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class="inline-flex items-center gap-1.5 Breadcrumbs_breadcrumbs__0fm1_ text-primary-foreground capitalize" aria-current="page"><span class="">algebra</span></li></ol></nav><h1 class="text-learn-hero-heading lg:text-learn-hero-heading-large lg:leading-learn-hero-line-height-large mb-6 font-extrabold tracking-tight">Learn algebra with online courses and programs</h1><div class="break-words [&>ul>li>p]:text-white [&>*]:text-white text-xl line-clamp-3"><p class="mb-8">Learn algebra to explore new ways of thinking and build problem-solving skills. Study algebra equations and practice advanced algebra problems with online courses delivered through edX. </p></div></div></div><div class="fullwidth bg-secondary text-primary-foreground p-8 sticky top-0 z-50"><div class="container"><div class="lg:flex hidden text-sm items-center "></div><div class="lg:hidden p-4 w-full"><button type="button" role="combobox" aria-controls="radix-:R2ijjttrkva:" aria-expanded="false" aria-autocomplete="none" dir="ltr" data-state="closed" class="flex h-9 w-full items-center justify-between whitespace-nowrap rounded border border-input bg-transparent px-3 py-2 text-sm shadow-sm ring-offset-background placeholder:text-putty-dark focus:outline-none focus:ring-1 focus:ring-ring disabled:cursor-not-allowed disabled:opacity-50 [&>span]:line-clamp-1 no-underline text-white hover:text-white"><span style="pointer-events:none"></span><svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" class="h-4 w-4 opacity-50" aria-hidden="true"><path d="M4.93179 5.43179C4.75605 5.60753 4.75605 5.89245 4.93179 6.06819C5.10753 6.24392 5.39245 6.24392 5.56819 6.06819L7.49999 4.13638L9.43179 6.06819C9.60753 6.24392 9.89245 6.24392 10.0682 6.06819C10.2439 5.89245 10.2439 5.60753 10.0682 5.43179L7.81819 3.18179C7.73379 3.0974 7.61933 3.04999 7.49999 3.04999C7.38064 3.04999 7.26618 3.0974 7.18179 3.18179L4.93179 5.43179ZM10.0682 9.56819C10.2439 9.39245 10.2439 9.10753 10.0682 8.93179C9.89245 8.75606 9.60753 8.75606 9.43179 8.93179L7.49999 10.8636L5.56819 8.93179C5.39245 8.75606 5.10753 8.75606 4.93179 8.93179C4.75605 9.10753 4.75605 9.39245 4.93179 9.56819L7.18179 11.8182C7.35753 11.9939 7.64245 11.9939 7.81819 11.8182L10.0682 9.56819Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button><select aria-hidden="true" tabindex="-1" style="position:absolute;border:0;width:1px;height:1px;padding:0;margin:-1px;overflow:hidden;clip:rect(0, 0, 0, 0);white-space:nowrap;word-wrap:normal"></select></div></div></div><div class="flex flex-wrap py-12"><div><img loading="lazy" decoding="async" class="hidden lg:block float-right ml-4 mb-4" src="https://images.cdn.edx.org/post745-algebra.png" alt="Algebra | Introduction Image Description" width="435" height="245"/><h2>What is algebra?</h2><p>Algebra is a branch of mathematics that uses letters and symbols to represent numbers in formulas and equations. Mathematicians use algebraic formulas to solve problems and understand how those symbols relate to each other. For example, the Pythagorean Theorem states that a²+b²=c², demonstrating a relationship between the lengths of a triangle’s sides.</p><p></p><p>The origins of algebra can be traced back to ninth-century Palestine. Mathematician Muhammad ibn Musa al-Khwarizmi wrote a book called “Kitab Al-Jabr,” from which the word algebra was derived.<sup><a href="#URJg5T6xvR8T541M889VZ">1</a></sup> The book covers numerous topics including how to solve quadratic equations and how to calculate area and volume.</p><p></p><p>As mathematicians discovered new applications and equations, algebra has expanded into many sub-branches, including:</p><p></p><ul><li><p><b>Elementary algebra:</b> Sometimes referred to as algebra 1, this branch covers basic algebra problems, symbols, and equations. It is the stepping stone for more complex algebraic equations.</p></li><li><p><b>Abstract algebra: </b>Sometimes referred to as modern algebra, this sub-branch includes the study of algebraic structures such as vector spaces and groups.</p></li><li><p><b>Linear algebra: </b>This branch covers linear mappings between vector spaces, as well as the study of planes and lines.</p></li><li><p><b>Commutative algebra:</b> This branch of abstract algebra studies communicative rings and their relation to vector space.</p></li></ul><p></p><p>Algebra is used in a variety of professions, from teaching to accounting to marketing research. Architects, data analysts, and fashion designers rely on algebra in their day-to-day work. Learning algebra can also be helpful in practical situations, such as calculating your average pace during a run, determining the amount of fencing needed for your yard, or comparing the price per unit between two competing products.</p></div></div><div class="fullwidth bg-putty-100"><div class="relative overflow-hidden py-3 bg-putty-light "><div class="container flex flex-col items-center justify-center text-center px-4 md:px-28 py-10 bg-putty-light"><h2 class="text-secondary font-extrabold scroll-m-20 tracking-tight text-3xl lg:text-5xl italic text-7xl font-black font-inter">Maximize Your Potential</h2><p class="md:px-24 py-3 text-base text-center ">Sign up for special offers, career resources, and recommendations that will help you grow, prepare, and advance in your career.</p><div class="flex gap-4"></div></div></div><a class="subnav-item -mt-1" name="Browse online Algebra courses" id="browse-online-algebra-courses"></a><div class="container py-3"><div dir="ltr" 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8.93179C4.75605 9.10753 4.75605 9.39245 4.93179 9.56819L7.18179 11.8182C7.35753 11.9939 7.64245 11.9939 7.81819 11.8182L10.0682 9.56819Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button><select aria-hidden="true" tabindex="-1" style="position:absolute;border:0;width:1px;height:1px;padding:0;margin:-1px;overflow:hidden;clip:rect(0, 0, 0, 0);white-space:nowrap;word-wrap:normal"></select></div><div data-state="active" data-orientation="horizontal" role="tabpanel" aria-labelledby="radix-:Rsjjttrkva:-trigger-Course" id="radix-:Rsjjttrkva:-content-Course" tabindex="0" class="mt-2 ring-offset-background focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2 flex flex-col max-w-[1128px] mx-auto" style="animation-duration:0s"><h3 class="mb-4">Courses</h3><div class="hidden lg:block"><div class="flex gap-4 py-4 flex-wrap undefined"></div></div><div class="lg:hidden"><div class="flex gap-4 py-4 overflow-x-scroll undefined"></div></div><div class="flex justify-center mx-auto mt-5"></div></div><div data-state="inactive" data-orientation="horizontal" role="tabpanel" aria-labelledby="radix-:Rsjjttrkva:-trigger-Executive Education" hidden="" id="radix-:Rsjjttrkva:-content-Executive Education" tabindex="0" class="mt-2 ring-offset-background focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2 flex flex-col max-w-[1128px] mx-auto"></div><div data-state="inactive" data-orientation="horizontal" role="tabpanel" aria-labelledby="radix-:Rsjjttrkva:-trigger-Masters" hidden="" id="radix-:Rsjjttrkva:-content-Masters" tabindex="0" class="mt-2 ring-offset-background focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2 flex flex-col max-w-[1128px] mx-auto"></div><div data-state="inactive" data-orientation="horizontal" role="tabpanel" aria-labelledby="radix-:Rsjjttrkva:-trigger-Bachelors" hidden="" id="radix-:Rsjjttrkva:-content-Bachelors" tabindex="0" class="mt-2 ring-offset-background focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ring focus-visible:ring-offset-2 flex flex-col max-w-[1128px] mx-auto"></div></div></div><div class="pt-0 pb-6 fullwidth bg-putty-100"><h3 class="mb-8 mt-0 text-2xl">Related Topics</h3><div class="flex gap-3 overflow-x-auto scroll-smooth not-prose"></div><div class="pt-4"></div></div><div class="flex flex-col gap-2 pb-10"><div class="Default_content__HO8we"><div id=""><h3>Algebra course curriculum</h3><p>Algebra is an essential aspect of arithmetic and a key part of both high school and some college math curricula. Through introductory and advanced online algebra courses delivered by edX, you can learn basic algebra and abstract algebra. </p><p></p><p>An introductory course in algebra can be a great way to learn algebra 1. These courses cover basics to help learners firmly grasp the foundational elements of algebra. This can be helpful for individuals who want to work toward a career in mathematics or prepare for an MBA program. Solving basic algebra equations and learning how to handle integers, decimals, fractions, exponents, and square roots is integral to understanding algebra. Other important elements of algebra often taught in introductory courses include inverse functions and graphing. </p><p></p><p>A more advanced algebra class or program may teach learners how to apply algebra to a wide range of real-world problems and study critical algebraic concepts like functions, domains, ranges, and linear algebra. Many online algebra tutorials and courses are self-paced so you can enroll and learn on a schedule that works for you.</p></div></div><a class="subnav-item -mt-1" name="Jobs that use algebra" id="jobs-that-use-algebra"></a><div class="Default_content__HO8we"><div id=""><h2>Jobs that use algebra</h2><p>Understanding algebra equations and how to use them can help you stand out in the professional world. In fact, many roles require a working knowledge of algebra to complete day-to-day responsibilities.</p><p></p><p>Accounting and banking are two professions that use algebra on a daily basis. Accountants use algebra to balance spreadsheets, forecast costs, and create business spending reports, while bankers use algebra to calculate interest rates and taxes. Business owners across all fields also use algebra to calculate run rates, revenue, and profit margins.</p><p></p><p>Medical professionals often use algebra to administer drugs, detect pattern irregularities, and fill prescriptions for their patients. Converting different drug doses is relatively common in the medical field, so being able to solve problems using algebra is important. </p><p></p><p>Architects rely on algebra to interpret a building’s height, as well as the width of rooms, hallways, and floors. Civil engineers apply algebraic formulas to calculate how much weight a bridge or road can handle.<sup><a href="#1Ot7qTlObzeQK9X6G3kwwu">2</a></sup> Computer scientists and software engineers frequently employ linear algebra to design algorithms and develop software.<sup><a href="#6MfJtxpqPHpz4V0qHyMdlG">3</a></sup> Many computer functions ranging from from graphic creation to machine learning are also powered by linear algebra concepts. </p><p></p><p>While algebra can be extremely useful in a multitude of professions, knowledge of algebra is not the only requirement to earn a job in one of these fields. If you’re interested in advancing your algebra skills, consider enrolling in a <a class="text-link underline" href="https://www.edx.org/boot-camps">boot camp</a> program, a <a class="text-link underline" href="https://www.edx.org/bachelors/">bachelor’s degree</a> program, or exploring a <a class="text-link underline" href="https://www.edx.org/masters">master’s degree</a>. </p><p></p><h3>How to become a computer scientist online</h3><p>Algebra, specifically linear algebra, is a key concept in computer science. If you enjoy algebra, computer science could be a fitting career path for you. Earning an online <a class="text-link underline" href="https://www.edx.org/bachelors/computer-data-sciences">bachelor's degree in computer science or data science</a> is an excellent way to kickstart a career in computer science. </p><p></p><p>Learning linear algebra is usually a requirement for obtaining a degree in computer science. Aspiring computer scientists may also consider enrolling in an <a class="text-link underline" href="https://www.edx.org/boot-camps/coding">online coding boot camp</a> to gain hands-on experience with the tools used in the field prior to starting a bachelor’s degree. Other required courses typically include information theory, theory of computation, calculus, and coding.</p><p></p><p>Once you have a basic understanding of computer science, and have graduated from a bachelor’s program, you can further your skills with an online <a class="text-link underline" href="https://www.edx.org/masters/data-science">master’s in data science</a>. Within the computer science field, the more experience you have with the tools in the industry, the better. While a master’s degree is not required to land a job in computer science, furthering your education in the field can help you advance your knowledge and become a specialist.</p></div></div></div><div class="fullwidth max-w-none py-12 md:py-16 not-prose bg-primary-gradient"><div class="container"><h2 class="text-4xl md:text-6xl my-5 text-white italic"><span class="text-primary-foreground">More opportunities</span> for you to learn</h2><p class="text-lg leading-9 text-white">We've added 500+ learning opportunities to create one of the world's most comprehensive free-to-degree online learning platforms.</p><ul class="block md:grid md:grid-cols-2 md:gap-x-[100px] mx-auto lg:grid-cols-3"></ul></div></div><a class="subnav-item -mt-1" name="Algebra FAQ" id="algebra-f-a-q"></a><a class="subnav-item" id="frequently-asked-questions"></a><div class="flex flex-col py-4 lg:py-16"><h2 class="mt-2 mb-4 text-3xl font-bold">Frequently Asked Questions</h2><div class="flex flex-col gap-3 [&_button]:no-underline [&_button]:text-gray-dark [&_button:hover]:text-gray-dark" data-orientation="vertical"><div data-state="closed" data-orientation="vertical" class="border-b AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E"><h3 data-orientation="vertical" data-state="closed" class="flex"><button type="button" aria-controls="radix-:Rja4jjttrkva:" aria-expanded="false" data-state="closed" data-orientation="vertical" id="radix-:R3a4jjttrkva:" class="flex flex-1 text-left items-center justify-between py-4 text-sm font-medium transition-all hover:underline [&[data-state=open]>svg]:rotate-180 AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J" data-radix-collection-item="">Can you learn algebra online?<svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" class="h-4 w-4 shrink-0 text-putty-dark transition-transform duration-200"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button></h3><div data-state="closed" id="radix-:Rja4jjttrkva:" hidden="" role="region" aria-labelledby="radix-:R3a4jjttrkva:" data-orientation="vertical" class="overflow-hidden text-sm data-[state=closed]:animate-accordion-up data-[state=open]:animate-accordion-down" style="--radix-accordion-content-height:var(--radix-collapsible-content-height);--radix-accordion-content-width:var(--radix-collapsible-content-width)"></div></div><div data-state="closed" data-orientation="vertical" class="border-b AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E"><h3 data-orientation="vertical" data-state="closed" class="flex"><button type="button" aria-controls="radix-:Rla4jjttrkva:" aria-expanded="false" data-state="closed" data-orientation="vertical" id="radix-:R5a4jjttrkva:" class="flex flex-1 text-left items-center justify-between py-4 text-sm font-medium transition-all hover:underline [&[data-state=open]>svg]:rotate-180 AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J" data-radix-collection-item="">How long does it take to complete a course in algebra? <svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" class="h-4 w-4 shrink-0 text-putty-dark transition-transform duration-200"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button></h3><div data-state="closed" id="radix-:Rla4jjttrkva:" hidden="" role="region" aria-labelledby="radix-:R5a4jjttrkva:" data-orientation="vertical" class="overflow-hidden text-sm data-[state=closed]:animate-accordion-up data-[state=open]:animate-accordion-down" style="--radix-accordion-content-height:var(--radix-collapsible-content-height);--radix-accordion-content-width:var(--radix-collapsible-content-width)"></div></div><div data-state="closed" data-orientation="vertical" class="border-b AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E"><h3 data-orientation="vertical" data-state="closed" class="flex"><button type="button" aria-controls="radix-:Rna4jjttrkva:" aria-expanded="false" data-state="closed" data-orientation="vertical" id="radix-:R7a4jjttrkva:" class="flex flex-1 text-left items-center justify-between py-4 text-sm font-medium transition-all hover:underline [&[data-state=open]>svg]:rotate-180 AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J" data-radix-collection-item="">Where is algebra used?<svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" class="h-4 w-4 shrink-0 text-putty-dark transition-transform duration-200"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button></h3><div data-state="closed" id="radix-:Rna4jjttrkva:" hidden="" role="region" aria-labelledby="radix-:R7a4jjttrkva:" data-orientation="vertical" class="overflow-hidden text-sm data-[state=closed]:animate-accordion-up data-[state=open]:animate-accordion-down" style="--radix-accordion-content-height:var(--radix-collapsible-content-height);--radix-accordion-content-width:var(--radix-collapsible-content-width)"></div></div><div data-state="closed" data-orientation="vertical" class="border-b AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E"><h3 data-orientation="vertical" data-state="closed" class="flex"><button type="button" aria-controls="radix-:Rpa4jjttrkva:" aria-expanded="false" data-state="closed" data-orientation="vertical" id="radix-:R9a4jjttrkva:" class="flex flex-1 text-left items-center justify-between py-4 text-sm font-medium transition-all hover:underline [&[data-state=open]>svg]:rotate-180 AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J" data-radix-collection-item="">What are the different types of algebra?<svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" class="h-4 w-4 shrink-0 text-putty-dark transition-transform duration-200"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button></h3><div data-state="closed" id="radix-:Rpa4jjttrkva:" hidden="" role="region" aria-labelledby="radix-:R9a4jjttrkva:" data-orientation="vertical" class="overflow-hidden text-sm data-[state=closed]:animate-accordion-up data-[state=open]:animate-accordion-down" style="--radix-accordion-content-height:var(--radix-collapsible-content-height);--radix-accordion-content-width:var(--radix-collapsible-content-width)"></div></div><div data-state="closed" data-orientation="vertical" class="border-b AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E"><h3 data-orientation="vertical" data-state="closed" 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AccordionTextItem_trigger__CiZ_J" data-radix-collection-item="">Is algebra hard to learn?<svg width="15" height="15" viewBox="0 0 15 15" fill="none" xmlns="http://www.w3.org/2000/svg" class="h-4 w-4 shrink-0 text-putty-dark transition-transform duration-200"><path d="M3.13523 6.15803C3.3241 5.95657 3.64052 5.94637 3.84197 6.13523L7.5 9.56464L11.158 6.13523C11.3595 5.94637 11.6759 5.95657 11.8648 6.15803C12.0536 6.35949 12.0434 6.67591 11.842 6.86477L7.84197 10.6148C7.64964 10.7951 7.35036 10.7951 7.15803 10.6148L3.15803 6.86477C2.95657 6.67591 2.94637 6.35949 3.13523 6.15803Z" fill="currentColor" fill-rule="evenodd" clip-rule="evenodd"></path></svg></button></h3><div data-state="closed" id="radix-:Rta4jjttrkva:" hidden="" role="region" aria-labelledby="radix-:Rda4jjttrkva:" data-orientation="vertical" class="overflow-hidden text-sm data-[state=closed]:animate-accordion-up data-[state=open]:animate-accordion-down" style="--radix-accordion-content-height:var(--radix-collapsible-content-height);--radix-accordion-content-width:var(--radix-collapsible-content-width)"></div></div></div></div><ol><li id="URJg5T6xvR8T541M889VZ"><p><a class="text-link underline" href="https://www.britannica.com/biography/al-Khwarizmi">al-Khwārizmī</a><i> Encyclopedia Britannica</i>. Retrieved December 13, 2022.</p></li><li id="1Ot7qTlObzeQK9X6G3kwwu"><p><a class="text-link underline" href="https://www.bls.gov/ooh/architecture-and-engineering/civil-engineers.htm#tab-4">How to Become a Civil Engineer</a><i> U.S. Bureau of Labor Statistics Occupational Handbook</i>. Retrieved December 13, 2022.</p></li><li id="6MfJtxpqPHpz4V0qHyMdlG"><p><a class="text-link underline" href="https://www.computersciencedegreehub.com/lists/5-types-of-math-used-in-computer-science/#:~:text=Algebra%20is%20used%20in%20computer,and%20for%20complete%20scientific%20computations">5 Types of Math Used in Computer Science</a><i> Computer Science Degree Hub. </i>Retrieved December 6, 2022.</p></li></ol></div></article></main></div><div class="bg-primary text-primary-foreground pt-16"><footer class="flex justify-between max-w-screen-xl mx-auto px-4 pb-4 "><div class="flex flex-col w-full"><div class="flex flex-wrap justify-between mb-6 w-full"><a href="/" class="mb-6"><img alt="edX homepage" data-ot-ignore="true" loading="lazy" width="127" height="67" decoding="async" data-nimg="1" class="optanon-category-C0001" style="color:transparent" src="/trademark-logos/edx-by-2u-white.svg"/></a><div><div class="flex gap-6 mb-4 items-center justify-center align-middle"><a 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Through introductory and advanced online algebra courses delivered by edX, you can learn basic algebra and abstract algebra. \"}],[\"$\",\"p\",\"2\",{\"children\":\"$undefined\"}],[\"$\",\"p\",\"3\",{\"children\":\"An introductory course in algebra can be a great way to learn algebra 1. These courses cover basics to help learners firmly grasp the foundational elements of algebra. This can be helpful for individuals who want to work toward a career in mathematics or prepare for an MBA program. Solving basic algebra equations and learning how to handle integers, decimals, fractions, exponents, and square roots is integral to understanding algebra. Other important elements of algebra often taught in introductory courses include inverse functions and graphing. \"}],[\"$\",\"p\",\"4\",{\"children\":\"$undefined\"}],[\"$\",\"p\",\"5\",{\"children\":\"A more advanced algebra class or program may teach learners how to apply algebra to a wide range of real-world problems and study critical algebraic concepts like functions, domains, ranges, and linear algebra. Many online algebra tutorials and courses are self-paced so you can enroll and learn on a schedule that works for you.\"}]]}]}],[\"$\",\"a\",\"1\",{\"className\":\"subnav-item -mt-1\",\"name\":\"Jobs that use algebra\",\"id\":\"jobs-that-use-algebra\",\"children\":\"$undefined\"}],[\"$\",\"div\",null,{\"className\":\"Default_content__HO8we\",\"children\":[\"$\",\"div\",null,{\"id\":\"\",\"children\":[[\"$\",\"h2\",\"0\",{\"children\":\"Jobs that use algebra\"}],[\"$\",\"p\",\"1\",{\"children\":\"Understanding algebra equations and how to use them can help you stand out in the professional world. In fact, many roles require a working knowledge of algebra to complete day-to-day responsibilities.\"}],[\"$\",\"p\",\"2\",{\"children\":\"$undefined\"}],[\"$\",\"p\",\"3\",{\"children\":\"Accounting and banking are two professions that use algebra on a daily basis. 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Other required courses typically include information theory, theory of computation, calculus, and coding.\"]}],[\"$\",\"p\",\"15\",{\"children\":\"$undefined\"}],[\"$\",\"p\",\"16\",{\"children\":[\"Once you have a basic understanding of computer science, and have graduated from a bachelor’s program, you can further your skills with an online \",[\"$\",\"a\",\"1\",{\"className\":\"text-link underline\",\"href\":\"https://www.edx.org/masters/data-science\",\"children\":\"master’s in data science\"}],\". Within the computer science field, the more experience you have with the tools in the industry, the better. While a master’s degree is not required to land a job in computer science, furthering your education in the field can help you advance your knowledge and become a specialist.\"]}]]}]}]]}],[\"$\",\"$L2cc\",null,{\"theme\":\"gradient\",\"children\":[]}],[\"$\",\"a\",\"6\",{\"className\":\"subnav-item -mt-1\",\"name\":\"Algebra FAQ\",\"id\":\"algebra-f-a-q\",\"children\":\"$undefined\"}],[[\"$\",\"a\",null,{\"className\":\"subnav-item\",\"id\":\"frequently-asked-questions\"}],[\"$\",\"div\",null,{\"className\":\"flex flex-col py-4 lg:py-16\",\"children\":[[\"$\",\"h2\",null,{\"className\":\"mt-2 mb-4 text-3xl font-bold\",\"children\":\"Frequently Asked Questions\"}],[\"$\",\"$L2cd\",null,{\"type\":\"single\",\"collapsible\":true,\"className\":\"flex flex-col gap-3 [\u0026_button]:no-underline [\u0026_button]:text-gray-dark [\u0026_button:hover]:text-gray-dark\",\"children\":[[\"$\",\"$L2ce\",null,{\"value\":\"Can you learn algebra online?\",\"className\":\"AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E\",\"children\":[[\"$\",\"$L2cf\",null,{\"className\":\"AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J\",\"children\":\"Can you learn algebra online?\"}],[\"$\",\"$L2d0\",null,{\"className\":\"AccordionTextItem_content__G0vl3 AccordionTextItem_content__G0vl3\",\"children\":[\"$\",\"p\",null,{\"children\":\"It is possible to learn algebra through online algebra courses. Beginners should consider taking an introductory algebra course first to gain a thorough understanding of the foundational elements of algebra. More advanced online algebra courses cover topics such as linear algebra and complex algebraic equations.\"}]}]]}],[\"$\",\"$L2ce\",null,{\"value\":\"How long does it take to complete a course in algebra? \",\"className\":\"AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E\",\"children\":[[\"$\",\"$L2cf\",null,{\"className\":\"AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J\",\"children\":\"How long does it take to complete a course in algebra? \"}],[\"$\",\"$L2d0\",null,{\"className\":\"AccordionTextItem_content__G0vl3 AccordionTextItem_content__G0vl3\",\"children\":[\"$\",\"p\",null,{\"children\":\"The lengths of online courses vary depending on the specific class and topic. Some courses are as short as four weeks, while others last over multiple months. There are also self-guided online algebra courses, meaning their duration depends on each individual learner. \"}]}]]}],[\"$\",\"$L2ce\",null,{\"value\":\"Where is algebra used?\",\"className\":\"AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E\",\"children\":[[\"$\",\"$L2cf\",null,{\"className\":\"AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J\",\"children\":\"Where is algebra used?\"}],[\"$\",\"$L2d0\",null,{\"className\":\"AccordionTextItem_content__G0vl3 AccordionTextItem_content__G0vl3\",\"children\":[\"$\",\"p\",null,{\"children\":\"Algebra is used in many professions and can be applied to a variety of industries. From computer science and software development to marketing research and accounting, various professions use algebra on a daily basis.\"}]}]]}],[\"$\",\"$L2ce\",null,{\"value\":\"What are the different types of algebra?\",\"className\":\"AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E\",\"children\":[[\"$\",\"$L2cf\",null,{\"className\":\"AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J\",\"children\":\"What are the different types of algebra?\"}],[\"$\",\"$L2d0\",null,{\"className\":\"AccordionTextItem_content__G0vl3 AccordionTextItem_content__G0vl3\",\"children\":[\"$\",\"p\",null,{\"children\":\"The different types of algebra include elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra. Elementary algebra deals with basic algebra problems such as solving inequalities and graphing equations, whereas advanced algebra and abstract algebra cover more complex topics such as exponential and logarithmic equations. Linear algebra is a type of algebra that deals with vector spaces, lines, and planes. \"}]}]]}],[\"$\",\"$L2ce\",null,{\"value\":\"What are the basics of algebra?\",\"className\":\"AccordionTextItem_item__adF2E AccordionTextItem_item__adF2E\",\"children\":[[\"$\",\"$L2cf\",null,{\"className\":\"AccordionTextItem_trigger__CiZ_J AccordionTextItem_trigger__CiZ_J\",\"children\":\"What are the basics of algebra?\"}],[\"$\",\"$L2d0\",null,{\"className\":\"AccordionTextItem_content__G0vl3 AccordionTextItem_content__G0vl3\",\"children\":[\"$\",\"p\",null,{\"children\":\"The basic elements of algebra include numbers, variables, constants, expressions, equations, linear equations, and quadratic equations. In algebra equations, variables are unknown numbers represented by placeholder symbols, while constants are fixed numbers. Expressions are made up of variables and constants, and equations are made up of two expressions connected by an equal sign. 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The more time you spend practicing basic algebra equations and interpreting algebra formulas, the more skilled you will be. \"}]}]]}]]}]]}]],[\"$\",\"ol\",\"8\",{\"children\":[[\"$\",\"li\",\"0\",{\"id\":\"URJg5T6xvR8T541M889VZ\",\"children\":[\"$\",\"p\",null,{\"children\":[[\"$\",\"a\",\"0\",{\"className\":\"text-link underline\",\"href\":\"https://www.britannica.com/biography/al-Khwarizmi\",\"children\":\"al-Khwārizmī\"}],[\"$\",\"i\",\"1\",{\"children\":\" Encyclopedia Britannica\"}],\". Retrieved December 13, 2022.\"]}]}],[\"$\",\"li\",\"1\",{\"id\":\"1Ot7qTlObzeQK9X6G3kwwu\",\"children\":[\"$\",\"p\",null,{\"children\":[[\"$\",\"a\",\"0\",{\"className\":\"text-link underline\",\"href\":\"https://www.bls.gov/ooh/architecture-and-engineering/civil-engineers.htm#tab-4\",\"children\":\"How to Become a Civil Engineer\"}],[\"$\",\"i\",\"1\",{\"children\":\" U.S. Bureau of Labor Statistics Occupational Handbook\"}],\". Retrieved December 13, 2022.\"]}]}],[\"$\",\"li\",\"2\",{\"id\":\"6MfJtxpqPHpz4V0qHyMdlG\",\"children\":[\"$\",\"p\",null,{\"children\":[[\"$\",\"a\",\"0\",{\"className\":\"text-link underline\",\"href\":\"https://www.computersciencedegreehub.com/lists/5-types-of-math-used-in-computer-science/#:~:text=Algebra%20is%20used%20in%20computer,and%20for%20complete%20scientific%20computations\",\"children\":\"5 Types of Math Used in Computer Science\"}],[\"$\",\"i\",\"1\",{\"children\":\" Computer Science Degree Hub. \"}],\"Retrieved December 6, 2022.