitra, P. Parrilo </div><div class="courseblock"> <h4 class="courseblocktitle">6.C25[J] Real World Computation with Julia</h4> Same subject as <a href="/search/?P=1.C25J" title="1.C25[J]" class="bubblelink code" onclick="return showCourse(this, '1.C25J');">1.C25[J]</a>, <a href="/search/?P=12.C25J" title="12.C25[J]" class="bubblelink code" onclick="return showCourse(this, '12.C25J');">12.C25[J]</a>, <a href="/search/?P=16.C25J" title="16.C25[J]" class="bubblelink code" onclick="return showCourse(this, '16.C25J');">16.C25[J]</a>, <a href="/search/?P=18.C25J" title="18.C25[J]" class="bubblelink code" onclick="return showCourse(this, '18.C25J');">18.C25[J]</a>, <a href="/search/?P=22.C25J" title="22.C25[J]" class="bubblelink code" onclick="return showCourse(this, '22.C25J');">22.C25[J]</a> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>, <a href="/search/?P=18.03" title="18.03" class="bubblelink code" onclick="return showCourse(this, '18.03');">18.03</a>, and <a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> U (Fall) 3-0-9 units See description under subject <a href="/search/?P=18.C25J" title="18.C25[J]" class="bubblelink code" onclick="return showCourse(this, '18.C25J');">18.C25[J]</a>. A. Edelman, R. Ferrari, B. Forget, C. Leiseron,Y. Marzouk, J. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.C27[J] Computational Imaging: Physics and Algorithms</h4> Same subject as <a href="/search/?P=2.C27J" title="2.C27[J]" class="bubblelink code" onclick="return showCourse(this, '2.C27J');">2.C27[J]</a>, <a href="/search/?P=3.C27J" title="3.C27[J]" class="bubblelink code" onclick="return showCourse(this, '3.C27J');">3.C27[J]</a> Subject meets with <a href="/search/?P=2.C67J" title="2.C67[J]" class="bubblelink code" onclick="return showCourse(this, '2.C67J');">2.C67[J]</a>, <a href="/search/?P=3.C67J" title="3.C67[J]" class="bubblelink code" onclick="return showCourse(this, '3.C67J');">3.C67[J]</a>, <a href="/search/?P=6.C67J" title="6.C67[J]" class="bubblelink code" onclick="return showCourse(this, '6.C67J');">6.C67[J]</a> Prereq: <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a> and (<a href="/search/?P=1.00" title="1.00" class="bubblelink code" onclick="return showCourse(this, '1.00');">1.00</a>, <a href="/search/?P=1.000" title="1.000" class="bubblelink code" onclick="return showCourse(this, '1.000');">1.000</a>, <a href="/search/?P=2.086" title="2.086" class="bubblelink code" onclick="return showCourse(this, '2.086');">2.086</a>, <a href="/search/?P=3.019" title="3.019" class="bubblelink code" onclick="return showCourse(this, '3.019');">3.019</a>, or <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>) U (Fall) 3-0-9 units See description under subject <a href="/search/?P=2.C27J" title="2.C27[J]" class="bubblelink code" onclick="return showCourse(this, '2.C27J');">2.C27[J]</a>. G. Barbastathis, J. LeBeau, R. Ram, S. You </div><div class="courseblock"> <h4 class="courseblocktitle">6.C35[J] Interactive Data Visualization and Society</h4> Same subject as <a href="/search/?P=11.C35J" title="11.C35[J]" class="bubblelink code" onclick="return showCourse(this, '11.C35J');">11.C35[J]</a> Subject meets with <a href="/search/?P=6.C85J" title="6.C85[J]" class="bubblelink code" onclick="return showCourse(this, '6.C85J');">6.C85[J]</a>, <a href="/search/?P=11.C85J" title="11.C85[J]" class="bubblelink code" onclick="return showCourse(this, '11.C85J');">11.C85[J]</a> Prereq: None U (Spring) 3-1-8 units Credit cannot also be received for <a href="/search/?P=6.8530" title="6.8530" class="bubblelink code" onclick="return showCourse(this, '6.8530');">6.8530</a>, <a href="/search/?P=11.154" title="11.154" class="bubblelink code" onclick="return showCourse(this, '11.154');">11.154</a>, <a href="/search/?P=11.454" title="11.454" class="bubblelink code" onclick="return showCourse(this, '11.454');">11.454</a> Covers the design, ethical, and technical skills for creating effective visualizations. Short assignments build familiarity with the data analysis and visualization design process. Weekly lab sessions present coding and