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<?xml version="1.0" encoding="UTF-8"?> <feed xml:lang="en-US" xmlns="http://www.w3.org/2005/Atom"> <id>tag:open.umn.edu,2005:/opentextbooks/subjects/mathematics</id> <link rel="alternate" type="text/html" href="https://open.umn.edu"/> <link rel="self" type="application/atom+xml" href="https://open.umn.edu/opentextbooks/textbooks"/> <title>Open Textbook Library - Mathematics Textbooks</title> <updated>2018-09-07T17:21:38Z</updated> <icon>https://open.umn.edu/assets/common/favicon/favicon-6666d4af5ecb597851b1bd6b4af4d8472feee5ef149656c053063f5c427c993c.ico</icon> <logo>https://open.umn.edu/assets/library/otl_logo-23d864367b91dd38b6ef8eeec20ee0ae733b8f3685c53f178fd4ea06f6a95100.webp</logo> <entry> <id>5</id> <published>2018-09-07T17:21:38Z</published> <updated>2024-09-02T13:01:14Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/a-first-course-in-linear-algebra"/> <title>A First Course in Linear Algebra</title> <content type="html"><img alt="Read more about A First Course in Linear Algebra" title="A First Course in Linear Algebra cover image" class="cover " width="350" height="500" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTI0ODUsInB1ciI6ImJsb2JfaWQifX0=--a9e73d721a2de09a42897124aa02de1ee4eec9d4/cover-350x700.png" />A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled &quot;Chapter V&quot; and the theorem that elementary matrices are nonsingular is labeled &quot;Theorem EMN.&quot; Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.</content> </entry> <entry> <id>7</id> <published>2018-09-07T17:21:38Z</published> <updated>2025-03-03T14:06:06Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/book-of-proof"/> <title>Book of Proof - Third Edition</title> <content type="html"><img alt="Read more about Book of Proof - Third Edition" title="Book of Proof - Third Edition cover image" class="cover " width="2100" height="3000" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTQyMTUsInB1ciI6ImJsb2JfaWQifX0=--56b89ca183f8abc2d90d2f65877f307ca067bcb8/Cover3BlueFront.jpg" />This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei, Christian Brothers High School, University of Texas Pan American, Schola Europaea, James Madison University, Heriot-Watt University, Prince of Songkla University, Queen Mary University of London, University of Nevada - Reno, University of Georgia - Athens, Saint Peter&#39;s University, California State University,Bogaziçi University, Pennsylvania State University, University of Notre Dame</content> </entry> <entry> <id>10</id> <published>2018-09-07T17:21:38Z</published> <updated>2023-12-04T14:00:32Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/calculus"/> <title>Calculus - Third Edition</title> <content type="html"><img alt="Read more about Calculus - Third Edition" title="Calculus - Third Edition cover image" class="cover " width="662" height="862" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTAzMzMsInB1ciI6ImJsb2JfaWQifX0=--d33da72254617dcf9f37378f4de1aef441d8c9f5/calculus.jpg" />Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.</content> </entry> <entry> <id>11</id> <published>2018-09-07T17:21:38Z</published> <updated>2024-08-19T13:05:27Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/collaborative-statistics"/> <title>Collaborative Statistics</title> <content type="html"><img alt="Read more about Collaborative Statistics" title="Collaborative Statistics cover image" class="cover " width="250" height="330" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NywicHVyIjoiYmxvYl9pZCJ9fQ==--121c091aceaea2a676b4ec5ad5f1a0ff738c2fa7/9780978745073.png" />Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza Collegein Cupertino, California. The textbook was developed over several years and has been used in regularand honors-level classroom settings and in distance learning classes. Courses using this textbook have beenarticulated by the University of California for transfer of credit. The textbook contains full materials forcourse offerings, including expository text, examples, labs, homework, and projects. A Teacher&#39;s Guide iscurrently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections willmeet the Section 508 standards for accessibility. An on-line course based on the textbook was also developed by Illowsky and Dean. It has won an awardas the best on-line California community college course. The on-line course will be available at a later dateas a collection in Connexions, and each lesson in the on-line course will be linked to the on-line textbookchapter. The on-line course will include, in addition to expository text and examples, videos of courselectures in captioned and non-captioned format. The original preface to the book as written by professors Illowsky and Dean, now follows: This book is intended for introductory statistics courses being taken by students at two– and four–yearcolleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite.The book focuses on applications of statistical knowledge rather than the theory behind it. Thetext is named Collaborative Statistics because students learn best by doing. In fact, they learn best byworking in small groups. The old saying “two heads are better than one” truly applies here. Our emphasis in this text is on four main concepts: thinking statistically incorporating technology working collaboratively writing thoughtfully These concepts are integral to our course. Students learn the best by actively participating, not by justwatching and listening. Teaching