\"]}]}]]}]]}]]}]}]]}],[\"$\",\"div\",null,{\"className\":\"bg-primary text-primary-foreground pt-16\",\"children\":[\"$\",\"footer\",null,{\"className\":\"flex justify-between max-w-screen-xl mx-auto px-4 pb-4 \",\"children\":[\"$\",\"div\",null,{\"className\":\"flex flex-col w-full\",\"children\":[[\"$\",\"div\",null,{\"className\":\"flex flex-wrap justify-between mb-6 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You’ll also be encouraged to consider how what you know fits into the wider mathematical world.\u003c/p\u003e2f1:T483,\u003cul\u003e\n\u003cli\u003e\u003cstrong\u003eImprove\u003c/strong\u003e fluency and accuracy when using laws of indices and surds in a variety of calculations\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eLearn\u003c/strong\u003e how to solve the types of inequalities you'll encounter at A-level and various ways to represent these\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eDiscover\u003c/strong\u003e how to divide any polynomial by either a linear or quadratic polynomial\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eLearn\u003c/strong\u003e about the information found in different forms of the Cartesian equation of a circle and use these to solve coordinate geometry problems\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eInvestigate\u003c/strong\u003e the main transformations of graphs; translation, enlargement and reflection, and use these transformations to sketch new graphs\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eUnderstand\u003c/strong\u003e the constant acceleration formulae through travel graphs illustration, speed, velocity, distance and displacement against time\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eExplore\u003c/strong\u003e statistical sampling methods and weigh up the advantages and disadvantages of each one\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eLearn\u003c/strong\u003e how to interpret data presented in a variety of forms including box plots, cumulative frequency curves, histograms and bar charts\u003c/li\u003e\n\u003c/ul\u003e2f2:T534,\u003cp\u003eWe live in a world of numbers. You see them every day: on clocks, in the stock market, in sports, and all over the news. Algebra is all about figuring out the numbers you \u003cem\u003edon't\u003c/em\u003e see. You might know how fast you can throw a ball, but can you use this number to determine how \u003cem\u003efar\u003c/em\u003e you can throw it? You might keep track of stock prices, but how can you figure out how much money you've made (or lost) in the market? And you may already know how to tell time, but can you calculate at what times a clock's hour and minute hands are \u003cem\u003eexactly\u003c/em\u003e aligned? With algebra, you can answer all of these questions, using"])</script><script>self.__next_f.push([1," the numbers you already know to solve for the \u003cem\u003eunknown\u003c/em\u003e. Algebra is an essential tool for all of high school and college-level math, science, and engineering. So if you're starting out in one of these fields and you haven't yet mastered algebra, then this is the course for you! \u003c/p\u003e\n\u003cp\u003eIn this course, you'll be able to choose your own path within each lesson, and you can jump between lessons to quickly review earlier material. AlgebraX covers a standard curriculum in high school Algebra I, and CCSS (common core) alignment is indicated where applicable.\u003ca href=\"https://www.edx.org/high-school-initiative\"\u003e\u003c/p\u003e\n\u003cp\u003eLearn more about our High School and AP* Exam Preparation Courses\u003c/a\u003e\u003c/p\u003e2f3:T4cc,\u003cp\u003eLinear algebra is at the core of all of modern mathematics, and is used everywhere from statistics and data science, to economics, physics and electrical engineering. However, learning the subject is not principally about acquiring computational ability, but is more a matter of fluency in its language and theory.\u003c/p\u003e\n\u003cp\u003eIn this course, we will start with systems of linear equations, and connect them to vectors and vector spaces, matrices, and linear transformations. We will be emphasizing the vocabulary throughout, so that students become comfortable working with the different aspects.\u003c/p\u003e\n\u003cp\u003eWe will then introduce matrix and vector operations such as matrix multiplication and inverses, paying particular attention to their underlying purposes. Students will learn not just how to calculate them, but also why they work the way that they do.\u003c/p\u003e\n\u003cp\u003eWe willdiscuss the key concepts of basis and dimension, which form the foundation for many of the more advanced concepts of linear algebra.\u003c/p\u003e\n\u003cp\u003eThe last chapter concerns inner products, which allow us to use linear algebra for approximating solutions; we will see how this allows for applications ranging from statistics and linear regression to digital audio.\u003c/p\u003e2f4:T5ae,\u003cp\u003eThis course is part of \u003ca href=\"https://www.edx.org/gfa\"\u003eGlobal Freshman Academy (GFA)\u003c/a\u003e, which m"])</script><script>self.__next_f.push([1,"eans you can earn transferable ASU credit toward your college degree.\u003c/p\u003e\n\u003cp\u003eIn this college level Algebra course, you will learn to apply algebraic reasoning to solve problems effectively. You’ll develop skills in linear and quadratic functions, general polynomial functions, rational functions, and exponential and logarithmic functions. You will also study systems of linear equations. This course will emphasize problem-solving techniques, specifically by means of discussing concepts in each of these topics.\u003c/p\u003e\n\u003cp\u003eContent in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.\u003c/p\u003e\n\u003cp\u003eThis is a 3-credit hour course at Arizona State University (MAT 117 College Algebra) and satisfies the Mathematical Studies (MA) general studies requirement. The cost to convert to credit is $600. This course may satisfy a general education requirement at other institutions; however, it is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring the credit.\u003c/p\u003e2f5:T6ae,\u003cp\u003eLinear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIt's visual.\u003c/li\u003e\n\u003cli\u003eIt connects hand calculations, mathematical abstractions, and computer programming.\u003c/li\u003e\n\u003cli\u003eIt illustrates the development of mathematical theory.\u003c/li\u003e\n\u003cli\u003eIt's applicable.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIn this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get mo"])</script><script>self.__next_f.push([1,"re! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.\u003c/p\u003e\n\u003cp\u003eMATLAB licenses will be made available to the participants free of charge for the duration of the course. \u003c/p\u003e\n\u003cp\u003eTo see what former learners have to say about the course, read reviews on \u003ca href=\"https://www.coursetalk.com/providers/edx/courses/linear-algebra-foundations-to-frontiers-2?page=1\u0026sort=-created_at%23incourse-reviews\"\u003ecoursetalk\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eWe invite you to LAFF with us!\u003c/p\u003e2f6:T782,\u003cp\u003eA strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.\u003c/p\u003e\n\u003cp\u003eIn many engineering master’s programs, you need to be familiar with linear algebra. This course will enable you to review the relevant topics.\u003c/p\u003e\n\u003cp\u003eThis course focuses on vectors (from both algebraic and geometric perspectives) and solving linear equations. It will help you refresh your knowledge, test your skills and review the relations between the many concepts in linear algebra.\u003c/p\u003e\n\u003cp\u003eThe linear algebra courses within this series will offer you an overview of this branch of mathematics common to most engineering bachelor’s programs. They provide enough depth to cover the linear algebra you need to succeed in your engineering master’s or profession in areas su"])</script><script>self.__next_f.push([1,"ch as computer graphics, systems and control, machine learning, quantum computing and more.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThis is a review course\u003c/strong\u003e\u003cbr /\u003e\nThis self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.\u003c/p\u003e\n\u003cp\u003eThis format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises and receive intelligent, personal and immediate feedback.\u003c/p\u003e\n\u003cp\u003eThis course is part of our series \u003cstrong\u003eMastering Mathematics for Engineers\u003c/strong\u003e , and together with the course Linear Algebra II part of the program \u003cstrong\u003eMastering Linear Algebra\u003c/strong\u003e.\u003c/p\u003e2f7:T487,\u003cp\u003eUpon completion of this course, learners will be able to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eApply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.\u003c/li\u003e\n\u003cli\u003eApply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.\u003c/li\u003e\n\u003cli\u003eCharacterize the invertibility of a matrix using the Invertible Matrix Theorem.\u003c/li\u003e\n\u003cli\u003eApply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.\u003c/li\u003e\n\u003cli\u003eCompute an LU factorization of a matrix and apply the LU factorization to solve systems of equations.\u003c/li\u003e\n\u003cli\u003eApply matrix algebra and inverses to solve and analyze Leontif Input-Output problems.\u003c/li\u003e\n\u003cli\u003eConstruct transformation matrices to represent composite transforms in 2D and 3D using homogeneous coordinates.\u003c/li\u003e\n\u003cli\u003eConstruct a basis for a subspace.\u003c/li\u003e\n\u003cli\u003eCalculate the coordinates of a vector in a given basis.\u003c/li\u003e\n\u003cli\u003eCharacterize a matrix using the concepts of rank, column space, and null space.\u003c/li\u003e\n\u003cli\u003eApply the Rank, Basis, and Matrix Invertibility theorems to describe matrices, subspace"])</script><script>self.__next_f.push([1,"s, and systems.\u003c/li\u003e\n\u003c/ul\u003e2f8:T453,\u003cp\u003eAt the beginning of this course we introduce the determinant, which yields two important concepts that you will use in this course. First, you will be able to apply an invertibility criterion for a square matrix that plays a pivotal role in, for example, the understanding of eigenvalues. You will also use the determinant to measure the amount by which a linear transformation changes the area of a region. This idea plays a critical role in computer graphics and in other more advanced courses, such as multivariable calculus. \u003c/p\u003e\n\u003cp\u003eThis course then moves on to eigenvalues and eigenvectors. The goal of this part of the course is to decompose the action of a linear transformation that may be visualized. The main applications described here are to discrete dynamical systems, including Markov chains. However, the basic concepts— eigenvectors and eigenvalues—are useful throughout industry, science, engineering and mathematics. \u003c/p\u003e\n\u003cp\u003eProspective students enrolling in this class are encouraged to first complete the linear equations and matrix algebra courses before starting this class.\u003c/p\u003e2f9:T486,\u003cp\u003eUpon completion of this course, learners will be able to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCompute determinants of using cofactor expansions and properties of determinants\u003c/li\u003e\n\u003cli\u003eCompute the area of regions in R^3 under a given linear transformation using determinants\u003c/li\u003e\n\u003cli\u003eModel and solve real-world problems using Markov chains\u003c/li\u003e\n\u003cli\u003eVerify that a given vector is an eigenvector of a matrix\u003c/li\u003e\n\u003cli\u003eVerify that a scalar is an eigenvalue of a matrix\u003c/li\u003e\n\u003cli\u003eConstruct an eigenspace for a matrix\u003c/li\u003e\n\u003cli\u003eCharacterize the invertibility of a matrix using determinants and eigenvalues\u003c/li\u003e\n\u003cli\u003eApply theorems related to eigenvalues (for example, to characterize the invertibility of a matrix)\u003c/li\u003e\n\u003cli\u003eFactorize 2 × 2 matrices that have complex eigenvalues\u003c/li\u003e\n\u003cli\u003eUse eigenvalues to determine identify the rotation and dilation of a linear transform\u003c/li\u003e\n\u003cli\u003eApply theorems to characterize matrices wit"])</script><script>self.__next_f.push([1,"h complex eigenvalues\u003c/li\u003e\n\u003cli\u003eApply matrix powers and theorems to characterize the long-term behavior of a Markov chain\u003c/li\u003e\n\u003cli\u003eConstruct a transition matrix, a Markov Chain, and a Google Matrix for a given web, and compute the PageRank of the web.\u003c/li\u003e\n\u003c/ul\u003e2fa:T523,\u003cp\u003eIn the first part of this course you will explore methods to compute an approximate solution to an inconsistent system of equations that have no solutions. Our overall approach is to center our algorithms on the concept of distance. To this end, you will first tackle the ideas of distance and orthogonality in a vector space. You will then apply orthogonality to identify the point within a subspace that is nearest to a point outside of it. This has a central role in the understanding of solutions to inconsistent systems. By taking the subspace to be the column space of a matrix, you will develop a method for producing approximate (“least-squares”) solutions for inconsistent systems. \u003c/p\u003e\n\u003cp\u003eYou will then explore another application of orthogonal projections: creating a matrix factorization widely used in practical applications of linear algebra. The remaining sections examine some of the many least-squares problems that arise in applications, including the least squares procedure with more general polynomials and functions. \u003c/p\u003e\n\u003cp\u003eThis course then turns to symmetric matrices. arise more often in applications, in one way or another, than any other major class of matrices. You will construct the diagonalization of a symmetric matrix, which gives a basis for the remainder of the course.\u003c/p\u003e2fb:T500,\u003cp\u003eUpon completion of this course, learners will be able to:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCompute dot product of two vectors, length of a vector, distance between points, and angles between vectors\u003c/li\u003e\n\u003cli\u003eApply theorems related to orthogonal complements, and their relationships to Row and Null\u003cbr /\u003e\nspace, to characterize vectors and linear systems\u003c/li\u003e\n\u003cli\u003eCompute orthogonal projections and distances to express a vector as a linear combination of orthogonal vecto"])</script><script>self.__next_f.push([1,"rs, construct vector approximations using projections, and characterize bases for subspaces, and construct orthonormal bases\u003c/li\u003e\n\u003cli\u003eApply the iterative Gram Schmidt Process, and the QR decomposition, to construct an orthogonal basis\u003c/li\u003e\n\u003cli\u003eConstruct the QR factorization of a matrix\u003c/li\u003e\n\u003cli\u003eCharacterize properties of a matrix using its QR decomposition\u003c/li\u003e\n\u003cli\u003eCompute general solutions and least squares errors to least squares problems using the normal\u003cbr /\u003e\nequations and the QR decomposition\u003c/li\u003e\n\u003cli\u003eApply least-squares and multiple regression to construct a linear model from a set of data\u003cbr /\u003e\npoints\u003c/li\u003e\n\u003cli\u003eApply least-squares to fit polynomials and other curves to data\u003c/li\u003e\n\u003cli\u003eConstruct an orthogonal diagonalization of a symmetric matrix\u003c/li\u003e\n\u003cli\u003eConstruct a spectral decomposition of a matrix\u003c/li\u003e\n\u003c/ul\u003e2fc:T70c,\u003cp\u003eA strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.\u003c/p\u003e\n\u003cp\u003eIn many engineering master’s programs, you need to be familiar with linear algebra. This course will enable you to review the relevant topics.\u003c/p\u003e\n\u003cp\u003eThis course focuses on matrices and linear transformations. Topics covered include matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization and singular value decomposition. The course will help you refresh your knowledge, test your skills and review the relations between the many concepts in linear algebra.\u003c/p\u003e\n\u003cp\u003eThe linear algebra courses within this series will offer you an overview of this branch of mathematics common to most engineering bachelor’s programs. They provide enough depth to cover the linear algebra you need to succeed in your engineering master’s/profession in areas such as computer graphics, systems and control, machine learning, quantum computing and more.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTh"])</script><script>self.__next_f.push([1,"is is a review course\u003c/strong\u003e\u003cbr /\u003e\nThis self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.\u003c/p\u003e\n\u003cp\u003eThis format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises and receive intelligent, personal and immediate feedback.\u003c/p\u003e2fd:T996,"])</script><script>self.__next_f.push([1,"\u003cp\u003eMatrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory online course in data analysis, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units. We perform statistical inference on these differences. Throughout the course we will use the R programming language to perform matrix operations.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. You will need to know some basic stats for this course. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"2fe:T57e,\u003cp\u003eThe first of the two courses will introduce systems of equations, which live at the heart of linear algebra. In this course you will explore fundamental concepts by exploring definitions and theorems that give a basis for this subject. You will apply an algorithm for solving linear systems that will be used for computations and for gaining insight into the properties of linear systems. This insight will all you to reduce problems involving linear combinations of vectors to approaches that involve systems of linear equations. You will also explore linear independence and linear transformations. They have an essential role throughout applications of linear algebra in many areas of industry, science, and engineering.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the second of these two courses you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept. You will then explore theorems and algorithms that will allow you to apply linear algebra in ways that involve two or more matrices. You will examine partitioned matrices and matrix factorizations, which appear in most modern uses of linear algebra. You will also explore two applications of matrix algebra, to economics and to computer graphics.\u003c/p\u003e2ff:T930,"])</script><script>self.__next_f.push([1,"\u003cp\u003eWhether you want to make a strong start to a master’s degree, solidify your knowledge in a professional context or simply brush up on fundamentals in linear algebra, this program will get you up to speed.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program will enable you to review the relevant topics and offer you an overview of the linear algebra common in most engineering bachelor programs.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe courses in this program provide enough depth to cover the linear algebra you need to succeed in your engineering master’s or professional work in areas such as computer graphics, systems and control, machine learning, quantum computing and more.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the first course you will review all the basic concepts and practice and refresh the skills related to vectors and linear equations. The course focuses on vectors (from both algebraic and geometric perspectives) and solving linear equations.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe second course will review all the basic concepts and practice and refresh the skills related to matrices and linear transformations. Topics covered include matrix algebra, determinants, eigenvalues and eigenvectors, diagonalization and singular value decomposition.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese courses are self-paced, self-contained and modular, to make it easier to review specific topics and practice as often as you want without having to follow the entire courses.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program is ideal for:\r\n\u003cul\u003e\r\n\u003cli\u003eProspective engineering students who want to meet the prerequisites for a MSc program, be better prepared or refresh their mathematics knowledge before starting a master’s degree.\u003c/li\u003e\r\n\u003cli\u003eEngineering or bachelor students who realize that they have a gap in their math knowledge or would like an additional challenge in mathematics not offered by their studies.\u003c/li\u003e\r\n\u003cli\u003eWorking professionals who would like to improve their math knowledge.\u003c/li\u003e\r\n\u003cli\u003eAnyone interested in university level mathematics.\u003c/li\u003e\r\n\u003c/ul\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program will refresh your knowledge, test your skills and review the relations between the various concepts in linear algebra. As review courses, you are expected to have previously studied or be familiar with most of the material.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program is part of our series ‘Mastering Mathematics for Engineers’, together with ‘Mastering Calculus’ and ‘Mastering Probability and Statistics’.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"300:T53f,\u003cp\u003eThis certificate program will take students through roughly seven weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.\u003c/p\u003e \r\n\r\n\u003cp\u003eIn the first course, you will explore the determinant, which yields two important results. First, you will be able to apply an invertibility criterion for a square matrix that plays a pivotal role in, for example, computer graphics and in other more advanced courses, such as multivariable calculus. The first course then moves on to eigenvalues and eigenvectors. The goal of this part of the course is to decompose the action of a linear transformation that may be visualized. The main applications described here are to discrete dynamical systems, including Markov chains. However, the basic concepts afforded by eigenvectors and eigenvalues are useful throughout industry, science, engineering and mathematics.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the second course you will explore methods to compute an approximate solution to an inconsistent system of equations that have no solutions. This has a central role in the understanding of current data science applications. The second course then turns to symmetric matrices. They arise often in applications of the singular value decomposition, which is another tool often found in data science and machine learning.\u003c/p\u003e301:T83d,"])</script><script>self.__next_f.push([1,"\u003cp\u003eEl álgebra es una de las ramas más importantes y bellas de la matemática ya que nos provee de un lenguaje simple que nos permite describir muchos de los fenómenos del mundo que nos rodea. Por ejemplo, una ecuación con 3 “letras” fue suficiente para que Einstein plasmara la teoría de la relatividad especial sin la cual no comprenderíamos varios aspectos del universo en el que vivimos. Por otro lado, dominar a plenitud el álgebra es fundamental para poder estudiar tópicos más avanzados en matemática como trigonometría, geometría, cálculo y estadística; cursos requeridos en cualquier carrera profesional en áreas STEM. De allí la importancia de contar con un sólido conocimiento de álgebra elemental, tópico central de este programa.\u003c/p\u003e\r\n\r\n\u003cp\u003ePara poder estudiar el lenguaje algebraico y sobre todo para comprenderlo a fondo es necesario sembrar bien los pilares que le sostienen. Es por ello que, en esta secuencia de cursos, iniciarás por repasar y consolidar las nociones fundamentales de la aritmética en los números reales. En el segundo curso, aprenderás el concepto de expresión algebraica y a realizar operaciones fundamentales entre ellas. Finalmente, en el tercer curso, aprenderás a modelar y resolver problemas de aplicación\r\nen diversos contextos utilizando ecuaciones y desigualdades.\u003c/p\u003e\r\n\r\n\u003cp\u003eEn cada curso te encontrarás con una gran cantidad de ejemplos resueltos y por supuesto con una amplia gama de problemas, ejercicios y retos que te ayudarán no solo a comprender el tema en cuestión sino también a medir tu progreso semanal. A pesar de ser un programa introductorio, cada uno de los temas se desarrolla con el rigor matemático necesario para fundamentar los resultados y herramientas a aplicar, para que así comprendas lo que estás haciendo y diste de un enfoque memorístico sin sentido. De esta manera, este programa te llevará paso a paso en el estudio del álgebra y desarrollará en ti las competencias necesarias para estudiar tópicos más avanzados en matemática, fortaleciendo a la vez tu pensamiento lógico y estructurado.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"302:T8c0,"])</script><script>self.__next_f.push([1,"\u003cp\u003e\u003cstrong\u003eAbout the Database Series of Courses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\"Databases\" was one of Stanford's three inaugural massive open online courses in the fall of 2011. It has been offered in synchronous and then in self-paced versions on a variety of platforms continuously since 2011. The material is now being offered as a set of five self-paced courses, which can be taken in a variety of ways to learn about different aspects of databases. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRelational Databases and SQL\u003c/em\u003e is the most popular course in the Databases series. It is applicable to learners seeking to gain a strong understanding of relational databases, and to master SQL, the long-accepted standard query language for relational database systems. Additional courses focus on advanced concepts in relational databases and SQL, formal foundations and database design methodologies, and semistructured data.\u003c/p\u003e\n\u003cp\u003eAll of the courses are based around video lectures and demos. Many of them include quizzes between video segments to check understanding, in-depth standalone quizzes, and/or a variety of automatically-checked interactive exercises. Each course also includes an unmoderated discussion forum and pointers to readings and resources. The courses are described briefly below. Taught by Professor Jennifer Widom, the overall curriculum draws from Stanford's popular longstanding Databases course.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhy Learn About Databases\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDatabases are incredibly prevalent -- they underlie technology used by most people every day if not every hour. Databases reside behind a huge number of websites; they're a crucial component of telecommunications systems, banking systems, video games, and just about any other software system or electronic device that maintains some amount of persistent information. In addition to persistence, database systems provide a number of other properties that make them exceptionally useful and convenient: reliability, efficiency, scalability, concurrency control, data abstractions, and high-level query languages. Databases are so ubiquitous and important that computer science graduates frequently cite their database class as the one most useful to them in their industry or graduate-school careers.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"303:T4f2,\u003cp\u003eThis course is one of five self-paced courses on the topic of Databases, originating as one of Stanford's three inaugural massive open online courses released in the fall of 2011. The original \"Databases\" courses are now all available on edx.org.\u003c/p\u003e\n\u003cp\u003eThis course covers underlying principles and design considerations related to databases; it can be taken either before or after taking other courses in the Databases series.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe Relational Algebra section of this course teaches the algebraic query language that provides the formal foundations of SQL.\u003c/li\u003e\n\u003cli\u003eThe Relational Design Theory section of the course provides comprehensive coverage of dependency theory and normal forms in relational databases, a well-accepted theoretical framework for developing good relational database schemas.\u003c/li\u003e\n\u003cli\u003eThe Unified Modeling Language section of this course introduces the data-modeling component of UML, and describes how UML diagrams are translated to relational database schemas.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe introductory videos in this course are the same as the introductory videos in \u003cem\u003eDatabases: Relational Databases and SQL\u003c/em\u003e ; they are included for the benefit of learners who have not taken \u003cem\u003eDatabases: Relational Databases and SQL\u003c/em\u003e.\u003c/p\u003e304:T805,"])</script><script>self.