technical skills. A final project provides experience working with real-world big data, provided by external partners, in order to expose and communicate insights about societal issues. Students taking graduate version complete additional assignments. Enrollment limited. Enrollment limited. C. D'Ignazio, A. Satyanarayan, S. Williams </div><div class="courseblock"> <h4 class="courseblocktitle">6.C40[J] Ethics of Computing (New)</h4> Same subject as <a href="/search/?P=24.C40J" title="24.C40[J]" class="bubblelink code" onclick="return showCourse(this, '24.C40J');">24.C40[J]</a> Prereq: None U (Fall) 3-0-9 units. HASS-H See description under subject <a href="/search/?P=24.C40J" title="24.C40[J]" class="bubblelink code" onclick="return showCourse(this, '24.C40J');">24.C40[J]</a>. B. Skow, A. Solar-Lezama </div><div class="courseblock"> <h4 class="courseblocktitle">6.C51 Modeling with Machine Learning: from Algorithms to Applications</h4> Subject meets with <a href="/search/?P=6.C01" title="6.C01" class="bubblelink code" onclick="return showCourse(this, '6.C01');">6.C01</a> Prereq: <a href="/search/?P=18.02|18.02A|18.022|18.024" onclick="return showCourse(this, '18.02|18.02A|18.022|18.024');">Calculus II (GIR)</a> and <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>; Coreq: <a href="/search/?P=1.C51" title="1.C51" class="bubblelink code" onclick="return showCourse(this, '1.C51');">1.C51</a>, <a href="/search/?P=2.C51" title="2.C51" class="bubblelink code" onclick="return showCourse(this, '2.C51');">2.C51</a>, <a href="/search/?P=3.C51" title="3.C51[J]" class="bubblelink code" onclick="return showCourse(this, '3.C51');">3.C51[J]</a>, <a href="/search/?P=6.C511" title="6.C511" class="bubblelink code" onclick="return showCourse(this, '6.C511');">6.C511</a>, <a href="/search/?P=7.C51" title="7.C51" class="bubblelink code" onclick="return showCourse(this, '7.C51');">7.C51</a>, <a href="/search/?P=22.C51" title="22.C51" class="bubblelink code" onclick="return showCourse(this, '22.C51');">22.C51</a>, or <a href="/search/?P=SCM.C51" title="SCM.C51" class="bubblelink code" onclick="return showCourse(this, 'SCM.C51');">SCM.C51</a> G (Spring; first half of term) 2-0-4 units Focuses on modeling with machine learning methods with an eye towards applications in engineering and sciences. Introduction to modern machine learning methods, from supervised to unsupervised models, with an emphasis on newer neural approaches. Emphasis on the understanding of how and why the methods work from the point of view of modeling, and when they are applicable. Using concrete examples, covers formulation of machine learning tasks, adapting and extending methods to given problems, and how the methods can and should be evaluated.聽Students taking graduate version complete additional assignments. Students cannot receive credit without completion of a 6-unit disciplinary module in the same semester. Enrollment may be limited. R. Barzilay, T. Jaakkola </div><div class="courseblock"> <h4 class="courseblocktitle">6.C511 Modeling with Machine Learning for Computer Science (New)</h4> Subject meets with <a href="/search/?P=6.C011" title="6.C011" class="bubblelink code" onclick="return showCourse(this, '6.C011');">6.C011</a> Prereq: <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>, <a href="/search/?P=6.C51" title="6.C51" class="bubblelink code" onclick="return showCourse(this, '6.C51');">6.C51</a>, (<a href="/search/?P=6.1200" title="6.1200[J]" class="bubblelink code" onclick="return showCourse(this, '6.1200');">6.1200[J]</a> or <a href="/search/?P=6.3700" title="6.3700" class="bubblelink code" onclick="return showCourse(this, '6.3700');">6.3700</a>), and (<a href="/search/?P=18.06" title="18.06" class="bubblelink code" onclick="return showCourse(this, '18.06');">18.06</a> or <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a>) G (Spring; second half of term) 3-0-3 units Focuses on in-depth modeling of engineering tasks as machine learning problems. Emphasizes聽framing, method design, and interpretation of results. In comparison to broader co-requisite聽<a