__next_f.push([1,"\u003cp\u003eStanford's online offering in Databases is now available as a set of five self-paced courses:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Relational Databases and SQL\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to the relational model and concepts in relational databases and relational database management systems\u003c/li\u003e\n\u003cli\u003eComprehensive coverage of SQL, the long-accepted standard query language for relational database management systems\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Advanced Topics in SQL (prerequisite: Relational Databases and SQL)\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCreating indexes for increased query performance\u003c/li\u003e\n\u003cli\u003eUsing transactions for concurrency control and failure recovery\u003c/li\u003e\n\u003cli\u003eDatabase constraints: key, referential integrity, and \"check\" constraints\u003c/li\u003e\n\u003cli\u003eDatabase triggers\u003c/li\u003e\n\u003cli\u003eHow views are created, used, and updated in relational databases\u003c/li\u003e\n\u003cli\u003eAuthorization in relational databases\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: OLAP and Recursion\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eStar schemas, the data cube concept, and On-Line Analytical Processing (OLAP) features in relational databases including the Cube and Rollup operators\u003c/li\u003e\n\u003cli\u003eThe SQL standard for queries over recursively-defined relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Modeling and Theory\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eRelational algebra – the algebraic query language that provides the formal foundations of SQL\u003c/li\u003e\n\u003cli\u003eDependency theory and normal forms in relational databases as the basis of schema design\u003c/li\u003e\n\u003cli\u003eThe data-modeling component of the Unified Modeling Language (UML), how UML diagrams are translated to relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Semistructured Data\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe XML model for semistructured and self-describing data, including DTDs and some features of XML Schema\u003c/li\u003e\n\u003cli\u003eThe JSON model for human-readable structured or semistructured data\u003c/li\u003e\n\u003cli\u003eThe XPath language for processing XML data, and many features of the more advanced XQuery language\u003c/li\u003e\n\u003cli\u003eAn introduction to the XSLT rule-based language for querying and transforming XML data\u003c/li\u003e\n\u003c/ul\u003e"])</script><script>self.__next_f.push([1,"305:T657,\u003cp\u003e\u003cspan lang=\"ES\"\u003eEn este curso de 4 módulos, desarrollarás competencias básicas para el cálculo identificando elementos de diferentes sistemas numéricos, obtendrás habilidades en el manejo de las operaciones básicas, el manejo de signos y resolviendo problemas que involucran la solución de ecuaciones de primer grado. También identificarás elementos de diferentes sistemas numéricos y el manejo de las operaciones básicas y de signos, y resolverás problemas que involucran la solución de ecuaciones de primer grado. \u003c/span\u003e\u003cspan lang=\"ES\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eEste curso, también te permitirá desarrollar competencias para resolver ejercicios y problemas que requieran exponentes o radicales para su modelización, es decir; para ser planteados, desarrollados y resueltos. Identificarás relaciones entre expresiones algebraicas, efectuar operaciones y reconocer situaciones que pueden ser resueltas con el uso del álgebra.\u003cspan lang=\"ES\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eAdicionalmente, comprenderás el uso de las ecuaciones y las desigualdades para resolver problemas que requieren de estos planteamientos y podrás resolver ecuaciones con potencias superiores, expresiones fraccionarias y radicales, también desigualdades lineales y cuadráticas, todo esto aplicado en la solución de problemas.\u003c/p\u003e\n\u003cp\u003eAl finalizar, encontrarás facilidad para leer, interpretar y predecir el comportamiento de situaciones de la cotidianidad representadas mediante gráficas, tablas o ecuaciones de dependencia. Así mismo, tendrás habilidad para construir modelos funcionales a partir de observaciones para apoyar otras disciplinas.\u003c/p\u003e306:T5e8,\u003cp\u003eMathematics is the most essential tool in any STEM professional’s toolbox. In this course, we will provide you with an introduction to linear algebra, multivariable calculus, and differential equations, through exploring the main definitions, theorems and practical examples required. \u003c/p\u003e\n\u003cp\u003eCan we use linear algebra to do data compression? What’s the meaning of an eigenvalue and an eigenvector in"])</script><script>self.__next_f.push([1," a mechanical system? How do vector fields help to describe wind flow? How can you make optimal parameter choices in industrial processes?\u003c/p\u003e\n\u003cp\u003eWe aim to answer all these questions and more, so that you can use these mathematical techniques when tackling problems in your own field of study.\u003c/p\u003e\n\u003cp\u003eWe will use examples, graphic representations, applets, and exercises to exemplify the various theorems and definitions.\u003c/p\u003e\n\u003cp\u003eYou will acquire the skills to cope with matrix-formulated problems typically arising from applications in science and technology. Not only will you be able to use practical algorithms, solve systems of equations and differential equations, compute the singular value and eigenvalue decomposition, and solve optimisation problems, you will also acquire a set of properties that will assist in simplifying and understanding mathematical problems.\u003c/p\u003e\n\u003cp\u003eThe course will give you the tools to transform optimisation problems and differential equations into matrix language. Most importantly, you will learn that matrix computations are ubiquitous in science and engineering.\u003c/p\u003e307:T48d,\u003cul\u003e\n\u003cli\u003eWhat vector spaces are and how their elements can be represented by coordinate vectors with respect to a basis\u003c/li\u003e\n\u003cli\u003eLinear transformations between vector spaces and how to represent them in matrix notation\u003c/li\u003e\n\u003cli\u003eTo compute inner products, norms, and orthogonal projections\u003c/li\u003e\n\u003cli\u003eTo define and calculate eigenvalues and eigenvectors and their algebraic and geometric multiplicities\u003c/li\u003e\n\u003cli\u003eTo calculate the singular value decomposition\u003c/li\u003e\n\u003cli\u003eTo understand the concepts of a real function of multiple variables, partial and directional derivatives and the multivariate chain rule\u003c/li\u003e\n\u003cli\u003eTo determine critical points and identify extrema of multivariate functions\u003c/li\u003e\n\u003cli\u003eTo understand the concepts of (conservative) vector fields and be able to calculate and simplify their line integrals\u003c/li\u003e\n\u003cli\u003eTo understand what gradient, divergence, and curl operators are and how to calculate them\u003c/li\u003e\n\u003cli\u003eTo classify a"])</script><script>self.__next_f.push([1,"nd solve (systems of) first-order differential equations\u003c/li\u003e\n\u003cli\u003eTo understand and apply linear algebra techniques to solve linear systems of differential equations with constant coefficients and analyse their stability\u003c/li\u003e\n\u003c/ul\u003e308:T776,\u003cp\u003eEn este curso abordaremos el aprendizaje automático de máquinas desde una perspectiva algebraica. Se abordarán cuatro temas, el primero de ellos será una introducción a los modelos de regresión y clasificación lineal, comenzando por la regresión lineal multivariada, sus aplicaciones y cómo evitar el sobre-ajuste utilizando regularización. Luego de esto introduciremos la regresión logística como uno de los métodos de clasificación más relevantes.\u003c/p\u003e\n\u003cp\u003eLa regresión logística nos permitirá realizar una conexión con la formulación de la arquitectura de una red neuronal artificial, ya que la neurona logística, la cual puede interpretarse como la unidad básica para el desarrollo de modelos de clasificación con redes neuronales, es el equivalente a una regresión logística.\u003c/p\u003e\n\u003cp\u003eEl tercer tema se enfoca en el estudio de diferentes metodologías utilizadas para el correcto entrenamiento de redes neuronales, tanto para regresión como clasificación, así mismo se introducirán algunos métodos utilizados para identificar los modelos que tienen el mejor rendimiento.\u003c/p\u003e\n\u003cp\u003eFinalmente, se describirán diferentes métodos para el aprendizaje no supervisado. Específicamente se abordará PCA para la reducción de dimensionalidad y \u003cem\u003ek-means\u003c/em\u003e para el desarrollo de modelos de agrupamiento. También se describirán algunas técnicas utilizadas para poder evaluar el rendimiento de estos modelos. Además, el curso abordará el uso de redes neuronales para el desarrollo de modelos de aprendizaje no supervisado, específicamente se explicarán las \u003cem\u003eRedes de Hopfield\u003c/em\u003e que permiten el almacenamiento de patrones en la arquitectura de su red, mediante el uso de memoria asociativa; y los mapas autoorganizados o redes de Kohonen que permite identificar estruc"])</script><script>self.__next_f.push([1,"turas en los datos de entrenamiento y que pueden utilizarse para la reducción de dimensionalidad.\u003c/p\u003e309:T46e,\u003cp\u003e\u003cspan lang=\"ES\"\u003eLa aritmética y el álgebra son dos de los pilares de las matemáticas que se usan frecuentemente tanto en situaciones de la cotidianidad como en los cursos de matemáticas universitarias. En este MOOC se abordan algunos temas de estos pilares en el marco de las matemáticas básicas cuyo estudio y comprensión brindarán herramientas para resolver problemas relacionados y estudiar temas posteriores. Se presentan además algunas situaciones relacionadas con matemáticas críticas, invitando a los participantes a la reflexión alrededor de problemáticas actuales.\u003c/span\u003e\u003cspan lang=\"ES\"\u003e\u003c/span\u003e\u003cspan lang=\"ES\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eEl curso \u003cstrong\u003eElementos matemáticos para el pensamiento crítico\u003c/strong\u003e\u003cspan lang=\"ES\"\u003e\u003c/span\u003e\u003cspan lang=\"ES\"\u003e hace parte de una serie de cinco MOOC en los que se persigue desarrollar competencias básicas en los campos de (1) matemáticas, (2) lecto escritura, (3) inglés, (4) competencias vocacionales y (5) competencias informacionales, manteniendo como componente transversal la reflexión y el análisis crítico que suscitan las situaciones de Justicia Social.\u003c/span\u003e\u003c/p\u003e30a:Tc23,"])</script><script>self.__next_f.push([1,"\u003cp\u003eEste curso fue imaginado y diseñado desde las aulas de clase a partir de varios años de experiencia: es el fruto de escuchar el lenguaje de los estudiantes, de observar su forma de recordar y asociar conceptos, de responder a sus preguntas, de identificar ejemplos clave que apoyan el aprendizaje, de reconocer errores recurrentes y puntos débiles e identificar las temáticas y detalles verdaderamente relevantes.\u003c/p\u003e\n\u003cp\u003eSe “rompe” el orden tradicional de los cursos de precálculo, para ayudar a establecer la conexión entre conceptos y dosificar la información de manera que se logre mayor retención y aprendizaje. Se dejan de lado detalles que se han identificado como poco relevantes en el aprendizaje de cálculo a nivel universitario.\u003c/p\u003e\n\u003cp\u003eSe parte del principio de que en las matemáticas hay diversas rutas de proceso, con ventajas o desventajas propias, algunas más o menos eficientes, pero se impulsa a que cada estudiante busque decidir sus propias rutas, de acuerdo con su nivel de experiencia y confianza.\u003c/p\u003e\n\u003cp\u003eMediante un lenguaje sencillo y el uso de elementos visuales y atractivos, se explica el proceso de razonamiento, con énfasis en el por qué o la lógica detrás de cada propiedad y herramienta, para lograr un aprendizaje desde la comprensión y el uso de argumentos lógicos. Esto contrasta con la clásica forma de aprender desde la memorización o la mecánica, entendiendo que es imposible volverse eficiente si no se encuentra sentido a cada paso de los procesos.\u003c/p\u003e\n\u003cp\u003eSe han seleccionado ejemplos simples que permiten comprender los conceptos acompañados de ejercicios prácticos nivel medio y algunos ejercicios tipo “reto” para aquellos estudiantes que busquen subir el desempeño personal.\u003c/p\u003e\n\u003cp\u003eSe inicia con el estudio de un conjunto básico de pilares matemáticos claves para el estudio del álgebra que permitan reconocer y superar frecuentes dificultades en el salto de la aritmética al álgebra, de forma que resulten comprensibles y memorables. Se introduce una terminología básica que será usada en el razonamiento en todas las unidades posteriores.\u003c/p\u003e\n\u003cp\u003eEn segunda instancia, se desarrolla una unidad temática alrededor de las expresiones polinomiales y sus operaciones básicas. La multiplicación y la factorización se estudian de forma simultánea como operaciones reversas, de modo que se genere conciencia y reconocimiento de las dos operaciones con naturalidad.\u003c/p\u003e\n\u003cp\u003eEn la tercera unidad se abordan las expresiones racionales, partiendo de las operaciones con fracciones numéricas, para conectar su lógica con la de las expresiones racionales algebraicas. Se finaliza esta unidad con las técnicas de racionalización que integran muchos de los conceptos previos.\u003c/p\u003e\n\u003cp\u003eFinalmente, se estudia de forma paralela la mecánica de solución de ecuaciones y desigualdades, identificando las coincidencias y diferencias en sus procesos. Esta unidad finaliza con la formulación de problemas aplicados mediante ecuaciones o desigualdades, presentando algunas claves para orientar la lectura, comprensión y formulación.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"30b:T4a4,\u003col\u003e\n\u003cli\u003e\u003cstrong\u003eAplicar\u003c/strong\u003e las leyes de los signos y las propiedades de exponentes y raíces para simplificar expresiones algebraicas de manera precisa, siguiendo una secuencia de pasos de acuerdo con las leyes del orden, agrupación, distribución y jerarquía de operaciones.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eDominar\u003c/strong\u003e expresiones polinomiales para transformarlas entre su forma expandida y su forma factorizada, identificando y aplicando las estrategias más eficientes, como productos notables, para obtener expresiones simplificadas y convenientes de acuerdo al contexto.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eManipular\u003c/strong\u003e expresiones racionales para realizar operaciones de suma, resta, multiplicación y división, resolviendo con eficiencia tanto expresiones simples como complejas, mediante la ejecución correcta de procesos de racionalización, cuando sea necesario.\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eResolver\u003c/strong\u003e ecuaciones y desigualdades lineales, cuadráticas, racionales y con raíces, utilizando la técnica adecuada en cada caso, siguiendo una secuencia de pasos consistente con los principios de equilibrio, presentando el conjunto solución y apropiando el uso del lenguaje matemático.\u003c/li\u003e\n\u003c/ol\u003e30c:T4ff,\u003cul\u003e\n\u003cli\u003eProbability distributions in finance\u003c/li\u003e\n\u003cli\u003eTime-series models: random walks, ARMA, and GARCH\u003c/li\u003e\n\u003cli\u003eContinuous-time stochastic processes\u003c/li\u003e\n\u003cli\u003eOptimization\u003c/li\u003e\n\u003cli\u003eLinear algebra of asset pricing\u003c/li\u003e\n\u003cli\u003eStatistical and econometric analysis\u003c/li\u003e\n\u003cli\u003eMonte Carlo simulation\u003c/li\u003e\n\u003cli\u003eApplied computational techniques\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cbr /\u003e\n\u003c/strong\u003e\u003cstrong\u003eHow to Prepare\u003c/strong\u003e \u003cstrong\u003e\u003cbr /\u003e\n\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere are a number of prerequisites for this course: Calculus (multivariable), probability and statistics, linear algebra, and basic programming skills. Learners are urged to thoroughly review the \u003ca href=\"https://learning.edx.org/course/course-v1:MITx+FIN.Px+2T2022\"\u003e15.455x Prerequisites and Resources site\u003c/a\u003e* which details these prerequisites and provides a robust suite of resources to prepare you fo"])</script><script>self.__next_f.push([1,"r this advanced math course, including a readiness assessment to help you confirm that you have a solid understanding of the 15.455x prerequisite material, and to indicate directions of study in case you need to build on your current foundations prior to starting the course.\u003c/p\u003e\n\u003cp\u003e*Please note that you will need to enroll in order to access the Prerequisite and Resources site. To do so, click the link above, then click \"Enroll.\"\u003c/p\u003e30d:T407,\u003cp\u003ePlanning to study for an MBA but unsure of your basic maths skills? All MBA programs, and in business generally require some maths, particularly on quantitative subjects such as Accounting, Economics and Finance.\u003c/p\u003e\n\u003cp\u003eIn this mathematics course, you will learn the fundamental business math skills needed to succeed in your MBA study and in the field of business. These math skills will also give you an edge in the workplace enabling you to apply greater analytical skill to your decision making.\u003c/p\u003e\n\u003cp\u003eYou will learn how to evaluate and manipulate the types of formulae that appear in an accounting syllabus, how to perform the calculus required to solve optimization problems in economics and how to apply the concept of geometric series to solving finance-related problems such as calculating compound interest payments.\u003c/p\u003e\n\u003cp\u003eThis course assumes no prior knowledge of business maths, concepts are explained clearly and regular activities give you the opportunity to practice your skills and improve your confidence.\u003c/p\u003e30e:T750,\u003cp\u003eData Science along with artificial intelligence (AI) and its various components such as statistical learning (SL), machine learning (ML) and deep learning algorithms (DL) are recognized as main drivers of organizational value creation. According to Dr Jim Gray, Data Science is the fourth paradigm which drives innovative solutions to organizational problems.\u003cspan lang=\"EN-US\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eIn this course we will start with basic concepts in probability such as joint and conditional probabilities. We will discuss the implementation of these concepts in M"])</script><script>self.__next_f.push([1,"L algorithms for Market Basket Analysis and Recommender Systems. After covering basic probability concepts, we move on to random variables, discrete and continuous probability distributions, sampling, estimation and central limit theorem.\u003c/p\u003e\n\u003cp\u003eAn important step in ML model building is feature selection to avoid overfitting and underfitting. ML models such as regression and logistic regression use hypothesis testing to select features. We will discuss various hypothesis tests and how they are used in feature selection. \u003c/p\u003e\n\u003cp\u003eEvery ML model has an optimization stage, either to fine-tune the feature weights, or to find an optimal set of features. We will discuss important optimization techniques, and algorithms such as Gradient Descent, that play an important role in AI and ML model development.\u003cspan lang=\"EN-US\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eData must be represented in a matrix for AI and ML model development. Matrix operations such as matrix inverse and multiplication are elementary steps in model development. These fundamental concepts in linear algebra will be discussed.\u003c/p\u003e\n\u003cp\u003eThis course is suitable for students/practitioners interested in improving their knowledge in the fundamental concepts of Data Science. The course will also prepare the learner for a career in the field of Data Analytics.\u003c/p\u003e30f:T8c0,"])</script><script>self.__next_f.push([1,"\u003cp\u003e\u003cstrong\u003eAbout the Database Series of Courses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\"Databases\" was one of Stanford's three inaugural massive open online courses in the fall of 2011. It has been offered in synchronous and then in self-paced versions on a variety of platforms continuously since 2011. The material is now being offered as a set of five self-paced courses, which can be taken in a variety of ways to learn about different aspects of databases. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRelational Databases and SQL\u003c/em\u003e is the most popular course in the Databases series. It is applicable to learners seeking to gain a strong understanding of relational databases, and to master SQL, the long-accepted standard query language for relational database systems. Additional courses focus on advanced concepts in relational databases and SQL, formal foundations and database design methodologies, and semistructured data.\u003c/p\u003e\n\u003cp\u003eAll of the courses are based around video lectures and demos. Many of them include quizzes between video segments to check understanding, in-depth standalone quizzes, and/or a variety of automatically-checked interactive exercises. Each course also includes an unmoderated discussion forum and pointers to readings and resources. The courses are described briefly below. Taught by Professor Jennifer Widom, the overall curriculum draws from Stanford's popular longstanding Databases course.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhy Learn About Databases\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDatabases are incredibly prevalent -- they underlie technology used by most people every day if not every hour. Databases reside behind a huge number of websites; they're a crucial component of telecommunications systems, banking systems, video games, and just about any other software system or electronic device that maintains some amount of persistent information. In addition to persistence, database systems provide a number of other properties that make them exceptionally useful and convenient: reliability, efficiency, scalability, concurrency control, data abstractions, and high-level query languages. Databases are so ubiquitous and important that computer science graduates frequently cite their database class as the one most useful to them in their industry or graduate-school careers.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"310:T805,"])</script><script>self.__next_f.push([1,"\u003cp\u003eStanford's online offering in Databases is now available as a set of five self-paced courses:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Relational Databases and SQL\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to the relational model and concepts in relational databases and relational database management systems\u003c/li\u003e\n\u003cli\u003eComprehensive coverage of SQL, the long-accepted standard query language for relational database management systems\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Advanced Topics in SQL (prerequisite: Relational Databases and SQL)\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCreating indexes for increased query performance\u003c/li\u003e\n\u003cli\u003eUsing transactions for concurrency control and failure recovery\u003c/li\u003e\n\u003cli\u003eDatabase constraints: key, referential integrity, and \"check\" constraints\u003c/li\u003e\n\u003cli\u003eDatabase triggers\u003c/li\u003e\n\u003cli\u003eHow views are created, used, and updated in relational databases\u003c/li\u003e\n\u003cli\u003eAuthorization in relational databases\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: OLAP and Recursion\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eStar schemas, the data cube concept, and On-Line Analytical Processing (OLAP) features in relational databases including the Cube and Rollup operators\u003c/li\u003e\n\u003cli\u003eThe SQL standard for queries over recursively-defined relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Modeling and Theory\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eRelational algebra – the algebraic query language that provides the formal foundations of SQL\u003c/li\u003e\n\u003cli\u003eDependency theory and normal forms in relational databases as the basis of schema design\u003c/li\u003e\n\u003cli\u003eThe data-modeling component of the Unified Modeling Language (UML), how UML diagrams are translated to relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Semistructured Data\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe XML model for semistructured and self-describing data, including DTDs and some features of XML Schema\u003c/li\u003e\n\u003cli\u003eThe JSON model for human-readable structured or semistructured data\u003c/li\u003e\n\u003cli\u003eThe XPath language for processing XML data, and many features of the more advanced XQuery language\u003c/li\u003e\n\u003cli\u003eAn introduction to the XSLT rule-based language for querying and transforming XML data\u003c/li\u003e\n\u003c/ul\u003e"])</script><script>self.__next_f.push([1,"311:T8c0,"])</script><script>self.__next_f.push([1,"\u003cp\u003e\u003cstrong\u003eAbout the Database Series of Courses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\"Databases\" was one of Stanford's three inaugural massive open online courses in the fall of 2011. It has been offered in synchronous and then in self-paced versions on a variety of platforms continuously since 2011. The material is now being offered as a set of five self-paced courses, which can be taken in a variety of ways to learn about different aspects of databases. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRelational Databases and SQL\u003c/em\u003e is the most popular course in the Databases series. It is applicable to learners seeking to gain a strong understanding of relational databases, and to master SQL, the long-accepted standard query language for relational database systems. Additional courses focus on advanced concepts in relational databases and SQL, formal foundations and database design methodologies, and semistructured data.\u003c/p\u003e\n\u003cp\u003eAll of the courses are based around video lectures and demos. Many of them include quizzes between video segments to check understanding, in-depth standalone quizzes, and/or a variety of automatically-checked interactive exercises. Each course also includes an unmoderated discussion forum and pointers to readings and resources. The courses are described briefly below. Taught by Professor Jennifer Widom, the overall curriculum draws from Stanford's popular longstanding Databases course.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhy Learn About Databases\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDatabases are incredibly prevalent -- they underlie technology used by most people every day if not every hour. Databases reside behind a huge number of websites; they're a crucial component of telecommunications systems, banking systems, video games, and just about any other software system or electronic device that maintains some amount of persistent information. In addition to persistence, database systems provide a number of other properties that make them exceptionally useful and convenient: reliability, efficiency, scalability, concurrency control, data abstractions, and high-level query languages. Databases are so ubiquitous and important that computer science graduates frequently cite their database class as the one most useful to them in their industry or graduate-school careers.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"312:T523,\u003cp\u003eThis course is one of five self-paced courses on the topic of Databases, originating as one of Stanford's three inaugural massive open online courses released in the fall of 2011. The original \"Databases\" courses are now all available on edx.org.\u003c/p\u003e\n\u003cp\u003eThis course is broad and practical, covering indexes, transactions, constraints, triggers, views, and authorization, all in the context of relational database systems and the SQL language. This course builds on concepts introduced in \u003cem\u003eDatabases: Relational Databases and SQL\u003c/em\u003e and is recommended for learners seeking to advance their understanding and use of relational databases.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe Indexes and Transactions section of this course covers two important features of database systems from the application-builder's perspective: indexing for increased performance, and transactions for concurrency control and failure recovery.\u003c/li\u003e\n\u003cli\u003eThe Constraints and Triggers section of this course explains key, referential integrity, and \"check\" constraints, followed by comprehensive coverage of database triggers.\u003c/li\u003e\n\u003cli\u003eThe Views and Authorization section of this course provides extensive coverage of how database views can be created, used, and updated, and introduces standard techniques for authorization in relational databases.\u003c/li\u003e\n\u003c/ul\u003e313:T805,"])</script><script>self.__next_f.push([1,"\u003cp\u003eStanford's online offering in Databases is now available as a set of five self-paced courses:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Relational Databases and SQL\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to the relational model and concepts in relational databases and relational database management systems\u003c/li\u003e\n\u003cli\u003eComprehensive coverage of SQL, the long-accepted standard query language for relational database management systems\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Advanced Topics in SQL (prerequisite: Relational Databases and SQL)\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCreating indexes for increased query performance\u003c/li\u003e\n\u003cli\u003eUsing transactions for concurrency control and failure recovery\u003c/li\u003e\n\u003cli\u003eDatabase constraints: key, referential integrity, and \"check\" constraints\u003c/li\u003e\n\u003cli\u003eDatabase triggers\u003c/li\u003e\n\u003cli\u003eHow views are created, used, and updated in relational databases\u003c/li\u003e\n\u003cli\u003eAuthorization in relational databases\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: OLAP and Recursion\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eStar schemas, the data cube concept, and On-Line Analytical Processing (OLAP) features in relational databases including the Cube and Rollup operators\u003c/li\u003e\n\u003cli\u003eThe SQL standard for queries over recursively-defined relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Modeling and Theory\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eRelational algebra – the algebraic query language that provides the formal foundations of SQL\u003c/li\u003e\n\u003cli\u003eDependency theory and normal forms in relational databases as the basis of schema design\u003c/li\u003e\n\u003cli\u003eThe data-modeling component of the Unified Modeling Language (UML), how UML diagrams are translated to relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Semistructured Data\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe XML model for semistructured and self-describing data, including DTDs and some features of XML Schema\u003c/li\u003e\n\u003cli\u003eThe JSON model for human-readable structured or semistructured data\u003c/li\u003e\n\u003cli\u003eThe XPath language for processing XML data, and many features of the more advanced XQuery language\u003c/li\u003e\n\u003cli\u003eAn introduction to the XSLT rule-based language for querying and transforming XML data\u003c/li\u003e\n\u003c/ul\u003e"])</script><script>self.__next_f.push([1,"314:T582,\u003cp\u003ePhysics is the foundation of many important science and engineering disciplines. Understanding its basics is fundamental for advanced studies. In this course, you will have the chance to review the fundamentals either for your own interest, or to ensure you have a smooth start in the first year of your Bachelor’s degree.\u003c/p\u003e\n\u003cp\u003eThe course aims to close the readiness gap between high school and university. It was specifically developed for potential future students: it covers physics topics that are a prerequisite for many engineering programs, but will also show you how these topics are applied in the various follow-up studies (For example in Applied Physics, Aerospace Engineering, Mechanical Engineering or Electrical Engineering). The course not only covers the content needed for further study but also introduces the different ways in which physics is presented at university level to ensure an easy entry to a new degree program.\u003c/p\u003e\n\u003cp\u003eThis course is intended for:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003eProspective engineering students who want to refresh their physics knowledge before starting university\u003c/li\u003e\n\u003cli\u003eHigh school students who would like an additional challenge in physics not offered by their school\u003c/li\u003e\n\u003cli\u003eEngineering students already enrolled in university who realize that they have a gap in their physics knowledge\u003c/li\u003e\n\u003cli\u003eOther people who are interested in university level physics\u003c/li\u003e\n\u003c/ol\u003e315:T429,\u003cp\u003eThis course provides learners with the foundational skills necessary to excel in mathematics. For school leavers, it acts as a bridge between their prior educational experiences and the requirements of tertiary education. Professionals who want to refresh their knowledge or return to higher education will benefit from the course's tools and techniques, equipping them to effectively communicate their mathematical ideas in a business or an academic setting.\u003c/p\u003e\n\u003cp\u003eThis standalone course may assist learners who wish to undertake \u003ca href=\"https://www.edx.org/xseries/adelaidex-mathtrackx?index=product\u0026queryID=d8259"])</script><script>self.__next_f.push([1,"b59ed34a6fc8aa7cc14dbb0982e\u0026position=3\u0026results_level=first-level-results\u0026term=adelaide\u0026objectID=program-6fe2404d-1a01-4c51-bff9-f350a7f5d219\u0026campaign=MathTrackX\u0026source=edX\u0026product_category=xseries\u0026placement_url=https%3A%2F%2Fwww.edx.org%2Fsearch\" rel=\"noopener\" target=\"_blank\" title=\"AdelaideX’s MathTrackX XSeries Program\"\u003eAdelaideX’s MathTrackX XSeries Program\u003c/a\u003e, however, it is not a mandatory course within the MathTrackX Program.\u003c/p\u003e316:T8c0,"])</script><script>self.__next_f.push([1,"\u003cp\u003e\u003cstrong\u003eAbout the Database Series of Courses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\"Databases\" was one of Stanford's three inaugural massive open online courses in the fall of 2011. It has been offered in synchronous and then in self-paced versions on a variety of platforms continuously since 2011. The material is now being offered as a set of five self-paced courses, which can be taken in a variety of ways to learn about different aspects of databases. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRelational Databases and SQL\u003c/em\u003e is the most popular course in the Databases series. It is applicable to learners seeking to gain a strong understanding of relational databases, and to master SQL, the long-accepted standard query language for relational database systems. Additional courses focus on advanced concepts in relational databases and SQL, formal foundations and database design methodologies, and semistructured data.\u003c/p\u003e\n\u003cp\u003eAll of the courses are based around video lectures and demos. Many of them include quizzes between video segments to check understanding, in-depth standalone quizzes, and/or a variety of automatically-checked interactive exercises. Each course also includes an unmoderated discussion forum and pointers to readings and resources. The courses are described briefly below. Taught by Professor Jennifer Widom, the overall curriculum draws from Stanford's popular longstanding Databases course.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhy Learn About Databases\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDatabases are incredibly prevalent -- they underlie technology used by most people every day if not every hour. Databases reside behind a huge number of websites; they're a crucial component of telecommunications systems, banking systems, video games, and just about any other software system or electronic device that maintains some amount of persistent information. In addition to persistence, database systems provide a number of other properties that make them exceptionally useful and convenient: reliability, efficiency, scalability, concurrency control, data abstractions, and high-level query languages. Databases are so ubiquitous and important that computer science graduates frequently cite their database class as the one most useful to them in their industry or graduate-school careers.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"317:T4a1,\u003cp\u003eThis course is one of five self-paced courses on the topic of Databases, originating as one of Stanford's three inaugural massive open online courses released in the fall of 2011. The original \"Databases\" courses are now all available on edx.org.\u003c/p\u003e\n\u003cp\u003ePart of the Databases series, this is a standalone course; learners seeking to develop an understanding of topics in this course do not need to take other Databases courses. This course covers the JSON and XML standards for semistructured data, along with query languages and schema declaration features for XML.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe XML Data section of this course introduces the XML model for semistructured and self-describing data, including DTDs and some features of XML Schema.\u003c/li\u003e\n\u003cli\u003eThe JSON Data section of this course introduces the JSON model for human-readable structured or semistructured data.\u003c/li\u003e\n\u003cli\u003eThe XPath and XQuery section of this course covers the XPath language for processing XML data, along with many features of the more advanced XQuery language.\u003c/li\u003e\n\u003cli\u003eThe XSLT section of this course provides a general introduction to the XSLT rule-based language for querying and transforming XML data.\u003c/li\u003e\n\u003c/ul\u003e318:T805,"])</script><script>self.__next_f.push([1,"\u003cp\u003eStanford's online offering in Databases is now available as a set of five self-paced courses:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Relational Databases and SQL\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to the relational model and concepts in relational databases and relational database management systems\u003c/li\u003e\n\u003cli\u003eComprehensive coverage of SQL, the long-accepted standard query language for relational database management systems\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Advanced Topics in SQL (prerequisite: Relational Databases and SQL)\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCreating indexes for increased query performance\u003c/li\u003e\n\u003cli\u003eUsing transactions for concurrency control and failure recovery\u003c/li\u003e\n\u003cli\u003eDatabase constraints: key, referential integrity, and \"check\" constraints\u003c/li\u003e\n\u003cli\u003eDatabase triggers\u003c/li\u003e\n\u003cli\u003eHow views are created, used, and updated in relational databases\u003c/li\u003e\n\u003cli\u003eAuthorization in relational databases\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: OLAP and Recursion\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eStar schemas, the data cube concept, and On-Line Analytical Processing (OLAP) features in relational databases including the Cube and Rollup operators\u003c/li\u003e\n\u003cli\u003eThe SQL standard for queries over recursively-defined relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Modeling and Theory\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eRelational algebra – the algebraic query language that provides the formal foundations of SQL\u003c/li\u003e\n\u003cli\u003eDependency theory and normal forms in relational databases as the basis of schema design\u003c/li\u003e\n\u003cli\u003eThe data-modeling component of the Unified Modeling Language (UML), how UML diagrams are translated to relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Semistructured Data\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe XML model for semistructured and self-describing data, including DTDs and some features of XML Schema\u003c/li\u003e\n\u003cli\u003eThe JSON model for human-readable structured or semistructured data\u003c/li\u003e\n\u003cli\u003eThe XPath language for processing XML data, and many features of the more advanced XQuery language\u003c/li\u003e\n\u003cli\u003eAn introduction to the XSLT rule-based language for querying and transforming XML data\u003c/li\u003e\n\u003c/ul\u003e"])</script><script>self.__next_f.push([1,"319:T772,\u003cp\u003eThis course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level further maths exams.\u003c/p\u003e\n\u003cp\u003eYou will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan lang=\"EN-US\"\u003eFluency – selecting and applying correct methods to answer with speed and efficiency\u003c/span\u003e\u003c/li\u003e\n\u003cli\u003e\u003cspan lang=\"EN-US\"\u003eConfidence – critically assessing mathematical methods and investigating ways to apply them\u003c/span\u003e\u003c/li\u003e\n\u003cli\u003eProblem-solving – analysing the ‘unfamiliar’ and identifying which skills and techniques you require to answer questions\u003c/li\u003e\n\u003cli\u003eConstructing mathematical argument – using mathematical tools such as diagrams, graphs, logical deduction, mathematical symbols, mathematical language, construct mathematical argument and present precisely to others\u003c/li\u003e\n\u003cli\u003eDeep reasoning – analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eOver eight modules, you will be introduced to\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan lang=\"EN-US\"\u003ecomplex numbers, their modulus and argument and how they can be represented diagrammatically\u003c/span\u003e\u003c/li\u003e\n\u003cli\u003ematrices, their order, determinant and inverse and their application to linear transformation\u003c/li\u003e\n\u003cli\u003eroots of polynomial equations and their relationship to coefficients\u003c/li\u003e\n\u003cli\u003eseries, partial fractions and the method of differences\u003c/li\u003e\n\u003cli\u003evectors, their scalar produce and how they can be used to define straight lines and planes in 2 and 3 dimensions.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eYour initial skillset will be extended to give a clear understanding of how background knowledge underpins the A-level further mathematics course. You’ll also be encouraged to consider how what you know fits into the wider mathematical world.\u003c/p\u003e31a:T548,\u003cp\u003eHow to extend the number system to include \u003cimg src='file:///C:/Users/HP/AppData/Local/Temp/msohtmlclip1/01/clip_image002"])</script><script>self.__next_f.push([1,".gif' width='28' height='19' /\u003e and the definition of a complex number.\u003c/p\u003e\n\u003cp\u003eHow to add, subtract, multiply and divide complex numbers.\u003c/p\u003e\n\u003cp\u003eHow to represent complex numbers on an Argand diagram and the modulus and argument of a complex number.\u003c/p\u003e\n\u003cp\u003eHow to write complex numbers in modulus-argument form.\u003c/p\u003e\n\u003cp\u003eHow to define loci in the complex plane.\u003c/p\u003e\n\u003cp\u003eHow to define a matrix by its order.\u003c/p\u003e\n\u003cp\u003eHow to add and subtract conformable matrices.\u003c/p\u003e\n\u003cp\u003eHow to multiply two conformable matrices.\u003c/p\u003e\n\u003cp\u003eHow to use matrices to define linear transformations.\u003c/p\u003e\n\u003cp\u003eHow to find invariant lines and lines of invariant points.\u003c/p\u003e\n\u003cp\u003eHow to find the determinant and inverse of a 2 x 2 and 3 x 3 matrix.\u003c/p\u003e\n\u003cp\u003eHow to use matrices to solve systems of linear equations.\u003c/p\u003e\n\u003cp\u003eHow to use standard series formulae to find the sums of other series.\u003c/p\u003e\n\u003cp\u003eHow to separate algebraic fractions into partial fractions.\u003c/p\u003e\n\u003cp\u003eHow to use the method of differences to find the sum of a series.\u003c/p\u003e\n\u003cp\u003eHow to find the scalar (dot) product of two vectors.\u003c/p\u003e\n\u003cp\u003eHow to define the equation of a line using vectors.\u003c/p\u003e\n\u003cp\u003eHow to define a plane using vectors.\u003c/p\u003e\n\u003cp\u003eHow to use vectors to solve problems involving lines and planes.\u003c/p\u003e31b:T5ed,\u003cp\u003eThis course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level maths exams.\u003c/p\u003e\n\u003cp\u003eYou will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eFluency – selecting and applying correct methods to answer with speed and efficiency\u003c/li\u003e\n\u003cli\u003eConfidence – critically assessing mathematical methods and investigating ways to apply them\u003c/li\u003e\n\u003cli\u003eProblem solving – analysing the ‘unfamiliar’ and identifying which skills and techniques you require to answer questions\u003c/li\u003e\n\u003cli\u003eConstructing mathematical argument – using mathematical tools such as diagrams, graphs, logical deduction, mathematical symbols, mathematical language,"])</script><script>self.__next_f.push([1," construct mathematical argument and present precisely to others\u003c/li\u003e\n\u003cli\u003eDeep reasoning – analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eOver seven modules, covering general motion in a straight line and two dimensions, projectile motion, a model for friction, moments, equilibrium of rigid bodies, vectors, differentiation methods, integration methods and differential equations, your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A -level course.\u003c/p\u003e\n\u003cp\u003eYou’ll also be encouraged to consider how what you know fits into the wider mathematical world.\u003c/p\u003e31c:T69c,\u003cp\u003eBy the end of this course, you'll be able to: \u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eUse calculus in kinematics for motion in a straight line\u003c/li\u003e\n\u003cli\u003eUse differentiation and integration of a vector with respect to time for motion in two dimensions\u003c/li\u003e\n\u003cli\u003eSolve projectile motion problems using both calculus/vector methods and constant acceleration formulae\u003c/li\u003e\n\u003cli\u003eUse a standard model for friction\u003c/li\u003e\n\u003cli\u003eCalculate moments understanding what they mean and how they might be used\u003c/li\u003e\n\u003cli\u003eSolve problems involving parallel and nonparallel coplanar forces\u003c/li\u003e\n\u003cli\u003eApply an understanding of moments to statics problems involving rigid bodies\u003c/li\u003e\n\u003cli\u003eUse the Normal distribution as a model for continuous data\u003c/li\u003e\n\u003cli\u003eConduct a hypothesis test of the mean using a Normal distribution\u003c/li\u003e\n\u003cli\u003eUse a Normal distribution as an approximation of a Binomial distribution\u003c/li\u003e\n\u003cli\u003eAdd vectors diagrammatically\u003c/li\u003e\n\u003cli\u003ePerform the algebraic operations of vector addition and multiplication by scalars\u003c/li\u003e\n\u003cli\u003eApply vector calculations to problems in pure mathematics\u003c/li\u003e\n\u003cli\u003eUse methods for differentiating a function of a function, differentiating a product and differentiating a quotient\u003c/li\u003e\n\u003cli\u003eDifferentiate trigonometric and inverse trigonometric functions\u003c/li\u003e\n\u003cli\u003eUse implicit and parametric differentiation\u003c/li\u003e\n\u003cli\u003eIdentify integrals that can"])</script><script>self.__next_f.push([1," be dealt with “by sight”\u003c/li\u003e\n\u003cli\u003eUse a substitution method to integrate a function\u003c/li\u003e\n\u003cli\u003eUse partial fractions to integrate rational functions\u003c/li\u003e\n\u003cli\u003eUse the method of integration by parts\u003c/li\u003e\n\u003cli\u003eUse the method of separating the variable to solve differential equations\u003c/li\u003e\n\u003cli\u003efind the family of solutions for a differential equation\u003c/li\u003e\n\u003c/ul\u003e31d:T8c0,"])</script><script>self.__next_f.push([1,"\u003cp\u003e\u003cstrong\u003eAbout the Database Series of Courses\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\"Databases\" was one of Stanford's three inaugural massive open online courses in the fall of 2011. It has been offered in synchronous and then in self-paced versions on a variety of platforms continuously since 2011. The material is now being offered as a set of five self-paced courses, which can be taken in a variety of ways to learn about different aspects of databases. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eRelational Databases and SQL\u003c/em\u003e is the most popular course in the Databases series. It is applicable to learners seeking to gain a strong understanding of relational databases, and to master SQL, the long-accepted standard query language for relational database systems. Additional courses focus on advanced concepts in relational databases and SQL, formal foundations and database design methodologies, and semistructured data.\u003c/p\u003e\n\u003cp\u003eAll of the courses are based around video lectures and demos. Many of them include quizzes between video segments to check understanding, in-depth standalone quizzes, and/or a variety of automatically-checked interactive exercises. Each course also includes an unmoderated discussion forum and pointers to readings and resources. The courses are described briefly below. Taught by Professor Jennifer Widom, the overall curriculum draws from Stanford's popular longstanding Databases course.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhy Learn About Databases\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDatabases are incredibly prevalent -- they underlie technology used by most people every day if not every hour. Databases reside behind a huge number of websites; they're a crucial component of telecommunications systems, banking systems, video games, and just about any other software system or electronic device that maintains some amount of persistent information. In addition to persistence, database systems provide a number of other properties that make them exceptionally useful and convenient: reliability, efficiency, scalability, concurrency control, data abstractions, and high-level query languages. Databases are so ubiquitous and important that computer science graduates frequently cite their database class as the one most useful to them in their industry or graduate-school careers.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"31e:T805,"])</script><script>self.__next_f.push([1,"\u003cp\u003eStanford's online offering in Databases is now available as a set of five self-paced courses:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Relational Databases and SQL\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to the relational model and concepts in relational databases and relational database management systems\u003c/li\u003e\n\u003cli\u003eComprehensive coverage of SQL, the long-accepted standard query language for relational database management systems\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Advanced Topics in SQL (prerequisite: Relational Databases and SQL)\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCreating indexes for increased query performance\u003c/li\u003e\n\u003cli\u003eUsing transactions for concurrency control and failure recovery\u003c/li\u003e\n\u003cli\u003eDatabase constraints: key, referential integrity, and \"check\" constraints\u003c/li\u003e\n\u003cli\u003eDatabase triggers\u003c/li\u003e\n\u003cli\u003eHow views are created, used, and updated in relational databases\u003c/li\u003e\n\u003cli\u003eAuthorization in relational databases\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: OLAP and Recursion\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eStar schemas, the data cube concept, and On-Line Analytical Processing (OLAP) features in relational databases including the Cube and Rollup operators\u003c/li\u003e\n\u003cli\u003eThe SQL standard for queries over recursively-defined relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Modeling and Theory\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eRelational algebra – the algebraic query language that provides the formal foundations of SQL\u003c/li\u003e\n\u003cli\u003eDependency theory and normal forms in relational databases as the basis of schema design\u003c/li\u003e\n\u003cli\u003eThe data-modeling component of the Unified Modeling Language (UML), how UML diagrams are translated to relations\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eDatabases: Semistructured Data\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe XML model for semistructured and self-describing data, including DTDs and some features of XML Schema\u003c/li\u003e\n\u003cli\u003eThe JSON model for human-readable structured or semistructured data\u003c/li\u003e\n\u003cli\u003eThe XPath language for processing XML data, and many features of the more advanced XQuery language\u003c/li\u003e\n\u003cli\u003eAn introduction to the XSLT rule-based language for querying and transforming XML data\u003c/li\u003e\n\u003c/ul\u003e"])</script><script>self.__next_f.push([1,"31f:T48c,\u003cp\u003e\u003cstrong\u003e\u003cspan lang=\"en\"\u003eArithmetics\u003c/span\u003e :\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eArithmetical terms and signs\u003c/li\u003e\n\u003cli\u003eMethods of basic calculation\u003c/li\u003e\n\u003cli\u003eFractions \u0026amp; decimals, factors \u0026amp; multiples, measures \u0026amp; conversion factors\u003c/li\u003e\n\u003cli\u003eRatio \u0026amp; proportion, averages \u0026amp; percentages\u003c/li\u003e\n\u003cli\u003eAreas \u0026amp; volumes\u003c/li\u003e\n\u003cli\u003eSquares \u0026amp; square roots, cubes \u0026amp; cube roots\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eAlgebra:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003esolve simple algebraic expressions\u003c/li\u003e\n\u003cli\u003eAddition, subtraction, multiplication, division\u003c/li\u003e\n\u003cli\u003eUse of brackets\u003c/li\u003e\n\u003cli\u003eSimple algebraic fractions\u003c/li\u003e\n\u003cli\u003eSolve simple linear equations\u003c/li\u003e\n\u003cli\u003eSimultaneously equations \u0026amp; 2nd degree equations with one unknow\u003c/li\u003e\n\u003cli\u003eIndices \u0026amp; powers, negative \u0026amp; fractional indices\u003c/li\u003e\n\u003cli\u003eBinary and other numbering systems\u003c/li\u003e\n\u003cli\u003eLogarithms\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGeometry:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eSimple geometrical constructions\u003c/li\u003e\n\u003cli\u003eGraphical representation\u003c/li\u003e\n\u003cli\u003eNature and use of graphs, graphs of equations and functions\u003c/li\u003e\n\u003cli\u003eSimple trigonometry \u0026amp; trigonometrical relationships\u003c/li\u003e\n\u003cli\u003eUse of tables\u003c/li\u003e\n\u003cli\u003eRectangular \u0026amp; polar coordinates\u003c/li\u003e\n\u003c/ul\u003e320:T6fb,\u003cp\u003eActualmente, en el mercado energético existen muchos fabricantes de sistemas de generación de energía renovable que requieren que los expertos y aprendices involucrados en el diseño y operación de estos sistemas, incluido el mantenimiento, comprendan e incluyan las herramientas y métodos disponibles en el área de circuitos eléctricos para ajustarlos correctamente. tus diseños e ideas.\u003c/p\u003e\n\u003cp\u003eTradicionalmente, un curso de circuitos contiene uno de dos componentes: análisis de corriente continua (CC) o análisis de corriente alterna (CA). Dado que los sistemas híbridos de energía renovable utilizan ambos tipos de voltaje debido a la integración de recursos energéticos, este curso proporciona las herramientas necesarias para comprender y analizar las redes eléctricas en sistemas de generación de energía eléctrica de corriente continua y"])</script><script>self.__next_f.push([1," corriente alterna.\u003c/p\u003e\n\u003cp\u003eDurante esta experiencia comprenderemos las variables para analizar el comportamiento de elementos eléctricos interconectados dentro de una red. También abordaremos la medición de variables de elementos de una red eléctrica, que a su vez son compartidos por varios elementos de la red. Posteriormente construiremos modelos y simularemos sistemas eléctricos de corriente alterna o continua con Simscape de Simulink (MATLAB).\u003c/p\u003e\n\u003cp\u003ePor otro lado, relacionaremos las herramientas del álgebra lineal con los modelos de sistemas eléctricos para comprenderlos, construir nuestros propios modelos y visualizar datos creados a partir de las simulaciones realizadas con Simscape de MATLAB. Finalmente, identificaremos las diferentes herramientas matemáticas disponibles para la solución y análisis de circuitos eléctricos, que nos permitirán comprender el funcionamiento de los modelos.\u003c/p\u003e321:T9e4,"])</script><script>self.__next_f.push([1,"\u003cp\u003eParte 1: El cerebro y el aprendizaje de matemáticas..\u003c/p\u003e\n\u003cp\u003eDerribando los mitos sobre matemáticas.\u003c/p\u003e\n\u003cp\u003eTodo el mundo puede aprender matemáticas bien. No hay tal cosa como una \"persona de matemáticas\". Esta sesión dará impresionante nueva evidencia sobre el crecimiento del cerebro, y considera lo que significa para los estudiantes de matemáticas.\u003c/p\u003e\n\u003cp\u003eMatemáticas y Mentalidad\u003c/p\u003e\n\u003cp\u003eCuando las personas cambian su mentalidad de fija a de crecimiento su potencial de aprendizaje aumenta drásticamente. En esta sesión se animará a los participantes a desarrollar una mentalidad de crecimiento para las matemáticas.\u003c/p\u003e\n\u003cp\u003eErrores y velocidad\u003c/p\u003e\n\u003cp\u003eEvidencia reciente del cerebro muestra el valor de que los estudiantes trabajen en contenido desafiante e incluso de cometer errores. Sin embargo, muchos estudiantes tienen miedo de los errores y creen que significa que no son una \"persona de matemáticas\". En esta sesión se animará a los estudiantes a pensar de manera positiva acerca de los errores. También se ayudará a disipar los mitos acerca de las matemáticas y la velocidad.\u003c/p\u003e\n\u003cp\u003eParte 2: Estrategias para el éxito..\u003c/p\u003e\n\u003cp\u003eFlexibilidad Numérica, Razonamiento Matemático y Conexiones\u003c/p\u003e\n\u003cp\u003eEn esta sesión los participantes participarán en una \"conversación de números\" y verán diferentes soluciones de problemas numéricos para entender y aprender maneras de actuar sobre los números flexiblemente. El sentido numérico es fundamental para todos los niveles de las matemáticas y la falta de sentido numérico es la razón por la que muchos estudiantes reprueban cursos de álgebra y más allá. Los participantes también aprenderán sobre el valor de hablar, razonar, y hacer conexiones en matemáticas.\u003c/p\u003e\n\u003cp\u003ePatrones numéricos y Representaciones\u003c/p\u003e\n\u003cp\u003eEn esta sesión, los participantes verán que las matemáticas son un tema que se compone de grandes ideas conectadas. Ellos aprenderán sobre el valor de el dar sentido, la intuición y el dibujo matemático. Una sección especial sobre fracciones ayudará a los estudiantes a aprender las grandes ideas en las fracciones y la importancia del conocimiento de las grandes ideas en las matemáticas en general.