href="/search/?P=6.C01" title="6.C01" class="bubblelink code" onclick="return showCourse(this, '6.C01');">6.C01</a>/<a href="/search/?P=6.C51" title="6.C51" class="bubblelink code" onclick="return showCourse(this, '6.C51');">6.C51</a>, this project oriented subject consists of deep dives into select technical areas or聽engineering tasks involving both supervised and exploratory uses of machine learning. Deep聽dives into technical areas such robustness, interpretability, fairness; engineering tasks such as recommender systems, performance optimization, automated聽design. Students taking graduate version complete additional assignments. Students cannot receive credit without completion of the core subject <a href="/search/?P=6.C51" title="6.C51" class="bubblelink code" onclick="return showCourse(this, '6.C51');">6.C51</a>. Enrollment may be limited. T. Jaakkola </div><div class="courseblock"> <h4 class="courseblocktitle">6.C57[J] Optimization Methods (New)</h4> Same subject as <a href="/search/?P=15.C57J" title="15.C57[J]" class="bubblelink code" onclick="return showCourse(this, '15.C57J');">15.C57[J]</a>, <a href="/search/?P=IDS.C57J" title="IDS.C57[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.C57J');">IDS.C57[J]</a> Subject meets with <a href="/search/?P=6.C571J" title="6.C571[J]" class="bubblelink code" onclick="return showCourse(this, '6.C571J');">6.C571[J]</a>, <a href="/search/?P=15.C571J" title="15.C571[J]" class="bubblelink code" onclick="return showCourse(this, '15.C571J');">15.C571[J]</a> Prereq: <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a> or permission of instructor G (Fall) 4-0-8 units See description under subject <a href="/search/?P=15.C57J" title="15.C57[J]" class="bubblelink code" onclick="return showCourse(this, '15.C57J');">15.C57[J]</a>. A. Jacquillat </div><div class="courseblock"> <h4 class="courseblocktitle">6.C571[J] Optimization Methods (New)</h4> Same subject as <a href="/search/?P=15.C571J" title="15.C571[J]" class="bubblelink code" onclick="return showCourse(this, '15.C571J');">15.C571[J]</a> Subject meets with <a href="/search/?P=6.C57J" title="6.C57[J]" class="bubblelink code" onclick="return showCourse(this, '6.C57J');">6.C57[J]</a>, <a href="/search/?P=15.C57J" title="15.C57[J]" class="bubblelink code" onclick="return showCourse(this, '15.C57J');">15.C57[J]</a>, <a href="/search/?P=IDS.C57J" title="IDS.C57[J]" class="bubblelink code" onclick="return showCourse(this, 'IDS.C57J');">IDS.C57[J]</a> Prereq: <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a> or permission of instructor U (Fall) 4-0-8 units See description under subject <a href="/search/?P=15.C571J" title="15.C571[J]" class="bubblelink code" onclick="return showCourse(this, '15.C571J');">15.C571[J]</a>. One section primarily reserved for Sloan students; check syllabus for details. A. Jacquillat </div><div class="courseblock"> <h4 class="courseblocktitle">6.C67[J] Computational Imaging: Physics and Algorithms</h4> Same subject as <a href="/search/?P=2.C67J" title="2.C67[J]" class="bubblelink code" onclick="return showCourse(this, '2.C67J');">2.C67[J]</a>, <a href="/search/?P=3.C67J" title="3.C67[J]" class="bubblelink code" onclick="return showCourse(this, '3.C67J');">3.C67[J]</a> Subject meets with <a href="/search/?P=2.C27J" title="2.C27[J]" class="bubblelink code" onclick="return showCourse(this, '2.C27J');">2.C27[J]</a>, <a href="/search/?P=3.C27J" title="3.C27[J]" class="bubblelink code" onclick="return showCourse(this, '3.C27J');">3.C27[J]</a>, <a href="/search/?P=6.C27J" title="6.C27[J]" class="bubblelink code" onclick="return showCourse(this, '6.C27J');">6.C27[J]</a> Prereq: <a href="/search/?P=18.C06" title="18.C06[J]" class="bubblelink code" onclick="return showCourse(this, '18.C06');">18.C06[J]</a> and (<a href="/search/?P=1.00" title="1.00" class="bubblelink code" onclick="return showCourse(this, '1.00');">1.00</a>, <a href="/search/?P=1.000" title="1.000" class="bubblelink code" onclick="return showCourse(this, '1.000');">1.000</a>, <a href="/search/?P=2.086" title="2.086" class="bubblelink