\u003c/p\u003e\n\u003cp\u003eMatemáticas en la vida, naturaleza, y trabajo\u003c/p\u003e\n\u003cp\u003eEn esta sesión, los participantes verán las matemáticas como algo valioso, emocionante, y presente en toda la vida. Verán patrones matemáticos en la naturaleza y en diferentes deportes, explorando a fondo las matemáticas en la danza y malabares.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"322:T4b6,\u003cul\u003e\u003cli\u003eHow to make conjectures, construct logical arguments, and justify your reasoning\u003c/li\u003e\n\t\u003cli\u003eThe concept of function in mathematics, function characteristics and properties, and rate of change of functions\u003c/li\u003e\n\t\u003cli\u003eModeling of common relations and functions such as linear, power, exponential, and logarithmic functions using statistical regression and matrix methods\u003c/li\u003e\n\t\u003cli\u003eAn exploration of algebra and geometry, and the connections between the two in analytic geometry\u003c/li\u003e\n\t\u003cli\u003eProperties and applications of exponential and logarithmic functions including exponential growth and decay and The Logistic Function\u003c/li\u003e\n\t\u003cli\u003eThe development of the trigonometric functions and identities along with applications of trigonometry\u003c/li\u003e\n\t\u003cli\u003eLimits and rate of change of functions as a precursor to Calculus\u003c/li\u003e\n\t\u003cli\u003eOther Coordinates Systems – an investigation of parametrization of the plane and the polar coordinate system along with exploration and use of vectors\u003c/li\u003e\n\t\u003cli\u003eSequences and Series including The Method of Induction\u003c/li\u003e\n\t\u003cli\u003eBasic probability and combinatorics used in an investigation and development of the Binomial Theorem and its connections to Pascal’s Triangle\u003c/li\u003e\n\u003c/ul\u003e323:T491,\u003cp\u003eIf you want to learn the basic physics of solids, fluids, heat and mass transport, this is the course you have been looking for. It combines the power and beauty of mathematics with physical intuition for a comprehensive understanding of continuum physics.\u003c/p\u003e\n\u003cp\u003eThe course begins with an overview of vectors and tensors. It then proceeds through fundamental concepts of motion, balance laws, constitutive relations and thermodynamics. This introductory course addresses mainly solid and fluid mechanics, but approaches them in a unified manner. The follow-up, advanced course extends this treatment to thermomechanics, variational principles and mass transport.\u003c/p\u003e\n\u003cp\u003eFinally, a word on the treatment of the subject: it is mathematical. We know of no other way to do continuum physics. While the course is rigorous, it"])</script><script>self.__next_f.push([1," is neither abstract nor formal. In every segment connections are made with the physics of the subject. Simple but instructive props such as a deformable plastic bottle, water and food coloring are used throughout the course. Finally, the time-honored continuum potato has been supplanted by an icon of American life: the continuum football.\u003c/p\u003e324:Tc05,"])</script><script>self.__next_f.push([1,"\u003cp\u003eThis comprehensive MicroBachelors program in Mathematics and Statistics Fundamentals introduces students to the essential mathematical and statistical concepts, methods and techniques which they can use to grow their skills in quantitative careers, or as a step towards further study at undergraduate level or in specialised subjects.\u003c/p\u003e\r\n\r\n\u2028\u003cp\u003eSpanning four individual courses, all of which are self-paced and asynchronous, this programme provides students with maximum flexibility to learn with a world-leading institution from anywhere in the world in a way that fits their schedule. Students will be introduced to foundational mathematical and statistical concepts, as well as gain essential skills in the methods of calculus and linear algebra required for economic-based subjects.\u003c/p\u003e\r\n\u2028\r\n\u003cp\u003eThese courses are based on service-level statistics courses offered as part of the University of London degree programmes in Economics, Management, Finance and the Social Sciences (EMFSS), with academic direction from the London School of Economics and Political Science (LSE). They equip students with the fundamental knowledge and tools to set them up for success in second and third-year courses in subjects such as economics, finance, data science, mathematics, statistics, business analytics and programming.\u003c/p\u003e\r\n\r\n\u003cp\u003eThose that complete this MicroBachelors program may wish to go on to apply to the University of London's academically rigorous EMFSS degree programmes that give learners the opportunity to earn a BSc from a top London university wherever they are in the world.\u003c/p\u003e\r\n\r\n\u003cp\u003eShould you wish, you may elect to just study some of the individual courses within the MicroBachelors program, perhaps to build or refresh quantitative skills for career advancement.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo prior mathematics or statistics knowledge is required for this programme.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cb\u003eMathematics 1a: Differential calculus\u003c/b\u003e \r\n\u003cul\u003e\r\n\u003cli\u003eFunctions and graphs\u003c/li\u003e\r\n\u003cli\u003eThe derivative\u003c/li\u003e\r\n\u003cli\u003eCurve sketching and optimisation\u003c/li\u003e \r\n\u003cli\u003eFunctions of two variables and partial derivatives\u003c/li\u003e \r\n\u003cli\u003eCritical points of two-variable functions\u003c/li\u003e\r\n\u003c/ul\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cb\u003eMathematics 1b: Integral calculus, algebra, and applications\u003c/b\u003e \r\n\u003cul\u003e\r\n\u003cli\u003eIntegration\u003c/li\u003e\r\n\u003cli\u003eProfit maximisation\u003c/li\u003e\r\n\u003cli\u003eConstrained optimisation\u003c/li\u003e \r\n\u003cli\u003eMatrices, vectors, and linear equations\u003c/li\u003e \r\n\u003cli\u003eSequences, series, and financial modelling\u003c/li\u003e\r\n\u003c/ul\u003e\r\n \r\n\u003cp\u003e\u003cb\u003eStatistics 1a: Introductory statistics, probability and estimation\u003c/b\u003e \r\n\u003cul\u003e\r\n\u003cli\u003eMathematical revision and the nature of statistics\u003c/li\u003e \r\n\u003cli\u003eData visualisation and descriptive statistics\u003c/li\u003e \r\n\u003cli\u003eProbability theory\u003c/li\u003e \r\n\u003cli\u003eThe normal distribution and ideas of sampling\u003c/li\u003e \r\n\u003cli\u003ePoint and interval estimation\u003c/li\u003e \r\n\u003c/ul\u003e\u003c/p\u003e\r\n \r\n\u003cp\u003e\u003cb\u003eStatistics 1b: Statistical methods\u003c/b\u003e \r\n\u003cul\u003e\r\n\u003cli\u003eHypothesis testing I\u003c/li\u003e \r\n\u003cli\u003eHypothesis testing II\u003c/li\u003e\r\n\u003cli\u003eContingency tables and the chi-squared test\u003c/li\u003e \r\n\u003cli\u003eSampling design and some ideas underlying causation\u003c/li\u003e \r\n\u003cli\u003eCorrelation and linear regression\u003c/li\u003e\r\n\u003c/ul\u003e\u003c/p\u003e"])</script><script>self.__next_f.push([1,"325:T919,"])</script><script>self.__next_f.push([1,"\u003cp\u003eWhether you want to make a strong start to a master’s degree, solidify your knowledge in a professional context or simply brush up on fundamentals in calculus, this program will get you up to speed.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program will enable you to review the relevant topics and offer you an overview of the calculus common in most engineering bachelor’s programs.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe courses in this program provide enough depth to cover the calculus you need to succeed in your engineering master’s or professional work in areas such as structural engineering, integrated product design, machine learning, geomatics and more.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the first course you will review all the basic concepts and practice and refresh your skills, from functions to differential equations. By the end you will be able to solve a wide range of differential equations.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe second course will review all the basic concepts and you will practice and refresh the skills related to functions of several variables. Topics covered include contour plots, partial and directional derivatives, extreme values, double and triple integrals and common coordinate changes.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese courses are self-paced, self-contained and modular, to make it easier to review specific topics and practice as often as you want without having to follow the entire courses.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program is ideal for:\r\n\u003cul\u003e\r\n\u003cli\u003eProspective engineering students who want to meet the prerequisites for a MSc program, be better prepared or refresh their mathematics knowledge before starting a master’s degree.\u003c/li\u003e\r\n\u003cli\u003eEngineering or bachelor students who realize that they have a gap in their math knowledge or would like an additional challenge in mathematics not offered by their studies.\u003c/li\u003e\r\n\u003cli\u003eWorking professionals who would like to improve their math knowledge.\u003c/li\u003e\r\n\u003cli\u003eAnyone interested in university level mathematics.\u003c/li\u003e\r\n\u003c/u\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program will refresh your knowledge, test your skills and review the relations between the many concepts in calculus. As review courses, you are expected to have previously studied or be familiar with most of the material.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program is part of our series ‘Mastering Mathematics for Engineers’, together with ‘Mastering Linear Algebra’ and ‘Mastering Probability and Statistics’.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"326:Tc66,"])</script><script>self.__next_f.push([1,"\u003cb\u003e\u003cp\u003eEssential Math for AI:\u003c/b\u003e\u003c/br\u003e\r\nEssential Math for AI is the first course within the two-part bridge series designed to ensure learners possess the prerequisite skills for more advanced courses in the \u003ca href=\"https://ai.engineering.columbia.edu/\"\u003eAI Professional Certificate program\u003c/a\u003e. This course serves as a review and refresher of the key mathematical concepts - discrete math, calculus, linear algebra, and probability theory. It is not an in-depth exploration of these topics; instead, it will focus on concepts that have applications in various areas of artificial intelligence.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy completing this course, you will be prepared to tackle advanced AI courses with confidence. This course is specifically crafted to bridge any gaps in mathematical knowledge, ensuring a robust understanding of fundamental concepts in math. Throughout this course, you will develop and refine essential skills and knowledge, recalling and articulating basic concepts in discrete math, calculus, linear algebra, and probability theory. Additionally, you will be able to apply the acquired knowledge to solve problems across various areas of artificial intelligence.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis course is offered by Professor Daniel Bauer, a renowned Lecturer in the discipline of natural language processing in the department of computer science at Columbia Engineering, Columbia University. It offers a unique opportunity to learn from one of the top engineering schools, enhancing your credentials and positioning you for success in the rapidly evolving field of artificial intelligence.\u003c/p\u003e \r\n\r\n\u003cb\u003e\u003cp\u003eProgramming \u0026 Data Structures:\u003c/b\u003e\u003c/br\u003e\r\nProgramming \u0026 Data Structures is the second course within the two-part bridge series designed to ensure learners possess the prerequisite skills for more advanced courses in the \u003ca href=\"https://ai.engineering.columbia.edu/\"\u003eAI Professional Certificate program\u003c/a\u003e. This course serves as a review and refresher of the key concepts in programming and data structures, emphasizing their applications in various areas of artificial intelligence.\u003c/p\u003e \r\n\r\n\u003cp\u003eBy taking this course, you will develop fundamental programming skills and utilize built-in data structures and object-oriented programming concepts in Python for effective data manipulation and algorithm development. By the end of this course, you will be familiar with essential Python packages for data analysis, visualization, numeric computing, and machine learning. Additionally, you will be able to write and debug simple programs in Python, including using functions, object-oriented programming, and built-in data structures like lists and dictionaries. Finally, you will understand and use basic functionality in NumPy, Matplotlib, Sci-kit learn, and Pandas.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis course is offered by Professor Daniel Bauer, a renowned Lecturer in the discipline of natural language processing in the department of computer science at Columbia Engineering, Columbia University. It offers a unique opportunity to learn from one of the top engineering schools, enhancing your credentials and positioning you for success in the rapidly evolving field of artificial intelligence.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"327:T925,"])</script><script>self.__next_f.push([1,"\u003cp\u003eWhether you want to make a strong start to a master’s degree, solidify your knowledge in a professional context or simply brush up on fundamentals in probability and statistics, this program will get you up to speed.\u003c/p\u003e\r\n\r\n\u003cp\u003eStatistics is used quite intensively in many engineering contexts and master’s programs. As soon as you are dealing with real-life data, you will need to get an idea of what these data tell you and how you can visualize this (descriptive statistics). You will also want to perform some analysis (inferential statistics), build a model that mimics reality, estimate some quantities, or test some hypotheses. Along the way you will learn how to apply these concepts to datasets, using the statistical software R.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program also provides an introduction to probability theory. You will encounter discrete and continuous random variables and learn in which situations they appear, what their properties are and how they interact. Probability theory can be applied to learn more about real-life problems, and it is useful for building models. Moreover, it provides the basis for statistics and applications in data analysis. Therefore, it is a useful subject for any aspiring engineer.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese courses are self-paced, self-contained and modular, to make it easier to review specific topics and practice as often as you want without having to follow the entire courses.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program is ideal for:\r\n\u003cul\u003e\r\n\u003cli\u003eProspective engineering students who want to meet the prerequisites for a MSc program, be better prepared or refresh their mathematics knowledge before starting a master’s degree.\u003c/li\u003e\r\n\u003cli\u003eEngineering or bachelor students who realize that they have a gap in their math knowledge or would like an additional challenge in mathematics not offered by their studies.\u003c/li\u003e\r\n\u003cli\u003eWorking professionals who would like to improve their math knowledge.\u003c/li\u003e\r\n\u003cli\u003eAnyone interested in university level mathematics.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program will refresh your knowledge and review the relevant topics. As review courses, you are expected to have previously studied or be familiar with most of the material.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis program is part of our series ‘Mastering Mathematics for Engineers’, together with ‘Mastering Calculus’ and ‘Mastering Linear Algebra’.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"328:T63e,\u003cp\u003eWant to learn how to think clearly about important financial decisions and improve your financial literacy? Finance for Everyone will showcase the beauty and power of finance. This introductory finance course will be a gateway into the world of finance and will examine multiple applications to apply to your everyday life. Join us to better understand how to apply frameworks and tools to make smart financial choices.\u003c/p\u003e\n\u003cp\u003eYou will be able to value the impact of different choices available to you: from renting or buying, evaluating car, home and student loans, or deciding whether to go to college versus pursuing a new idea to simply understanding how the financial world works.\u003c/p\u003e\n\u003cp\u003eStarting with time value of money, the course will help you develop a full appreciation for the many applications of finance. Using real world examples, the course will enable you to understand and analyze many personal and professional decisions we confront on a daily basis. You will understand stocks and bonds, learn to allocate scarce resources in a value-add way, and adopt smart tools for making every day decisions.\u003c/p\u003e\n\u003cp\u003eFinance is simultaneously a way of thinking and a set of tools. Finance is everywhere. There are no prerequisites for this course except for a sense of curiosity and a positive attitude. However, a comfort level with algebra and numbers and an understanding of accounting (the language of business) will clearly help. We will, however, try to cover everything starting with fundamentals and highlight when there is a need to do some further work in specific subjects.\u003c/p\u003e329:Tbfc,"])</script><script>self.__next_f.push([1,"\u003cp\u003eThis course aims at acquainting you with the modeling and simulation of complex articulated mechanical systems, denoted as multibody systems, such as vehicles, merry-go-rounds, motorbikes, cranes, human bodies, suspensions, robot manipulators, mechanical transmissions, etc.\u003c/p\u003e\n\u003cp\u003eThis course is based on (1) video clips focusing on the main theoretical background and concepts, (2) well-illustrated written sections giving more details about the mathematical formulation, and (3) questions, exercises and modeling projects.\u003c/p\u003e\n\u003cp\u003eDespite the intrinsic complexity of such systems in terms of morphology and motions, basic skills in Newtonian mechanics, linear algebra and numerical methods are sufficient to model them, provided that the endless and tedious computation related to their internal kinematics and dynamics are at our disposal. This is the purpose of the symbolic program ROBOTRAN*, which can be used with this course and can automatically generate the full set of equations of motion of MBS, in a symbolic manner, i.e. exactly as if you were writing them by hand, whatever the size and the morphological complexity of the application. Hence, this course will instead teach you how to intervene upstream and downstream this generation step.\u003c/p\u003e\n\u003cp\u003eUpstream the latter, you will learn how to translate a real system, e.g. a car suspension, into a virtual multibody model comprising bodies, joints, internal or external forces and torques and imposed motion… with a level of refinement that will be dictated by the original issue. For example, what is the minimum tire ground force when the car suspension is excited by a shaker?\u003c/p\u003e\n\u003cp\u003eDownstream the symbolic generation, your intervention will consist in:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eCompleting the symbolic model with features that are specific to your system, e.g. a tire force model or the tuning of a motion controller, among other things;\u003c/li\u003e\n\u003cli\u003eImplementing under the form of a program (in Python, Matlab, or C) a time simulation to solve the differential equations of motion, given the original question: e.g. find the transient motion of the system submitted to forces and torques and compute a specific force time history or the maximal acceleration of a particular point.\u003c/li\u003e\n\u003cli\u003eSelecting the most suitable results, including self-explanatory - and sometimes funny - video animations of your multibody system in motion.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIn sum, this course, based on the use of the ROBOTRAN* symbolic generator, will allow you to focus on the most interesting aspects of the multibody modeling process, by entirely mastering your computer model from the input data to the results, instead of using a black-box multibody software that clearly goes against the educational objective of this course. \u003c/p\u003e\n\u003cp\u003eEnjoy Multibody Dynamics! \u003c/p\u003e\n\u003cp\u003e*Note: The course was built to teach modeling and simulation of multibody systems, and not to teach any specific software. However, we suggest that you use the symbolic ROBOTRAN program to model and study the various multibody systems proposed in this course.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"32a:T733,\u003cp dir=\"ltr\"\u003eIn this course about ADME and PK, students will learn how the PK properties of drug candidate are analyzed to guide decisions by the entire drug discovery team. The three-week course starts with the use of drug concentration-time data points to determine the key pharmacokinetic parameters of a compound. The second week focuses on the types of laboratory and animal studies that assist in the prediction of the human PK properties of a compound. In the final week, students will learn how the PK properties are used with efficacy data to predict the human efficacious dose and assist in drug formulation.\u003c/p\u003e\n\u003cp dir=\"ltr\"\u003e\n\nStudents in the course should understand human anatomy and cell structure. Students should also be comfortable with algebraic expressions, including logarithmic and exponential functions. A fundamental understanding of the structure of organic molecules and their functional groups will also be helpful. The course is designed in modules. Each module opens with a short video on a selected topic. The module continues with a short reading or exercise with an assessment activity. Each module will require approximately 1 hour to complete, and the course includes 15 modules. Two approaches to the course are recommended. One, a student might spend an hour per day on the course and complete all 15 modules in approximately three weeks. Two, a student with additional available time may be able to work through the entire course in just a single week or over an extended weekend.\u003c/p\u003e\n\u003cp dir=\"ltr\"\u003e\n\nStudents signed up for the Audit Track have access to the instructional video materials. Students enrolled through the Verified Track have access to the instructional videos, the readings and activities, the assessments, as well as selected additional videos related to the primary instructional videos.\u003c/p\u003e32b:T551,\u003cp\u003e\u003cspan lang=\"EN\"\u003eBasics of Bayesian Data Analysis Using R is part one of the Bayesian Data Analysis in R professional certificate. \u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eBayesian approac"])</script><script>self.__next_f.push([1,"h is becoming increasingly popular in all fields of data analysis, including but not limited to epidemiology, ecology, economics, and political sciences. It also plays an increasingly important role in data mining and deep learning. Let this course be your first step into Bayesian statistics.\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eHere, you will find a practical introduction to applied Bayesian data analysis with the emphasis on formulating and answering real life questions. You will learn how to combine the data generating mechanism, likelihood, with prior distribution using Bayes’ Theorem to produce the posterior distribution. You will investigate the underlying theory and fundamental concepts by way of simple and clear practical examples, including a case of linear regression.\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eYou will be introduced to the Gibbs sampler – the simplest version of the powerful Markov Chain Monte Carlo (MCMC) algorithm. And you will see how the popular R-software can be used in this context, and encounter some Bayesian R packages .\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eA facility in basic algebra and calculus as well as programming in R is recommended.\u003c/p\u003e32c:T527,\u003cp\u003e\u003cspan lang=\"EN\"\u003e•\u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Bayes’ Theorem. Differences between classical (frequentist) and Bayesian inference.\u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Posterior inference: summarizing posterior distributions, credible intervals, posterior probabilities, posterior predictive distributions and data visualisation.\u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Gamma-poisson, beta-binomial and normal conjugate models for data analysis.\u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Bayesian regression analysis and analysis of variance (ANOVA).\u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Use of simulations for posterior inference. Simple applications of Markov chain-Monte Car"])</script><script>self.__next_f.push([1,"lo (MCMC)\u003c/span\u003e methods and their implementation in R.\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Bayesian cluster analysis. \u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Model diagnostics and comparison.\u003c/span\u003e\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e•\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003cspan lang=\"EN\"\u003e Ensuring you answer the actual research question rather than “apply methods to the data”\u003c/span\u003e\u003c/p\u003e32d:T72c,\u003cp\u003ePodemos afirmar sin temor a equivocarnos que un buen curso de Cálculo amplía la visión del estudiante en su campo y en su área de estudio.\u003c/p\u003e\n\u003cp\u003eEl Cálculo Diferencial es el lenguaje en el que algunas leyes de la naturaleza se expresan, por ejemplo: nos permite describir el movimiento y el cálculo de trayectorias en dinámica, nos ayuda a resolver problemas de áreas y volúmenes, a resolver problemas extremales en campos como economía y matemática financiera.\u003c/p\u003e\n\u003cp\u003eEn este curso se presentan los conceptos y demostraciones con extrema precisión y cuidado; se hace énfasis en los fundamentos del Cálculo para que lo que se enseña quede fundamentado y claramente explicado.\u003c/p\u003e\n\u003cp\u003eSe estudia el calculo diferencial de funciones de variable real, por lo tanto, se parte de una estructura algebráica de los números reales, Se utilizan conceptos puramente métricos, se introduce el concepto de distancia para explicar que nos vamos acercando a algo, es decir, se define la estructura del espacio métrico que da paso al primer tema sucesiones de números reales para continuar con sucesiones convergentes, límite funcional, continuidad y la derivada de una función hasta llegar a problemas de aplicación.\u003c/p\u003e\n\u003cp\u003eEste curso esta en modalidad \"self-paced\", es decir, \"a tu propio ritmo de aprendizaje\". ¿Qué significa esto? Que puedes empezar el curso cuando quieras y seguirlo a tu ritmo ya que no hay fecha prevista de cierre o apertura \u003cstrong\u003ede lecciones\u003c/strong\u003e , no sigue un calendario establecido; los trabajos y exámenes no tienen fecha de inicio o e"])</script><script>self.__next_f.push([1,"ntrega, puedes enviarlos en cualquier momento antes de la fecha de finalización del curso.\u003c/p\u003e\n\u003cp\u003eEsperamos que este curso en línea de Cálculo Diferencial logre cambiar la percepción de los estudiantes en cuanto a su aplicación e importancia.\u003c/p\u003e32e:Td6d,"])</script><script>self.__next_f.push([1,"\u003cp\u003eThis course aims at acquainting you with the modeling and simulation of constrained multibody systems, and especially mechanical systems with kinematic loops, such as real vehicle or bicycle suspensions, parallel manipulators or robots, musculoskeletal systems, etc. \u003c/p\u003e\n\u003cp\u003eYou will also learn to deal with more advanced numerical analyses: \u003cbr /\u003e\n• Direct kinematics;\u003cbr /\u003e\n• Inverse kinematics;\u003cbr /\u003e\n• Equilibrium;\u003cbr /\u003e\n• Modal analysis;\u003cbr /\u003e\n• Direct Dynamics;\u003cbr /\u003e\n• Inverse Dynamics. \u003c/p\u003e\n\u003cp\u003eThis course is based on (1) video clips focusing on the main theoretical background and concepts, (2) well-illustrated written sections given more details about the mathematical formulation, and (3) questions, exercises and modeling projects. \u003c/p\u003e\n\u003cp\u003eDespite the intrinsic complexity of such systems in terms of morphology and motions, basic skills in Newtonian mechanics, linear algebra and numerical methods are sufficient to model them, provided that the endless and tedious computation related to their internal kinematics and dynamics are at our disposal. This is the purpose of the symbolic program ROBOTRAN, which can be used with this course and can automatically generate the full set of equations of motion of a constrained MBS, in a symbolic manner, i.e. exactly as if you were writing them by hand, whatever the size and their morphological complexity of the application. Hence, this course will instead teach you how to intervene upstream and downstream this generation step. \u003c/p\u003e\n\u003cp\u003eUpstream the latter, you will learn how to translate a real system, e.g. a car suspension, into a virtual multibody model comprising algebraic constraints between joints, kinematic loops, etc. \u003c/p\u003e\n\u003cp\u003eDownstream the symbolic generation, your intervention will consist in: \u003c/p\u003e\n\u003cp\u003e• Completing the symbolic model with features that are specific for your system, e.g. a tire force model or the tuning of a motion controller, among other things; \u003c/p\u003e\n\u003cp\u003e• Selecting and implementing under the form of a program (in Python, Matlab, or C) the suitable numerical method to solve the differential equations of motion, given the original question; (1) an equilibrium solution can give you the static forces and the system deflection, (2) a time simulation can compute any transient motion of the system submitted to forces and torques, (3) a modal analysis will provide you with the eigenmodes that inform you about the system stability and damping characteristics, (4) an inverse dynamics study can provide you with the necessary forces and torques for any prescribed motion of the system, (5) etc. \u003c/p\u003e\n\u003cp\u003e• Selecting the most suitable results, including self-explanatory - and sometimes funny - video animations of your multibody system in motion. \u003c/p\u003e\n\u003cp\u003eIn sum, this course, based on the use of the ROBOTRAN* symbolic generator, will allow you to focus on the most interesting aspects of the multibody modeling process, by entirely mastering your computer model from the input data to the results, instead of using a black-box multibody program that clearly goes against the educational objective of such a course. \u003c/p\u003e\n\u003cp\u003eEnjoy Multibody Dynamics! \u003c/p\u003e\n\u003cp\u003e*Note: The course was built to teach modeling and simulation of multibody systems, and not to teach any specific software. However, we suggest that you use the symbolic ROBOTRAN program to model and study the various multibody systems proposed in this course.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"32f:T6a5,\u003cp dir=\"ltr\"\u003eIn this course about measuring biological activity, students will learn different methods of activity measurement encountered at different stages of a drug program. The three-week course starts with an introduction to drug targets, which are biological molecules affected by drugs. The second week emphasizes biochemical, cellular, and computational methods for determining the extent to which a drug can affect the action of its target and associated signal pathways. In the final week, students will transition to in vivo studies and the interpretation of dose-response curves.\u003c/p\u003e\n\u003cp dir=\"ltr\"\u003e\n\nStudents in the course should understand the concepts of proteins and biological pathways. Students should also be comfortable with algebraic expressions, including logarithmic functions. The course is designed in modules. Each module opens with a short video on a selected topic. The module continues with a short reading or exercise with an assessment activity. Each module will require approximately 1 hour to complete, and the course includes 15 modules. Two approaches to the course are recommended. One, a student might spend an hour per day on the course and complete all 15 modules in approximately three weeks. Two, a student with additional available time may be able to work through the entire course in just a single week or over an extended weekend.\u003c/p\u003e\n\u003cp dir=\"ltr\"\u003e\n\nStudents signed up for the Audit Track have access to the instructional video materials. Students enrolled through the Verified Track have access to the instructional videos, the readings and activities, the assessments, as well as selected additional videos related to the primary instructional videos.\u003c/p\u003e330:T50c,\u003cp\u003e\u003cspan lang=\"EN\"\u003eAdvanced\u003c/span\u003e Bayesian Data Analysis Using R is part two of the Bayesian Data Analysis in R professional certificate.\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eThis course is directed at people who are already familiar with the fundamentals of Bayesian inference. It explores further the concepts, methods, and algorithm"])</script><script>self.__next_f.push([1,"s introduced in the part one (Introductory Bayesian Data Analysis Using R).\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eThe course places mixed effects regression models useful for experiments with repeated measures or additional hierarchy often encountered in biostatistics, ecology and health sciences among others within the Bayesian context. It takes a closer look at the Markov Chain Monte Carlo (MCMC) algorithms, why they work and how to implement them in the R programming language. Convergence assessment and visualisation of the results are discussed in some detail. The course also explores Bayesian model averaging, often used in machine learning, all within the context of practical examples. \u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eFinally, we discuss different kinds of missing data, and the Bayesian methods of dealing with such situations.\u003cspan lang=\"EN\"\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003ePrior facility in basic algebra and calculus as well as programming in R is highly recommended.\u003c/p\u003e331:T5a7,\u003cp\u003e\u003cem\u003eThis course is part of the IPSAMOOC project, a joint venture Federica Weblearning - IPSA, the International Political Science Association\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eEmile Durkheim, one of the founders of modern empirical social science, once stated that the comparative method is the only one that suits the social sciences. But Descartes hadposited that \"comparaison n'est pas raison,\" which means that comparison is not reason (or theory) by itself. So what's the right answer? \u003c/p\u003e\n\u003cp\u003eThis course provides an introduction and overview of systematic comparative analysis in the social sciences, and shows you how to use this method for constructive explanation and theory building. \u003c/p\u003e\n\u003cp\u003eA major portion of the course is devoted to new approaches and software that have been developed in recent yearsto handle highly complex cases. Such cases includecomparisons of EU member states, Latin American political systems,and particular policy areas. Procedures such as Qualitative Comparative Analysis (QCA) and related methods are able to reduce complexity and to arrive at \"configura"])</script><script>self.__next_f.push([1,"tional\" solutions based on set theory and Boolean algebra. These are more meaningful in this context thancommonly used, broad-based statistical methods. \u003c/p\u003e\n\u003cp\u003eInthe last section, these methods are contrasted with more common statistical comparative methods at the macro-level. We'll discuss various states or societies and their respective strengths and weaknesses.\u003c/p\u003e332:T751,\u003cp dir=\"ltr\"\u003eIn this course about lead selection and lead optimization, students will learn methods for discovering and optimizing leads with the end goal of advancing a compound into the clinic. The three-week course starts with the processes for finding molecules with promising activity for initiation of a drug program. The second week covers the criteria used to select the best molecules as new leads for the optimization stage. In the final week, students will learn different methods for identifying structural changes that will optimize a lead’s efficacy and PK properties as well as reduce toxicity.\u003c/p\u003e\n\u003cp dir=\"ltr\"\u003e\n\nStudents in the course should understand pharmacodynamics, drug activity, pharmacokinetics, and preclinical safety. Students should also be comfortable with algebraic expressions, including logarithmic and exponential functions. A fundamental understanding of the structure of organic molecules and their functional groups is also required. The course is designed in modules. Each module opens with a short video on a selected topic. The module continues with a short reading or exercise with an assessment activity. Each module will require approximately 1 hour to complete, and the course includes 15 modules. Two approaches to the course are recommended. One, a student might spend an hour per day on the course and complete all 15 modules in approximately three weeks. Two, a student with additional available time may be able to work through the entire course in just a single week or over an extended weekend.\u003c/p\u003e\n\u003cp dir=\"ltr\"\u003e\n\nStudents signed up for the Audit Track have access to the instructional video materials. Students enro"])</script><script>self.__next_f.push([1,"lled through the Verified Track have access to the instructional videos, the readings and activities, the assessments, as well as selected additional videos related to the primary instructional videos.\u003c/p\u003e333:T5d6,\u003cp\u003eIs my code fast? Can it be faster? Scientific computing, machine learning, and data science are about solving problems that are compute intensive. Choosing the right algorithm, extracting parallelism at various levels, and amortizing the cost of data movement are vital to achieving scalable speedup and high performance. \u003c/p\u003e\n\u003cp\u003eIn this course, the simple but important example of matrix-matrix multiplication is used to illustrate fundamental techniques for attaining high-performance on modern CPUs. A carefully designed and scaffolded sequence of exercises leads the learner from a naive implementation to one that effectively utilizes instruction level parallelism and culminates in a high-performance multithreaded implementation. Along the way, it is discovered that careful attention to data movement is key to efficient computing. \u003c/p\u003e\n\u003cp\u003ePrerequisites for this course are a basic understanding of matrix computations (roughly equivalent toWeeks 1-5 of Linear Algebra: Foundations to Frontiers on edX) and an exposure to programming. Hands-on exercises start with skeletal code in the C programming language that is progressively modified, so that extensive experience with C is not required. Access to a relatively recent x86 processor such as Intel Haswell or AMD Ryzen (or newer) running Linux is required. \u003c/p\u003e\n\u003cp\u003eMATLAB Online licenses will be made available to the participants free of charge for the duration of the course. \u003c/p\u003e\n\u003cp\u003eJoin us to satisfy your need for speed!\u003c/p\u003e334:T6ac,\u003cp\u003eIs my program correct? Will it give the right output for all possible permitted inputs? Computers are now essential in everyday life. Incorrect programs lead to frustration in the best case and disaster in the worst. Thus, knowing how to construct correct programs is a skill that all who program computers must strive to master"])</script><script>self.__next_f.push([1,".\u003c/p\u003e\n\u003cp\u003eIn this computer science course, we will present \"goal oriented programming\" the way Edsger Dijkstra, one of the most influential computer scientists, intended. You will learn how to derive programs hand-in-hand with their proofs of correctness. The course presents a methodology that illustrates goal-oriented programming, starting with the formalization of what is to be computed, and then growing the program hand-in-hand with its proof of correctness. The methodology demonstrates that, for a broad class of matrix operations, the development, implementation, and establishment of correctness of a program can be made systematic.\u003c/p\u003e\n\u003cp\u003eSince this technique focuses on program specifications, it often leads to clearer, correct programs in less time. The approach rapidly yields a family of algorithms from which you can then pick the algorithm that has desirable properties, such as attaining better performance on a given architecture.\u003c/p\u003e\n\u003cp\u003eThe audience of this MOOC extends beyond students and scholars interested in the domains of linear algebra algorithms and scientific computing. This course shows how to make the formal derivation of algorithms practical and will leave you pondering how our results might extend to other domains.\u003c/p\u003e\n\u003cp\u003eAs a result of support from MathWorks, learners will be granted access to MATLAB for the duration of the course.\u003c/p\u003e335:T759,\u003cp\u003eEste curso forma parte del proyecto IPSAMOOC, una iniciativa conjunta entre Federica Weblearning e IPSA, la Asociación Internacional de Ciencias Políticas.\u003c/p\u003e\n\u003cp\u003eEmile Durkheim, uno de los fundadores de las ciencias sociales modernas y empíricas, declaró una vez que el método comparativo es el único que encaja con las ciencias sociales. Pero Descartes había dicho que “comparaison n’est pas raison”, que significa que la comparación no es una razón (o teoría) por sí misma. Así que, ¿cuál es la respuesta correcta?\u003c/p\u003e\n\u003cp\u003eEste curso ofrece una introducción y vista general del análisis comparativo sistemático en las ciencias sociale"])</script><script>self.__next_f.push([1,"s, y te muestra cómo usar este método para una explicación útil y la construcción de una teoría.\u003c/p\u003e\n\u003cp\u003eUna buena parte del curso se dedica a los nuevos enfoques y al software que se ha desarrollado en los últimos años para ocuparse de casos altamente complejos. Dichos casos incluyen comparaciones entre estados miembros de la UE, los sistemas políticos de América Latina y de particulares áreas políticas. Procedimientos como el Análisis Comparativo Cualitativo (ACC) y los métodos relacionados son capaces de reducir la complejidad para obtener soluciones “configurativas” basadas en la teoría de los conjuntos y el álgebra booleana. Estos son más importantes en este contexto que en el uso común, los métodos estadísticos de amplio espectro.\u003c/p\u003e\n\u003cp\u003eEn la última sección, estos métodos se contrastan con métodos estadísticos y comparativos más comunes en un macro nivel. Debatiremos sobre varios países o sociedades y sus respectivas fuerzas y debilidades.\u003c/p\u003e\n\u003cp\u003eEste curso ha sido posible gracias a la colaboración del profesor Luis Castellano y a la \"Convocación de traductores para IPSAMOOCs\" organizada por la Asociación Internacional de Estudiantes de Ciencias Políticas.\u003c/p\u003e336:Tb4d,"])</script><script>self.__next_f.push([1,"\u003cp\u003eThis course teaches the R programming language in the context of statistical data and statistical analysis in the life sciences.\u003c/p\u003e\n\u003cp\u003eWe will learn the basics of statistical inference in order to understand and compute p-values and confidence intervals, all while analyzing data with R code. We provide R programming examples in a way that will help make the connection between concepts and implementation. Problem sets requiring R programming will be used to test understanding and ability to implement basic data analyses. We will use visualization techniques to explore new data sets and determine the most appropriate approach. We will describe robust statistical techniques as alternatives when data do not fit assumptions required by the standard approaches. By using R scripts to analyze data, you will learn the basics of conducting reproducible research.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the course materials into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. We start with simple calculations and descriptive statistics. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"337:Tc54,"])</script><script>self.__next_f.push([1,"\u003cp\u003eIf you’re interested in data analysis and interpretation, then this is the data science course for you. We start by learning the mathematical definition of distance and use this to motivate the use of the singular value decomposition (SVD) for dimension reduction of high-dimensional data sets, and multi-dimensional scaling and its connection to principle component analysis. We will learn about the \u003cem\u003ebatch effect,\u003c/em\u003e the most challenging data analytical problem in genomics today, and describe how the techniques can be used to detect and adjust for batch effects. Specifically, we will describe the principal component analysis and factor analysis and demonstrate how these concepts are applied to data visualization and data analysis of high-throughput experimental data.\u003c/p\u003e\n\u003cp\u003eFinally, we give a brief introduction to machine learning and apply it to high-throughput, large-scale data. We describe the general idea behind clustering analysis and descript K-means and hierarchical clustering and demonstrate how these are used in genomics and describe prediction algorithms such as k-nearest neighbors along with the concepts of training sets, test sets, error rates and cross-validation.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"338:T12ef,"])</script><script>self.__next_f.push([1,"\u003cp\u003eWe will explain how to perform the standard processing and normalization steps, starting with raw data, to get to the point where one can investigate relevant biological questions. Throughout the case studies, we will make use of exploratory plots to get a general overview of the shape of the data and the result of the experiment. We start with RNA-seq data analysis covering basic concepts and a first look at FASTQ files. We will also go over quality control of FASTQ files; aligning RNA-seq reads; visualizing alignments and move on to analyzing RNA-seq at the gene-level : counting reads in genes; Exploratory Data Analysis and variance stabilization for counts; count-based differential expression; normalization and batch effects. Finally, we cover RNA-seq at the transcript-level : inferring expression of transcripts (i.e. alternative isoforms); differential exon usage. We will learn the basic steps in analyzing DNA methylation data, including reading the raw data, normalization, and finding regions of differential methylation across multiple samples. The course will end with a brief description of the basic steps for analyzing ChIP-seq datasets, from read alignment, to peak calling, and assessing differential binding patterns across multiple samples.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e\n\u003cp\u003eHarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the \u003ca href=\"https://www.edx.org/edx-terms-service\" title=\"Follow link\"\u003eedX honor code\u003c/a\u003e, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.\u003c/p\u003e\n\u003cp\u003eHarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our \u003ca href=\"http://harvardx.harvard.edu/research-statement\" title=\"Follow link\"\u003eresearch statement \u003c/a\u003eto learn more.\u003c/p\u003e\n\u003cp\u003eHarvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact \u003ca href=\"mailto:harvardx@harvard.edu\"\u003eharvardx@harvard.edu\u003c/a\u003e and/or \u003ca href=\"https://www.edx.org/contact-us\" title=\"Follow link\"\u003ereport your experience through the edX contact form\u003c/a\u003e.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"339:T1129,"])</script><script>self.__next_f.push([1,"\u003cp\u003eWe begin with an introduction to the relevant biology, explaining what we measure and why. Then we focus on the two main measurement technologies: next generation sequencing and microarrays. We then move on to describing how raw data and experimental information are imported into R and how we use Bioconductor classes to organize these data, whether generated locally, or harvested from public repositories or institutional archives. Genomic features are generally identified using intervals in genomic coordinates, and highly efficient algorithms for computing with genomic intervals will be examined in detail. Statistical methods for testing gene-centric or pathway-centric hypotheses with genome-scale data are found in packages such as limma, some of these techniques will be illustrated in lectures and labs.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e\n\u003cp\u003eHarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the \u003ca href=\"https://www.edx.org/edx-terms-service\" title=\"Follow link\"\u003eedX honor code\u003c/a\u003e, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.\u003c/p\u003e\n\u003cp\u003eHarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our \u003ca href=\"http://harvardx.harvard.edu/research-statement\" title=\"Follow link\"\u003eresearch statement \u003c/a\u003eto learn more.\u003c/p\u003e\n\u003cp\u003eHarvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact \u003ca href=\"mailto:harvardx@harvard.edu\"\u003eharvardx@harvard.edu\u003c/a\u003e and/or \u003ca href=\"https://www.edx.org/contact-us\" title=\"Follow link\"\u003ereport your experience through the edX contact form\u003c/a\u003e.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"33a:Tab6,"])</script><script>self.__next_f.push([1,"\u003cp\u003eIn this course you’ll learn various statistics topics including multiple testing problem, error rates, error rate controlling procedures, false discovery rates, q-values and exploratory data analysis. We then introduce statistical modeling and how it is applied to high-throughput data. In particular, we will discuss parametric distributions, including binomial, exponential, and gamma, and describe maximum likelihood estimation. We provide several examples of how these concepts are applied in next generation sequencing and microarray data. Finally, we will discuss hierarchical models and empirical bayes along with some examples of how these are used in practice. We provide R programming examples in a way that will help make the connection between concepts and implementation.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"33b:T11a6,"])</script><script>self.__next_f.push([1,"\u003cp\u003eIn this course, we begin with approaches to visualization of genome-scale data, and provide tools to build interactive graphical interfaces to speed discovery and interpretation. Using knitr and rmarkdown as basic authoring tools, the concept of reproducible research is developed, and the concept of an executable document is presented. In this framework reports are linked tightly to the underlying data and code, enhancing reproducibility and extensibility of completed analyses. We study out-of-memory approaches to the analysis of very large data resources, using relational databases or HDF5 as \"back ends\" with familiar R interfaces. Multiomic data integration is illustrated using a curated version of The Cancer Genome Atlas. Finally, we explore cloud-resident resources developed for the Encyclopedia of DNA Elements (the ENCODE project). These address transcription factor binding, ATAC-seq, and RNA-seq with CRISPR interference.\u003c/p\u003e\n\u003cp\u003eGiven the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.\u003c/p\u003e\n\u003cp\u003eThese courses make up two Professional Certificates and are self-paced:\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Analysis for Life Sciences:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistics-and-r\"\u003ePH525.1x: Statistics and R for the Life Sciences\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-linear-models-and-matrix-algebra\"\u003ePH525.2x: Introduction to Linear Models and Matrix Algebra\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/statistical-inference-and-modeling-for-high-throug\"\u003ePH525.3x: Statistical Inference and Modeling for High-throughput Experiments\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/high-dimensional-data-analysis\"\u003ePH525.4x: High-Dimensional Data Analysis\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eGenomics Data Analysis:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/introduction-to-bioconductor-annotation-and-analys\"\u003ePH525.5x: Introduction to Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/case-studies-in-functional-genomics\"\u003ePH525.6x: Case Studies in Functional Genomics\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://www.edx.org/course/advanced-bioconductor\"\u003ePH525.7x: Advanced Bioconductor\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis class was supported in part by NIH grant R25GM114818.\u003c/p\u003e\n\u003cp\u003eHarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the \u003ca href=\"https://www.edx.org/edx-terms-service\" title=\"Follow link\"\u003eedX honor code\u003c/a\u003e, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.\u003c/p\u003e\n\u003cp\u003eHarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our \u003ca href=\"http://harvardx.harvard.edu/research-statement\" title=\"Follow link\"\u003eresearch statement \u003c/a\u003eto learn more.\u003c/p\u003e\n\u003cp\u003eHarvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact \u003ca href=\"mailto:harvardx@harvard.edu\"\u003eharvardx@harvard.edu\u003c/a\u003e and/or \u003ca href=\"https://www.edx.org/contact-us\" title=\"Follow link\"\u003ereport your experience through the edX contact form\u003c/a\u003e.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"33c:T45b,\u003cp\u003eThis quantum computing course explores the basic design principles of today's quantum computer systems. In this course, students will learn to work with the IBM Qiskit software tools to write simple programs in Python and execute them on cloud-accessible quantum hardware. Topics covered in this course include:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to systems research in quantum computing\u003c/li\u003e\n\u003cli\u003eFundamental rules in quantum computing, Bloch Sphere, Feynman Path Sum\u003c/li\u003e\n\u003cli\u003eSequential and parallel execution of quantum gates, EPR pair, no-cloning theorem, quantum teleportation\u003c/li\u003e\n\u003cli\u003eMedium-size algorithms for NISQ (near-term intermediate scale quantum) computers\u003c/li\u003e\n\u003cli\u003eQuantum processor microarchitecture: classical and quantum control\u003c/li\u003e\n\u003cli\u003eQuantum program compilation and qubit memory management\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eKeywords: quantum computing, computer science, linear algebra, compiler, circuit optimization, python, qiskit, quantum algorithms, quantum technology, superposition, entanglement, qubit technology, superconducting qubit, transmon qubit, ion-trap qubit, photonic qubit, real quantum computers\u003c/p\u003e33d:T4b8,Computational thinking is becoming widely recognized as a skill necessary for every educated person in a technologically advanced society.\u0026nbsp; \u003cbr /\u003e\u003cbr /\u003eWe will focus on just a subset of computational thinking which concerns creating models of the physical world \u0026ndash; something that engineers frequently need to do.\u0026nbsp; Because of that choice, this course covers many topics normally viewed as within the domain of mathematics such as algebra and calculus, but the solution procedures are algorithmic rather than symbolic. \u003cbr /\u003e \u003cbr /\u003eThe major themes of the course are:\u003cbr /\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eRepresentation -- How do you encode information about the world in a computer?\u0026nbsp; How do your choices in representation affect the ease with which you can solve problems?\u003c/li\u003e\r\n\u003cli\u003eDecomposition -- How do you break a large and diverse problem into many simpler parts?\u003c/li\u003e\r\n\u003cli\u003eDiscretization -- How do you break u"])</script><script>self.__next_f.push([1,"p space and time into a large number of relatively small pieces?\u0026nbsp; What are the alternative ways of doing this?\u0026nbsp; What are the consequences of discretization procedures for accuracy and speed?\u003c/li\u003e\r\n\u003cli\u003eVerification -- How do you build confidence in the results of a model?\u003c/li\u003e\r\n\u003c/ul\u003e33e:T886,"])</script><script>self.__next_f.push([1,"\u003cp\u003ePrinciples of Electric Circuits (20220214x) is one of the kernel courses in the broad EECS subjects. Almost all the required courses in EECS are based on the concepts learned in this course, so it’s the gateway to a qualified EECS engineer.\u003c/p\u003e\n\u003cp\u003eThe main content of this course contains linear and nonlinear resistive circuits, time domain analysis of the dynamic circuits, and the steady state analysis of the dynamic circuits with sinusoidal excitations. Important concepts, e.g. filters, resonance, quiescent point, etc., cutting-edge elements, e.g. MOSFETs and Op Amps, etc., systematic analyzing tools, e.g. node method and phasor method, etc., and real-world engineering applications, e.g. square wave generator and pulse power supply for railgun, etc., will be discussed in depth.\u003c/p\u003e\n\u003cp\u003eIn order to facilitate the learning for students with middle school level, we prepare the necessary knowledge for calculus and linear algebra in week 0. With your effort, we can show you the fantastic view of electricity.\u003c/p\u003e\n\u003cp\u003eThe circuit principle course is the most important basic course for all electrical majors. Subsequent basic courses and professional courses for all majors are based on the knowledge system of this course. Therefore, it is one of the \"housekeeping courses\" for undergraduates in electrical majors. The main contents of the circuit principle course include: linear resistance circuit analysis, non-linear resistance circuit analysis, time domain analysis of dynamic circuits and steady-state analysis of dynamic circuits under sinusoidal excitation. The teaching of the Circuit Principles course at Tsinghua University includes basic methods of circuit analysis, contemporary circuit components, practical engineering applications of circuit principles, etc., providing students with a solid foundation and rich applications.\u003c/p\u003e\n\u003cp\u003eIn order to facilitate the learning of students with only middle school knowledge, the Circuit Principles MOOC specifically uses week 0 to prepare the necessary foundations of calculus, linear algebra and college physics and electricity. We are confident that you can understand the wonders of the electrical world.