code" onclick="return showCourse(this, '2.086');">2.086</a>, <a href="/search/?P=3.019" title="3.019" class="bubblelink code" onclick="return showCourse(this, '3.019');">3.019</a>, or <a href="/search/?P=6.100A" title="6.100A" class="bubblelink code" onclick="return showCourse(this, '6.100A');">6.100A</a>) G (Fall) 3-0-9 units See description under subject <a href="/search/?P=2.C67J" title="2.C67[J]" class="bubblelink code" onclick="return showCourse(this, '2.C67J');">2.C67[J]</a>. G. Barbastathis, J. LeBeau, R. Ram, S. You </div><div class="courseblock"> <h4 class="courseblocktitle">6.C85[J] Interactive Data Visualization and Society</h4> Same subject as <a href="/search/?P=11.C85J" title="11.C85[J]" class="bubblelink code" onclick="return showCourse(this, '11.C85J');">11.C85[J]</a> Subject meets with <a href="/search/?P=6.C35J" title="6.C35[J]" class="bubblelink code" onclick="return showCourse(this, '6.C35J');">6.C35[J]</a>, <a href="/search/?P=11.C35J" title="11.C35[J]" class="bubblelink code" onclick="return showCourse(this, '11.C35J');">11.C35[J]</a> Prereq: None G (Spring) 3-1-8 units Credit cannot also be received for <a href="/search/?P=6.8530" title="6.8530" class="bubblelink code" onclick="return showCourse(this, '6.8530');">6.8530</a>, <a href="/search/?P=11.154" title="11.154" class="bubblelink code" onclick="return showCourse(this, '11.154');">11.154</a>, <a href="/search/?P=11.454" title="11.454" class="bubblelink code" onclick="return showCourse(this, '11.454');">11.454</a> Covers the design, ethical, and technical skills for creating effective visualizations. Short assignments build familiarity with the data analysis and visualization design process. Students participate in hour-long studio reading sessions. A final project provides experience working with real-world big data, provided by external partners, in order to expose and communicate insights about societal issues. Students taking graduate version complete additional assignments. C. D'Ignazio, A. Satyanarayan, S. Williams </div></div> </div> </div>  </div> </div>  <div id="footer" role="contentinfo"> <div class="wrap"> <div id="footer-links"> <a href="http://mitadmissions.org/apply" target="_blank">Admissions</a><a href="http://sfs.mit.edu/" target="_blank">Financial Aid</a><a href="http://web.mit.edu/registrar/" target="_blank">Registrar</a><a href="http://web.mit.edu/iap/" target="_blank">IAP</a><a href="/summer/">Summer</a><a href="http://professional.mit.edu" target="_blank">Professional Education</a><a href="https://www.edx.org/school/mitx" class="mitx" target="_blank">MITx</a><a href="https://outreach.mit.edu/" target="_blank">K-12</a><a href="http://whereis.mit.edu/" target="_blank">Campus Map</a> <a href="https://officesdirectory.mit.edu/" target="_blank">Directories</a><a href="/about-bulletin/">About the Bulletin</a><a href="/nondiscrimination-policy/">Nondiscrimination Policy</a><a href="/changelog/">Changes</a><a href="/help/">Help</a><a href="https://accessibility.mit.edu/" target="_blank">Accessibility</a> </div> <div id="footer-branding" class="clearfix"> <div class="foot-col" id="right"> <div id="footer-mit-logo"><img src="/images/mit-logo-footer.svg" alt="MIT" width="185px" /></div> </div> <div class="foot-col" id="left"> <div id="footer-bulletin"><img src="/images/mit-bulletin-logo-footer-24-25.png" alt="MIT Academic Bulletin" /></div> <div id="footer-contact">77 Massachusetts Avenue Cambridge, MA 02139-4307</div> </div> </div> </div> <a href="#header" id="totop">Back to top</a> </div>  <div id="print-dialog" class="screen noscript" role="dialog"> <div class="print-header"> Print Options </div> <div class="print-body"> <div class="print-option"> <div class="option-head"> <a href="#" onclick="hidePrintDialog();window.print();return false">Send Page to Printer</a> </div> Print this page. </div> <div class="print-option"><div class="option-head"><a href="6.pdf" target="_blank">Download PDF of this Page</a></div>The PDF includes all information on this page and its related tabs. 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