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"33f:T45b,\u003cp\u003eThis quantum computing course explores the basic design principles of today's quantum computer systems. In this course, students will learn to work with the IBM Qiskit software tools to write simple programs in Python and execute them on cloud-accessible quantum hardware. Topics covered in this course include:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to systems research in quantum computing\u003c/li\u003e\n\u003cli\u003eFundamental rules in quantum computing, Bloch Sphere, Feynman Path Sum\u003c/li\u003e\n\u003cli\u003eSequential and parallel execution of quantum gates, EPR pair, no-cloning theorem, quantum teleportation\u003c/li\u003e\n\u003cli\u003eMedium-size algorithms for NISQ (near-term intermediate scale quantum) computers\u003c/li\u003e\n\u003cli\u003eQuantum processor microarchitecture: classical and quantum control\u003c/li\u003e\n\u003cli\u003eQuantum program compilation and qubit memory management\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eKeywords: quantum computing, computer science, linear algebra, compiler, circuit optimization, python, qiskit, quantum algorithms, quantum technology, superposition, entanglement, qubit technology, superconducting qubit, transmon qubit, ion-trap qubit, photonic qubit, real quantum computers\u003c/p\u003e340:T45b,\u003cp\u003eThis quantum computing course explores the basic design principles of today's quantum computer systems. In this course, students will learn to work with the IBM Qiskit software tools to write simple programs in Python and execute them on cloud-accessible quantum hardware. Topics covered in this course include:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIntroduction to systems research in quantum computing\u003c/li\u003e\n\u003cli\u003eFundamental rules in quantum computing, Bloch Sphere, Feynman Path Sum\u003c/li\u003e\n\u003cli\u003eSequential and parallel execution of quantum gates, EPR pair, no-cloning theorem, quantum teleportation\u003c/li\u003e\n\u003cli\u003eMedium-size algorithms for NISQ (near-term intermediate scale quantum) computers\u003c/li\u003e\n\u003cli\u003eQuantum processor microarchitecture: classical and quantum control\u003c/li\u003e\n\u003cli\u003eQuantum program compilation and qubit memory management\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eKeywords: quantum computing, computer science, linear algebra, compiler, circuit optimization, "])</script><script>self.__next_f.push([1,"python, qiskit, quantum algorithms, quantum technology, superposition, entanglement, qubit technology, superconducting qubit, transmon qubit, ion-trap qubit, photonic qubit, real quantum computers\u003c/p\u003e341:T8f7,"])</script><script>self.__next_f.push([1,"\u003cp\u003e\u003cstrong\u003eComing Soon February 2021.\u003c/strong\u003e Technological innovations have revolutionized the way we view and interact with the world around us. Editing a photo, re-mixing a song, automatically measuring and adjusting chemical concentrations in a tank: each of these tasks requires real-world data to be captured by a computer and then manipulated digitally to extract the salient information. Ever wonder how signals from the physical world are sampled, stored, and processed without losing the information required to make predictions and extract meaning from the data?\u003c/p\u003e\r\n\u003cp\u003eStudents will find out in this rigorous mathematical introduction to the engineering field of signal processing: the study of signals and systems that extract information from the world around us. This course will teach students to analyze discrete-time signals and systems in both the time and frequency domains. Students will learn convolution, discrete Fourier transforms, the z-transform, and digital filtering. Students will apply these concepts in interactive MATLAB programming exercises (all done in browser, no download required).\u003c/p\u003e\r\n\u003cp\u003eLearners should have strong problem solving skills, the ability to understand mathematical representations of physical systems, and advanced mathematical background (one-dimensional integration, matrices, vectors, basic linear algebra, imaginary numbers, and sum and series notation). This course is an excerpt from an advanced undergraduate class at Rice University taught to all electrical and computer engineering majors.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cb\u003e\u003ca href=\"https://support.edx.org/hc/en-us/articles/360060426873-MicroBachelors-Coaching-FAQs\"\u003eCoaching\u003c/a\u003e\u003c/b\u003e\u003cbr\u003e\r\nIf you are enrolled in the verified track (paid track) in any course that is a part of a MicroBachelors program, including this course, you are eligible for \u003ci\u003ecoaching at no additional cost. Please note that coaching is only available via SMS to U.S. phone lines.\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eOur coaches (real humans) are ready to help you with career exploration, navigating resources, staying motivated, and solving problems along the way to your goals.\u003c/p\u003e\r\n\r\n\u003cp\u003eLearn more about the \u003ca href=\"https://www.youtube.com/watch?v=14QVCTJvHQo\u0026feature=youtu.be\"\u003evalue of coaching\u003c/a\u003e directly from one of our coaches, Erin.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"342:T5a6,\u003cp\u003eThis course is part of \u003ca href=\"https://www.edx.org/gfa\"\u003eGlobal Freshman Academy (GFA)\u003c/a\u003e, which means you can earn transferable ASU credit toward your college degree.\u003c/p\u003e\n\u003cp\u003eIn this college-level Precalculus course, you will prepare for calculus by focusing on quantitative reasoning and functions. You’ll develop the skills to describe the behavior and properties of linear, exponential, logarithmic, polynomial, rational, and trigonometric functions.\u003c/p\u003e\n\u003cp\u003eContent in this course will be adaptive, allowing you to achieve mastery in a certain concept before moving on to the next. Utilizing the ALEKS learning system, students in this personalized, self-paced course will be instructed on the topics they are most ready to learn while also providing individualized coaching as you move through each topic.\u003c/p\u003e\n\u003cp\u003eBefore taking this course, you should already have a strong understanding of algebraic skills such as factoring, basic equation solving, and the rules of exponents and radicals.\u003c/p\u003e\n\u003cp\u003eThis 3 credit hour course satisfies the Mathematical Studies (MA) general studies requirement at Arizona State University. The cost to convert to credit is $600. This course may satisfy a general education requirement at other institutions; however, it is strongly encouraged that you consult with your institution of choice to determine how these credits will be applied to their degree requirements prior to transferring the credit.\u003c/p\u003e343:T682,\u003cp\u003eThe skills and expertise required for a career in finance are in high demand across countless industries. From asset management, to corporations, to official institutions, the career opportunities for qualified finance professionals continue to grow and evolve. For example, demand for financial analysts is predicted to grow at a faster than average rate of 11% through 2026 (\u003ca href=\"https://www.thebalancecareers.com/top-jobs-for-finance-majors-2064048\"\u003eSource\u003c/a\u003e). And according to Glassdoor, the median salary of a quantitative financial analyst was $106,575. (\u003ca href=\"https"])</script><script>self.__next_f.push([1,"://www.wallstreetmojo.com/quantitative-financial-analyst/\"\u003eSource\u003c/a\u003e)\u003c/p\u003e\r\n\r\n\u003cp\u003eThe MITx MicroMasters® Program in Finance offers recent graduates, early to mid-stage professionals, and other individuals interested in pursuing a career in finance, an opportunity to advance in the finance field or fast-track an MIT Sloan Master of Finance through a rigorous, comprehensive online curriculum, delivered by the world-renowned MIT Sloan School of Management.\u003c/p\u003e \r\n\r\n\u003cp\u003eDrawn from the STEM-based curriculum taught on campus, all five online courses in this program mirror on-campus graduate-level MIT coursework and cover the following topics: modern finance, financial accounting, mathematical methods for quantitative finance, and derivatives markets. Learners who complete and pass each course in this online program may earn a MicroMasters program certificate in finance, and are considered affiliate members of the MIT Alumni Association. Those learners are eligible to apply to the MIT Sloan Master of Finance and upon acceptance, earn credit for the work performed online.\u003c/p\u003e344:T6d4,\u003cp\u003eEn este programa Xseries se aborda el estudio del universo físico desde diversas perspectivas, para que un estudiante de física comience con éxito su carrera universitaria.\u003c/p\u003e\r\n\r\n\u003cp\u003eEl programa está compuesto por tres cursos, los cuales ayudarán al estudiante a obtener los conocimientos de física que son fundamentales para estudiar ingeniería. En el programa el estudiante:\r\n\r\n\u003cul\u003e\r\n\u003cli\u003eAnalizará los objetos en movimiento y las fuerzas que provocan dicho movimiento. Conocerá las definiciones y analizará todas las magnitudes y leyes físicas que permiten describir geométrica y causalmente el movimiento de cuerpos representados por un punto.\u003c/li\u003e\r\n\u003cli\u003eEstudiará la gran variedad de fenómenos ondulatorios que se observan en la naturaleza.\u003c/li\u003e\r\n\u003cli\u003eConocerá las definiciones y analizará las magnitudes físicas que permiten caracterizar los diferentes tipos de ondas que existen, resaltando la importancia de la naturaleza del medio"])</script><script>self.__next_f.push([1," físico donde se esté propagando la onda.\u003c/li\u003e\r\n\u003cli\u003eAsí mismo obtendrá conocimientos sobre los fenómenos que pueden experimentar las ondas cuando se propagan en el espacio analizando: el principio de Huygens, fenómenos de reflexión, refracción, difracción, superposición y polarización de las ondas y el efecto Doppler.\u003c/li\u003e\r\n\u003cli\u003eInvestigará las causas y conocerá las leyes de la interacción electromagnética. Esta interacción es una de las más importantes que caracterizan nuestra vida diaria, ya que muchos de los fenómenos que se observan a nuestro alrededor, incluidos los químicos y biológicos, son debidos a la interacción electromagnética entre átomos y moléculas. Analizará el origen de esta interacción y conocerá las leyes físicas que la gobiernan.\u003c/li\u003e345:T9c5,"])</script><script>self.__next_f.push([1,"\u003cp\u003eVous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises durant vos études en économie, ingénierie, physique, ou statistique? Ou simplement pour la beauté de la matière? Alors ce cours est fait pour vous! Outre remplir le rôle d'outil dans les différentes branches mentionnées ci-dessus (permettant la résolution de problèmes concrets), l'algèbre linéaire, qui capture l'essence des mathématiques -à savoir, l'algèbre et la géométrie- vous introduira au monde plus abstrait des mathématiques.\u003c/p\u003e\n\u003cp\u003eProposé comme complément de cours aux ingénieurs de première année à l'Ecole Polytechnique Fédérale de Lausanne, ce MOOC (composé de trois parties) n'en est pas moins un cours à part entière et peut être considéré comme une base solide d'algèbre linéaire pour tout étudiant intéressé par l'apprentissage de cette matière.\u003c/p\u003e\n\u003cp\u003eBien que les vidéos constituent le coeur du cours, des exercices de type QCM (Questions à choix multiples) ainsi que des séries au format PDF seront disponibles chaque semaine, ainsi que des corrigés appropriés. Plus précisément, les séries d'exercices seront accompagnées d'un corrigé au format PDF et certains problèmes bénéficieront d'une correction détaillée en vidéo, dans laquelle l'un des enseignants présentera la solution, étape par étape. Finalement, chaque vidéo de cours sera suivie d'un quiz, dont le but est de tester le degré d’assimilation des connaissances acquises.\u003c/p\u003e\n\u003cp\u003eLe cours est organisé en dix chapitres dans lesquels une approche très détaillée des concepts théoriques est proposée, ainsi que de multiples exemples illustratifs :\u003c/p\u003e\n\u003cp\u003e1) Systèmes d'équations linéaires.\u003c/p\u003e\n\u003cp\u003e2) Algèbre matricielle.\u003c/p\u003e\n\u003cp\u003e3) Espaces vectoriels.\u003c/p\u003e\n\u003cp\u003e4) Bases et dimensions.\u003c/p\u003e\n\u003cp\u003e5) Applications linéaires. \u003c/p\u003e\n\u003cp\u003e6) Matrices et applications linéaires.\u003c/p\u003e\n\u003cp\u003e7) Déterminants.\u003c/p\u003e\n\u003cp\u003e8) Vecteurs propres, valeurs propres, diagonalisation.\u003c/p\u003e\n\u003cp\u003e9) Produits scalaires et espaces euclidiens.\u003c/p\u003e\n\u003cp\u003e10) Matrices orthogonales et matrices symétriques.\u003c/p\u003e\n\u003cp\u003eCette première partie du cours sera dévouée à l'étude des quatre premiers chapitres cités plus haut. Aucune connaissance particulière n’est requise pour comprendre les concepts abordés dans ce MOOC, mais il est conseillé de travailler régulièrement et de manière assidue, de façon à ne pas prendre de retard lors de l'apprentissage de la matière.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"346:T9ca,"])</script><script>self.__next_f.push([1,"\u003cp\u003eVous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises durant vos études en économie, ingénierie, physique, ou statistique? Ou simplement pour la beauté de la matière? Alors ce cours est fait pour vous! Outre remplir le rôle d'outil dans les différentes branches mentionnées ci-dessus (permettant la résolution de problèmes concrets), l'algèbre linéaire, qui capture l'essence des mathématiques -à savoir, l'algèbre et la géométrie- vous introduira au monde plus abstrait des mathématiques.\u003c/p\u003e\n\u003cp\u003eProposé comme complément de cours aux ingénieurs de première année à l'Ecole Polytechnique Fédérale de Lausanne, ce MOOC (composé de trois parties) n'en est pas moins un cours à part entière et peut être considéré comme une base solide d'algèbre linéaire pour tout étudiant intéressé par l'apprentissage de cette matière.\u003c/p\u003e\n\u003cp\u003eBien que les vidéos constituent le coeur du cours, des exercices de type QCM (Questions à choix multiples) ainsi que des séries au format PDF seront disponibles chaque semaine, ainsi que des corrigés appropriés. Plus précisément, les séries d'exercices seront accompagnées d'un corrigé au format PDF et certains problèmes bénéficieront d'une correction détaillée en vidéo, dans laquelle l'un des enseignants présentera la solution, étape par étape. Finalement, chaque vidéo de cours sera suivie d'un quiz, dont le but est de tester le degré d’assimilation des connaissances acquises.\u003c/p\u003e\n\u003cp\u003eLe cours est organisé en dix chapitres dans lesquels une approche très détaillée des concepts théoriques est proposée, ainsi que de multiples exemples illustratifs :\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003eSystèmes d'équations linéaires.\u003c/li\u003e\n\u003cli\u003eAlgèbre matricielle.\u003c/li\u003e\n\u003cli\u003eEspaces vectoriels.\u003c/li\u003e\n\u003cli\u003eBases et dimensions.\u003c/li\u003e\n\u003cli\u003eApplications linéaires. \u003c/li\u003e\n\u003cli\u003eMatrices et applications linéaires.\u003c/li\u003e\n\u003cli\u003eDéterminants.\u003c/li\u003e\n\u003cli\u003eVecteurs propres, valeurs propres, diagonalisation.\u003c/li\u003e\n\u003cli\u003eProduits scalaires et espaces euclidiens.\u003c/li\u003e\n\u003cli\u003eMatrices orthogonales et matrices symétriques.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eCette deuxième partie du cours sera dévouée à l'étude des chapitres 5 à 8 cités plus haut. Une bonne connaissance de la matière enseignée dans le MOOC \u003cem\u003eAlgèbre Linéaire (Partie 1)\u003c/em\u003e est requise. Aussi, il est conseillé de travailler régulièrement et de manière assidue, de façon à ne pas prendre de retard lors de l'apprentissage de la matière.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"347:T9f9,"])</script><script>self.__next_f.push([1,"\u003cp\u003eVous voulez apprendre l'algèbre linéaire, un précieux outil complémentaire à vos connaissances acquises durant vos études en économie, ingénierie, physique, ou statistique? Ou simplement pour la beauté de la matière? Alors ce cours est fait pour vous! Outre remplir le rôle d'outil dans les différentes branches mentionnées ci-dessus (permettant la résolution de problèmes concrets), l'algèbre linéaire, qui capture l'essence des mathématiques -à savoir, l'algèbre et la géométrie- vous introduira au monde plus abstrait des mathématiques.\u003c/p\u003e\n\u003cp\u003eProposé comme complément de cours aux ingénieurs de première année à l'Ecole Polytechnique Fédérale de Lausanne, ce MOOC (composé de trois parties) n'en est pas moins un cours à part entière et peut être considéré comme une base solide d'algèbre linéaire pour tout étudiant intéressé par l'apprentissage de cette matière.\u003c/p\u003e\n\u003cp\u003eBien que les vidéos constituent le coeur du cours, des exercices de type QCM (Questions à choix multiples) ainsi que des séries au format PDF seront disponibles chaque semaine, ainsi que des corrigés appropriés. Plus précisément, les séries d'exercices seront accompagnées d'un corrigé au format PDF et certains problèmes bénéficieront d'une correction détaillée en vidéo, dans laquelle l'un des enseignants présentera la solution, étape par étape. Finalement, chaque vidéo de cours sera suivie d'un quiz, dont le but est de tester le degré d’assimilation des connaissances acquises.\u003c/p\u003e\n\u003cp\u003eLe cours est organisé en dix chapitres dans lesquels une approche très détaillée des concepts théoriques est proposée, ainsi que de multiples exemples illustratifs :\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003eSystèmes d'équations linéaires.\u003c/li\u003e\n\u003cli\u003eAlgèbre matricielle.\u003c/li\u003e\n\u003cli\u003eEspaces vectoriels.\u003c/li\u003e\n\u003cli\u003eBases et dimensions.\u003c/li\u003e\n\u003cli\u003eApplications linéaires. \u003c/li\u003e\n\u003cli\u003eMatrices et applications linéaires.\u003c/li\u003e\n\u003cli\u003eDéterminants.\u003c/li\u003e\n\u003cli\u003eVecteurs propres, valeurs propres, diagonalisation.\u003c/li\u003e\n\u003cli\u003eProduits scalaires et espaces euclidiens.\u003c/li\u003e\n\u003cli\u003eMatrices orthogonales et matrices symétriques.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eCette troisième (et dernière) partie du cours sera dévouée à l'étude des chapitres 9 et 10 cités plus haut. Une bonne connaissance de la matière enseignée dans les MOOCs _Algèbre Linéaire (Partie 1) _et _Algébre Linéaire (Partie 2) _est requise. Aussi, il est conseillé de travailler régulièrement et de manière assidue, de façon à ne pas prendre de retard lors de l'apprentissage de la matière.\u003c/p\u003e"])</script><script>self.__next_f.push([1,"348:T489,\u003cp\u003eA la fin du cours, l'étudiant sera capable\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003ede définir les concepts théoriques introduits en cours et d'en donner des exemples illustratifs ;\u003c/li\u003e\n\u003cli\u003ede reconnaître un produit scalaire et maîtriser les propriétés associées à un tel objet (e.g. Inégalité de Cauchy-Schwarz, inégalité du triangle) ;\u003c/li\u003e\n\u003cli\u003ede et maîtriser les notions de bases liées à l'orthogonalité (e.g. familles/bases orthogonales, familles/bases orthonormales, orthogonal d'un sous-espace, Théorème de Pythagore) ;\u003c/li\u003e\n\u003cli\u003ede construire une base orthonormée d'un sous-espace vectoriel d'un espace euclidien à l'aide du procédé de Gram-Schmidt ;\u003c/li\u003e\n\u003cli\u003ede calculer la meilleure approximation quadratique d'un vecteur ;\u003c/li\u003e\n\u003cli\u003ede calculer la solution au sens des moindres carrés d'un système linéaire ;\u003c/li\u003e\n\u003cli\u003ede calculer la factorisation QR d'une matrice donnée, lorsque cela est possible ;\u003c/li\u003e\n\u003cli\u003ede diagonaliser orthogonalement une matrice symétrique donnée ;\u003c/li\u003e\n\u003cli\u003ede déterminer les axes principaux d'une forme quadratique donnée ;\u003c/li\u003e\n\u003cli\u003ede calculer la décomposition en valeurs singulières d'une matrice donnée.\u003c/li\u003e\n\u003c/ul\u003e349:T6c0,\u003cp\u003eUne suite de nombres réels est une fonction f:N→R . Il est habituel d'écrire an:=f(n) pour la valeur de f en n. Par exemple, on pourrait définir une suite f(n):=an:=12n, c'est-à-dire a0=1,a1=12,a2=14,a3=18,... . Le concept central est celui de la limite d'une suite : c'est un nombre réel auquel, intuitivement, la suite donnée s'approche de plus en plus. Par exemple la suite an donnée en haut admet comme limite le nombre zéro. Nous définirons le concept de la limite d'une manière rigoureuse et développerons des méthodes pour établir l'existence d'une limite. En plus, nous découvrirons un lien entre le concept de la limite et celui de l'infimum et du supremum d'un ensemble. Une application très importante des suites de nombres réels est le fait que chaque nombre réel peut être considéré comme la limite d'une suite de nombres rationnel"])</script><script>self.__next_f.push([1,"s. Nous verrons comment obtenir le nombre irrationnel racione de 5 comme limite d'une suite de nombres rationnels. Nos étudions le concept des suites de Cauchy et des suites définies par récurrence linéaire. Nous montrons certaines propriétés des suites définies par récurrence linéaire, en faisant en lien avec les suites de Cauchy. Nous nous intéressons aux limites des suites et des sous-suites, ce qui nous amène au théorème de Bolzano-Weierstrass. A l'aide des suites, nous définissons aussi le concept des séries numériques que nous illustrons à l'aide de différents exemples. Nous définissons certains critères de convergence pour les séries, notamment le critère de d'Alembert, le critère de Cauchy, le critère de comparaison et le critère de Leibniz. Finalement, nous étudions les séries numériques avec un paramètre.\u003c/p\u003e34a:T64e,\u003cp\u003eNous introduisons les fonctions réelles d'une variable réelle. Nous commençons par définir certaines de leurs propriétés, notamment la monotonie, la parité et la périodicité ainsi que les opérations entre fonctions. Nous définissons des fonctions particulières comme les fonctions hyperboliques. Nous continuons notre étude des fonctions, en définissant les fonctions définies par étapes, en particulier les fonctions Signum et Heaviside. Des manipulations importantes en pratique sur les fonctions sont les transformations affines. Nous rentrons finalement dans le cœur du sujet en définissant la limite épointée d'une fonction en un point et donnons des exemples de limites de fonctions. Nous finissons cette discussion par le concept de la limite à gauche et à droite. Dans la suite nous reprenons l'étude de la limite d’une fonctions en commençant par définir les opérations algébriques sur les limites. Nous étudions ensuite les limites infinies de fonctions. Afin de pouvoir calculer les limites de fonctions, nous donnons le théorème des deux gendarmes et nous discutons quelques exemples avec des fonctions algébriques, exponentielles e"])</script><script>self.__next_f.push([1,"t trigonométriques. Nous reprenons le concept de la limite épointée définie précédemment, en donnant une définition différente mais équivalente. Nous introduisons le concept de la continuité. Nous la définissons de deux manières différentes comme pour les limites de fonctions. Finalement, nous utilisons la continuité pour prolonger certaines fonctions, et nous étudions la continuité sur les intervalles ouverts.\u003c/p\u003e34b:T70f,\u003cp\u003eNous arrivons au cœur du sujet de notre discussion sur les fonctions : le concept de la dérivabilité d'une fonction. Nous nous intéressons en particulier à la question de la continuité des fonctions dérivées. Nous commençons le chapitre en complétant l'étude sur les fonctions continues par l'étude de leurs propriétés sur des intervalles fermés. Ceci nous permet de définir le maximum et le minimum de fonctions continues. Nous continuons en définissant la méthode de la bissection, et en la démontrant. L'introduction des concepts du maximum et du minimum permet d'introduire certains théorèmes importants, notamment le théorème des valeurs intermédiaires et le théorème du point fixe. Ces théorèmes sont essentiels dans l'étude des fonctions. Finalement, nous arrivons à la définition de la dérivabilité et de la différentiabilité. Nous donnons quelques interprétations de ces deux définitions ainsi que la démonstration de l'équivalence de ces deux définitions. Ces discussions résultent en la construction de la fonction dérivée. Nous étudions en détail cette fonction en particulier les opérations algébriques sur ces fonctions. Nous continuons notre étude de la dérivabilité des fonctions. Nous présentons les propriétés des fonctions dérivables : la dérivée de composition de fonctions, le théorème de Rolle ainsi que le théorème des accroissements finis. Nous nous intéressons aussi à savoir si la fonction dérivée est continue, nous donnons certains exemples et contre-exemples. Finalement, nous montrons l'intérêt du théorè"])</script><script>self.__next_f.push([1,"me des accroissements finis qui est une généralisation du théorème de Rolle. Ce théorème est très important étant donnée qu'il a des implications sur la monotonie d'une fonction dérivable.\u003c/p\u003e34c:T92c,"])</script><script>self.__next_f.push([1,"\u003cp\u003eThe convergence of various fields, such as data mining, statistics, optimisation, and computing, has given rise to machine learning, which is rapidly gaining adoption across diverse industries. One of the key advantages of machine learning is its capability to handle large datasets and solve complex problems. From commercial applications like search engines and recommendation systems (think Netflix and Amazon) to financial institutions for predicting customer behaviour, compliance, risk, and algorithmic trading, machine learning is proving to be a game-changer.\u003c/p\u003e\n\u003cp\u003eIf you're looking to upskill in machine learning and its applications, the London School of Economics and Political Science (LSE) offers an eight-week online technical course that covers a comprehensive range of machine learning methods. Through practical case studies and hands-on exercises, you'll learn how to apply machine learning models to real-world problems and interpret the resulting predictions to make informed business decisions. The course is designed to help you build your expertise in modern business analytics and gain valuable insights into how machine learning is used today.\u003c/p\u003e\n\u003cp\u003eIf you are a mid to senior manager, data specialist, consultant, analyst, IT, or business professional looking to integrate machine learning techniques to improve data analytics in your organization, this online certificate course is designed for you. This course offers an in-depth exploration of core principles and machine learning methods, which will benefit those interested in practical applications. Whether you are looking to upskill, transition into a data science role, or improve your understanding of business applications of data science, this course will help develop and validate your practical machine learning skills and knowledge.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cstrong\u003ePrerequisites\u003c/strong\u003e\u003c/em\u003e \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThis course is technical in nature. It makes use of coding in R and covers the application of machine learning in business. Some algebraic and calculus knowledge is strongly advised, but is not required. Training in tertiary-level statistics and knowledge of a functional or object-oriented language are advantageous. HTML is not considered a programming language in this context. No specific software is required for this online certificate course.\u003c/em\u003e\u003c/p\u003e"])</script><script>self.__next_f.push([1,"34d:T499,In today's dynamic business landscape, data-driven decision-making is key. That's why we've designed a skills-based learning program that not only equips you with the latest analytics tools and techniques but also connects you with industry micro-credentials that are in high demand.\r\nBecome a data analyst ready to analyze and to visualize data for strategic decision making \r\nStudy contemporary data analyst skills from content derived from leading, global organizations\r\nStudy consumers’ buying habits to help businesses make more strategic decisions about how they market their products and services. \r\nMaster the process of gleaning insights from data to inform better business decisions\r\nLearn in-demand job skills from first day of instruction and bring them into the workplace\r\nThe Masters of Science in Business Analytics is designed to prepare learners for data analyst careers. A data analyst finds a solution to a problem or provides an answer to a question. This career tasks a data analyst to gather, purify, and analyze data sets. Contemporary data analysts work in a variety of fields, including government, business, finance, law enforcement, and science.34e:Ta08,"])</script><script>self.__next_f.push([1,"Louisiana State University is a Top 100 Public University with a dedicated focus on student involvement, research opportunities, and experiential learning. With more than 330 fields of study and 70 majors, LSU offers students opportunities for hands-on experience working alongside world-class faculty. Top-ranked and popular programs include business, engineering, petroleum engineering, and STEM.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"34f:T966,"])</script><script>self.__next_f.push([1,"- #147 National Universities - U.S. News \u0026 World Report, 2019\n- A true campus experience just minutes from the cultural and financial capital of the world\n- 240+ major companies recruit on campus Apple, IBM, AIG, Pepsi and Merrill Lynch\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"350:T707,UMass Boston, located in America’s most celebrated college city, combines the resources of a major research university and the accessibility of a public institution. With 65+ courses of study and a prestigious Honors College, UMass Boston gives you access to career opportunities, research projects, and a strong alumni network. With 11% of the student body representing 140+ countries and speaking 60+ languages, UMass Boston is truly global.\n-An undergraduate degree in Mathematics teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of geometry, topology, and number theory.\n-Mathematics students develop problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics in fields such as physics, engineering, finance, and computer science.\n-Students study the principles of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics students learn how to use mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-They also study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-Mathematics students learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.351:T9f5,"])</script><script>self.__next_f.push([1,"The University of Illinois Chicago provides a hands-on learning experience in a supportive, diverse environment. Located in downtown Chicago, UIC offers you the opportunity to live, learn, and excel in the third-largest city in the US. UIC’s top-ranked programs include engineering, business, architecture, design, education, health sciences, public health, and public affairs.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"352:Ta0b,"])</script><script>self.__next_f.push([1,"Gonzaga University’s humanistic heritage focuses on educating the mind, body, and spirit, and developing personal, academic, and professional growth through critical thought and creative innovation. Gonzaga University’s humanistic heritage focuses on educating the mind, body, and spirit, and developing personal, academic, and professional growth through critical thought and creative innovation.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"353:T9fa,"])</script><script>self.__next_f.push([1,"The University of South Carolina is a globally recognized, high-impact research university committed to a superior student experience and dedicated to innovation in learning, research, and community engagement. UofSC offers 350+ degree programs and is one of only 40 public universities to receive Carnegie Classifications for both top-tier research activity and community engagement.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"354:Tb2b,"])</script><script>self.__next_f.push([1,"Western New England University offers a hands-on and personalized educational experience, with small class sizes and nurturing faculty. The 215-acre campus offers a vibrant community where students can explore cutting-edge research, entrepreneurial prospects, and creative pursuits, all while building a wide professional network. With degree programs in high-demand fields such as engineering, health, pharmaceuticals, and business, Western New England University prepares students to get started on their career journey. Learn from industry professionals as you develop key skills and gain in-depth knowledge that will help you stand out to employers in the US, or anywhere in the world.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"355:T85d,"])</script><script>self.__next_f.push([1,"Western New England University offers a hands-on and personalized educational experience, with small class sizes and nurturing faculty. The 215-acre campus offers a vibrant community where students can explore cutting-edge research, entrepreneurial prospects, and creative pursuits, all while building a wide professional network. With degree programs in high-demand fields such as engineering, health, pharmaceuticals, and business, Western New England University prepares students to get started on their career journey. Learn from industry professionals as you develop key skills and gain in-depth knowledge that will help you stand out to employers in the US, or anywhere in the world.\n-An undergraduate degree in Mathematical Sciences teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about the use of mathematical models to solve real-world problems in fields such as engineering, physics, and finance.\n-They study probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematical Sciences students learn about the foundations of computer science, including algorithms, programming, and data structures.\n-They also study the principles of mathematical logic and the foundations of mathematics, including set theory and topology.\n-Students develop skills in problem-solving, critical thinking, and logical reasoning, which are useful in a wide range of fields.\n-They learn about the use of mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-Mathematical Sciences students study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-They learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematical Sciences prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs."])</script><script>self.__next_f.push([1,"356:Ta6f,"])</script><script>self.__next_f.push([1,"Gonzaga University’s humanistic heritage focuses on educating the mind, body, and spirit, and developing personal, academic, and professional growth through critical thought and creative innovation. Gonzaga University’s humanistic heritage focuses on educating the mind, body, and spirit, and developing personal, academic, and professional growth through critical thought and creative innovation.\n-In an undergraduate Applied Mathematics degree, students learn mathematical theories and modeling techniques and apply them to solve real-world problems in various fields. The curriculum typically includes courses in calculus, linear algebra, differential equations, probability theory, statistics, numerical analysis, and optimization. The degree program includes projects, research opportunities, and internships, and students may also study advanced topics in mathematics.\n-Calculus: Students learn calculus, including differentiation and integration, which is used to model real-world problems and analyze changes in physical and mathematical systems.\n-Linear algebra: Students learn linear algebra, including matrix algebra and eigenvalue analysis, which is used to solve systems of linear equations and in data analysis.\n-Differential equations: Students learn differential equations, which are used to model physical phenomena and systems that change over time.\n-Probability theory: Students learn probability theory, including random variables and distributions, which is used in data analysis and modeling of random phenomena.\n-Statistics: Students learn statistical methods and techniques, including regression analysis, hypothesis testing, and sampling theory, which are used in data analysis and empirical research.\n-Numerical analysis: Students learn numerical methods for solving mathematical problems that are difficult or impossible to solve analytically, such as systems of differential equations or optimization problems.\n-Optimization: Students learn optimization techniques, including linear and nonlinear programming, which are used to solve problems and model decision-making in various fields.\n-Mathematical modeling: Students learn how to model real-world problems using mathematical tools and techniques, and how to interpret and communicate the results.\n-Computer programming: Students learn computer programming and algorithm design, which is used to solve mathematical problems and implement numerical methods.\n-Advanced topics: Students may study advanced topics in mathematics, such as abstract algebra, topology, real analysis, and partial differential equations, to gain a deeper understanding of mathematical theories and applications."])</script><script>self.__next_f.push([1,"357:T99c,"])</script><script>self.__next_f.push([1,"The University of Kansas is a top-tier public research university with a commitment to a research-focused academic curriculum and career support. At KU, you can choose from over 190 fields of study, including top-ranked business, engineering, pharmacy, education, and architecture programs.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"358:T9d9,"])</script><script>self.__next_f.push([1,"Auburn University prepares you for success with its prestigious academic programs, emphasis on hands-on learning experiences, and family spirit. Auburn University offers more than 150 undergraduate degrees, including top-ranked programs in engineering, business, supply chain management, journalism, architecture and design, and fisheries/aquaculture.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"359:T636,- #147 National Universities - U.S. News \u0026 World Report, 2019\n- A true campus experience just minutes from the cultural and financial capital of the world\n- 240+ major companies recruit on campus Apple, IBM, AIG, Pepsi and Merrill Lynch\n-An undergraduate degree in Mathematics teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of geometry, topology, and number theory.\n-Mathematics students develop problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics in fields such as physics, engineering, finance, and computer science.\n-Students study the principles of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics students learn how to use mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-They also study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-Mathematics students learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.35a:T7ae,Florida International University is one of the largest public research universities in the US. The FIU Global First Year program prepares you for academic, social, and professional success. Florida International University offers 110+ undergraduate programs. International business, hospitality, engineering, and criminal justice are among FIU’s top fields of study.\n-An undergraduate degree in Mathematics and Statistics teaches students"])</script><script>self.__next_f.push([1," the principles of pure and applied mathematics, including calculus, algebra, and analysis, as well as statistical theory and methods.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics and Statistics students develop problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics and statistics in fields such as physics, engineering, finance, and data science.\n-Students study the principles of mathematical modeling and simulation, using mathematical and statistical tools to solve real-world problems.\n-Mathematics and Statistics students learn how to use mathematical and statistical software and computer programming languages to solve mathematical and statistical problems.\n-They also study the history and philosophy of mathematics and statistics, exploring the development of mathematical and statistical ideas and their relationship to other fields of study.\n-Mathematics and Statistics students learn how to communicate mathematical and statistical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics and Statistics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.35b:Ta16,"])</script><script>self.__next_f.push([1,"University of the Pacific's undergraduate programs are offered at the Stockton, California campus and offer world-class instruction in a supportive and challenging atmosphere. University of the Pacific offers 80+ undergraduate majors, small class sizes, a diverse campus experience, and internship opportunities.\n-In an undergraduate Applied Mathematics degree, students learn mathematical theories and modeling techniques and apply them to solve real-world problems in various fields. The curriculum typically includes courses in calculus, linear algebra, differential equations, probability theory, statistics, numerical analysis, and optimization. The degree program includes projects, research opportunities, and internships, and students may also study advanced topics in mathematics.\n-Calculus: Students learn calculus, including differentiation and integration, which is used to model real-world problems and analyze changes in physical and mathematical systems.\n-Linear algebra: Students learn linear algebra, including matrix algebra and eigenvalue analysis, which is used to solve systems of linear equations and in data analysis.\n-Differential equations: Students learn differential equations, which are used to model physical phenomena and systems that change over time.\n-Probability theory: Students learn probability theory, including random variables and distributions, which is used in data analysis and modeling of random phenomena.\n-Statistics: Students learn statistical methods and techniques, including regression analysis, hypothesis testing, and sampling theory, which are used in data analysis and empirical research.\n-Numerical analysis: Students learn numerical methods for solving mathematical problems that are difficult or impossible to solve analytically, such as systems of differential equations or optimization problems.\n-Optimization: Students learn optimization techniques, including linear and nonlinear programming, which are used to solve problems and model decision-making in various fields.\n-Mathematical modeling: Students learn how to model real-world problems using mathematical tools and techniques, and how to interpret and communicate the results.\n-Computer programming: Students learn computer programming and algorithm design, which is used to solve mathematical problems and implement numerical methods.\n-Advanced topics: Students may study advanced topics in mathematics, such as abstract algebra, topology, real analysis, and partial differential equations, to gain a deeper understanding of mathematical theories and applications."])</script><script>self.__next_f.push([1,"35c:T951,"])</script><script>self.__next_f.push([1,"The University of Dayton is a top-tier research university dedicated to academic excellence, community leadership, entrepreneurship, and creating a positive global impact. University of Dayton offers international students 80+ undergraduate degree options. The University of Dayton’s popular and highly ranked programs include engineering, entrepreneurship, business, and aerospace and aviation engineering.\n-In an undergraduate Applied Mathematical Economics degree, students learn mathematical modeling techniques to analyze economic systems and data, including courses in calculus, linear algebra, probability theory, statistics, optimization, game theory, and econometrics. They also apply these tools to real-world economic problems and may study microeconomics, macroeconomics, international trade, and development economics. \n-Mathematical modeling: Students learn mathematical modeling techniques to represent and analyze economic systems and data.\n-Calculus: Students learn calculus, including differentiation and integration, which is used extensively in economic analysis and optimization.\n-Linear algebra: Students learn linear algebra, including matrix algebra and eigenvalue analysis, which is used to solve systems of linear equations and in data analysis.\n-Differential equations: Students learn differential equations, which are used to model dynamic economic systems.\n-Probability theory: Students learn probability theory, including random variables and distributions, which is used in econometric analysis and financial modeling.\n-Statistics: Students learn statistical methods and techniques, including regression analysis, hypothesis testing, and sampling theory, which are used in data analysis and empirical research.\n-Optimization: Students learn optimization techniques, including linear and nonlinear programming, which are used to solve economic problems and model decision-making.\n-Game theory: Students learn game theory, which is used to analyze strategic interactions between individuals or groups in economic systems.\n-Econometrics: Students learn econometric methods, which are used to estimate and test economic models using data.\n-Microeconomics and macroeconomics: Students study microeconomic and macroeconomic concepts, including consumer and producer behavior, market structures, national income accounting, monetary policy, and fiscal policy."])</script><script>self.__next_f.push([1,"35d:Ta37,"])</script><script>self.__next_f.push([1,"UMass Boston, located in America’s most celebrated college city, combines the resources of a major research university and the accessibility of a public institution. With 65+ courses of study and a prestigious Honors College, UMass Boston gives you access to career opportunities, research projects, and a strong alumni network. With 11% of the student body representing 140+ countries and speaking 60+ languages, UMass Boston is truly global.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"35e:Ta33,"])</script><script>self.__next_f.push([1,"The University of Utah is located on a picturesque campus in Salt Lake City. Utah creates global leaders by placing a strong emphasis on entrepreneurship, innovation, and quality of life. The Utah College of Engineering - ranked #61 in Undergraduate Engineering by U.S. News \u0026 World Report (2020) - prepares students to improve the productivity, health, safety, and enjoyment of human life through leading-edge research and tech development.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"35f:T9a9,"])</script><script>self.__next_f.push([1,"- #78 National Universities - U.S. News \u0026 World Report, 2019\n- #5 Best U.S. Cities for Jobs - Fortune, 2018\n- Create meaningful change in America’s vibrant political, historical \u0026 cultural capital city\n-In an undergraduate Applied Mathematics degree, students learn mathematical theories and modeling techniques and apply them to solve real-world problems in various fields. The curriculum typically includes courses in calculus, linear algebra, differential equations, probability theory, statistics, numerical analysis, and optimization. The degree program includes projects, research opportunities, and internships, and students may also study advanced topics in mathematics.\n-Calculus: Students learn calculus, including differentiation and integration, which is used to model real-world problems and analyze changes in physical and mathematical systems.\n-Linear algebra: Students learn linear algebra, including matrix algebra and eigenvalue analysis, which is used to solve systems of linear equations and in data analysis.\n-Differential equations: Students learn differential equations, which are used to model physical phenomena and systems that change over time.\n-Probability theory: Students learn probability theory, including random variables and distributions, which is used in data analysis and modeling of random phenomena.\n-Statistics: Students learn statistical methods and techniques, including regression analysis, hypothesis testing, and sampling theory, which are used in data analysis and empirical research.\n-Numerical analysis: Students learn numerical methods for solving mathematical problems that are difficult or impossible to solve analytically, such as systems of differential equations or optimization problems.\n-Optimization: Students learn optimization techniques, including linear and nonlinear programming, which are used to solve problems and model decision-making in various fields.\n-Mathematical modeling: Students learn how to model real-world problems using mathematical tools and techniques, and how to interpret and communicate the results.\n-Computer programming: Students learn computer programming and algorithm design, which is used to solve mathematical problems and implement numerical methods.\n-Advanced topics: Students may study advanced topics in mathematics, such as abstract algebra, topology, real analysis, and partial differential equations, to gain a deeper understanding of mathematical theories and applications."])</script><script>self.__next_f.push([1,"360:T6d8,Louisiana State University is a Top 100 Public University with a dedicated focus on student involvement, research opportunities, and experiential learning. With more than 330 fields of study and 70 majors, LSU offers students opportunities for hands-on experience working alongside world-class faculty. Top-ranked and popular programs include business, engineering, petroleum engineering, and STEM.\n-An undergraduate degree in Mathematics teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of geometry, topology, and number theory.\n-Mathematics students develop problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics in fields such as physics, engineering, finance, and computer science.\n-Students study the principles of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics students learn how to use mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-They also study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-Mathematics students learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.361:T945,"])</script><script>self.__next_f.push([1,"- #78 National Universities - U.S. News \u0026 World Report, 2019\n- #5 Best U.S. Cities for Jobs - Fortune, 2018\n- Create meaningful change in America’s vibrant political, historical \u0026 cultural capital city\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"362:T9d2,"])</script><script>self.__next_f.push([1,"Cleveland State University partners with world-class hospitals, Fortune 500 companies, government research centers, and cultural institutions to give its students academic, research, and job opportunities. With more than 175+ undergraduate degrees to choose from, Cleveland State Global students are prepared to succeed in the global workforce.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"363:Ta13,"])</script><script>self.__next_f.push([1,"The University of Dayton is a top-tier research university dedicated to academic excellence, community leadership, entrepreneurship, and creating a positive global impact. University of Dayton offers international students 80+ undergraduate degree options. The University of Dayton’s popular and highly ranked programs include engineering, entrepreneurship, business, and aerospace and aviation engineering.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"364:T9ea,"])</script><script>self.__next_f.push([1,"Florida International University is one of the largest public research universities in the US. The FIU Global First Year program prepares you for academic, social, and professional success. Florida International University offers 110+ undergraduate programs. International business, hospitality, engineering, and criminal justice are among FIU’s top fields of study.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"365:T6a9,Auburn University prepares you for success with its prestigious academic programs, emphasis on hands-on learning experiences, and family spirit. Auburn University offers more than 150 undergraduate degrees, including top-ranked programs in engineering, business, supply chain management, journalism, architecture and design, and fisheries/aquaculture.\n-An undergraduate degree in Mathematics teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of geometry, topology, and number theory.\n-Mathematics students develop problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics in fields such as physics, engineering, finance, and computer science.\n-Students study the principles of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics students learn how to use mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-They also study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-Mathematics students learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.366:T6c5,The University of Illinois Chicago provides a hands-on learning experience in a supportive, diverse environment. Located in downtown Chicago, UIC offers you the opportunity to live, learn, and excel in the third-largest city in the US. UIC’s top-ranked programs include engineering, business, architecture, design, educatio"])</script><script>self.__next_f.push([1,"n, health sciences, public health, and public affairs.\n-An undergraduate degree in Mathematics teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of geometry, topology, and number theory.\n-Mathematics students develop problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics in fields such as physics, engineering, finance, and computer science.\n-Students study the principles of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics students learn how to use mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-They also study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-Mathematics students learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.367:T66c,The University of Kansas is a top-tier public research university with a commitment to a research-focused academic curriculum and career support. At KU, you can choose from over 190 fields of study, including top-ranked business, engineering, pharmacy, education, and architecture programs.\n-An undergraduate degree in Mathematics teaches students the principles of pure and applied mathematics, including calculus, algebra, and analysis.\n-Students learn about mathematical proof and how to construct rigorous and logical arguments.\n-They study the foundations of geometry, topology, and number theory.\n-Mathematics students develo"])</script><script>self.__next_f.push([1,"p problem-solving skills, critical thinking, and logical reasoning that are useful in a wide range of fields.\n-They learn about the applications of mathematics in fields such as physics, engineering, finance, and computer science.\n-Students study the principles of probability theory and statistics, including methods of statistical inference and data analysis.\n-Mathematics students learn how to use mathematical software and computer programming languages to solve mathematical problems and simulate real-world scenarios.\n-They also study the history and philosophy of mathematics, exploring the development of mathematical ideas and their relationship to other fields of study.\n-Mathematics students learn how to communicate mathematical ideas and findings through technical writing and presentations.\n-Finally, an undergraduate degree in Mathematics prepares students for careers in various fields such as academia, industry, and government, as well as for further study in graduate and professional programs.368:T9b2,"])</script><script>self.__next_f.push([1,"University of the Pacific's undergraduate programs are offered at the Stockton, California campus and offer world-class instruction in a supportive and challenging atmosphere. University of the Pacific offers 80+ undergraduate majors, small class sizes, a diverse campus experience, and internship opportunities.\n-In an undergraduate computer science degree, students learn programming, software engineering, computer organization, databases, computer networks, artificial intelligence, and mathematics. The program includes lectures, lab work, and projects.\n-Programming languages: Students learn to write code in various programming languages, such as Java, Python, and C++, and to apply programming constructs such as loops, functions, and conditionals to solve problems.\n-Data structures and algorithms: Students learn how to represent and manipulate data efficiently using structures such as arrays, lists, stacks, queues, and trees, and how to design and analyze algorithms for searching, sorting, and graph traversal.\n-Software engineering principles: Students learn how to apply principles of software engineering, such as design patterns, testing, and version control, to build maintainable and scalable software systems.\n-Computer organization and architecture: Students learn how computers work at a low level, including topics such as digital logic, instruction set architecture, and memory hierarchy.\n-Operating systems: Students learn about the design and implementation of operating systems, including topics such as process management, memory management, and file systems.\n-Databases: Students learn how to design and use databases to store, manipulate, and retrieve data using query languages such as SQL and to work with different database management systems such as MySQL and Oracle.\n-Computer networks: Students learn how to design and manage computer networks, including topics such as TCP/IP, routing, and network security.\n-Artificial intelligence: Students learn about the principles and applications of artificial intelligence, including machine learning, natural language processing, and computer vision.\n-Mathematics: Students learn mathematical concepts and methods that are foundational to computer science, such as discrete mathematics, calculus, and linear algebra.\n-Web development: Students learn how to design and develop web applications using languages and tools such as HTML, CSS, JavaScript, and web frameworks such as Django and Ruby on Rails."])</script><script>self.__next_f.push([1,"2ca:[\"$\",\"$L2ef\",null,{\"title\":\"Algebra\",\"topic\":\"Algebra\",\"categories\":[{\"productType\":\"Course\",\"categoryLabel\":\"Courses\",\"products\":[{\"productUuid\":\"502f792c-6469-49ae-bf04-b6b2ce882f14\",\"productName\":\"College Algebra\",\"productSlug\":\"learn/algebra/doane-university-college-algebra\",\"productImageUrl\":\"https://prod-discovery.edx-cdn.org/media/course/image/502f792c-6469-49ae-bf04-b6b2ce882f14-9d5ab9bfbf95.jpeg\",\"productType\":\"Course\",\"attributes\":[\"Math\"],\"partnerName\":\"Doane University\",\"partnerLogoUrl\":\"https://prod-discovery.edx-cdn.org/organization/logos/e9e90c9f-85ec-4ae5-bea8-2ecae2258446-85b6b8c0a212.png\",\"fullDescription\":\"\u003cp\u003eThis College Algebra course will cover fundamental concepts of algebra required to interpret a variety of functions and equations. 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