should be highly interactive. Students need to be thoroughly engagedin the learning process in order to make sense of statistical concepts. Collaborative Statistics providestechniques for students to write across the curriculum, to collaborate with their peers, to think statistically,and to incorporate technology. This book takes students step by step. The text is interactive. Therefore, students can immediately applywhat they read. Once students have completed the process of problem solving, they can tackle interestingand challenging problems relevant to today&#39;s world. The problems require the students to apply theirnewly found skills. In addition, technology (TI-83 graphing calculators are highlighted) is incorporatedthroughout the text and the problems, as well as in the special group activities and projects. The book alsocontains labs that use real data and practices that lead students step by step through the problem solvingprocess. At De Anza, along with hundreds of other colleges across the country, the college audience involves alarge number of ESL students as well as students from many disciplines. The ESL students, as well asthe non-ESL students, have been especially appreciative of this text. They find it extremely readable andunderstandable. Collaborative Statistics has been used in classes that range from 20 to 120 students, and inregular, honor, and distance learning classes.</content> </entry> <entry> <id>12</id> <published>2018-09-07T17:21:38Z</published> <updated>2024-01-22T14:52:22Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/college-algebra"/> <title>College Algebra</title> <content type="html"><img alt="Read more about College Algebra" title="College Algebra cover image" class="cover " width="240" height="313" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6OCwicHVyIjoiYmxvYl9pZCJ9fQ==--e1d523ddf3aefd719fbb7cef0b18503120f13a6b/0000CollegeAl.png" />College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as &quot;Functions First,&quot; believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.</content> </entry> <entry> <id>13</id> <published>2018-09-07T17:21:38Z</published> <updated>2024-01-22T18:49:51Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/elementary-algebra"/> <title>Elementary Algebra</title> <content type="html"><img alt="Read more about Elementary Algebra" title="Elementary Algebra cover image" class="cover " width="300" height="391" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6OSwicHVyIjoiYmxvYl9pZCJ9fQ==--fe937de771d99d8408fe066815ea4616912cea06/9781453300923.png" />It is essential to lay a solid foundation in mathematics if a student is to be competitive in today&#39;s global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course. This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below: Equivalent mathematical notation using standard text found on a keyboard A variety of applications and word problems included in most exercise sets Clearly enumerated steps found in context within carefully chosen examples Alternative methods and notation, modularly integrated, where appropriate Video examples available, in context, within the online version of the textbook Robust and diverse exercise sets with discussion board questions Key words and key takeaways summarizing each section This text employs an early-and-often approach to real-world applications, laying the foundation for students to translate problems described in words into mathematical equations. It also clearly lays out the steps required to build the skills needed to solve these equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. In addition to embedded video examples and other online learning resources, the importance of practice with pencil and paper is stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.</content> </entry> <entry> <id>21</id> <published>2018-09-07T17:21:39Z</published> <updated>2025-02-17T14:00:13Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/introduction-to-probability"/> <title>Introduction to Probability</title> <content type="html"><img alt="Read more about Introduction to Probability" title="Introduction to Probability cover image" class="cover " width="300" height="394" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTYsInB1ciI6ImJsb2JfaWQifX0=--f9ce94f1af6a792bc9a632d6315283a746607658/0000IntroPro.png" />Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continuedto influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting the risks of new medical treatments. This text is designed for an introductory probability course taken by sophomores,juniors, and seniors in mathematics, the physical and social sciences, engineering,and computer science. It presents a thorough treatment of probability ideas andtechniques necessary for a form understanding of the subject. The text can be usedin a variety of course lengths, levels, and areas of emphasis. For use in a standard one-term course, in which both discrete and continuousprobability is covered, students should have taken as a prerequisite two terms ofcalculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theoryis necessary. The text can also be used in a discrete probability course. The material has beenorganized in such a way that the discrete and continuous probability discussions arepresented in a separate, but parallel, manner. This organization dispels an overlyrigorous or formal view of probability and o?ers some strong pedagogical valuein that the discrete discussions can sometimes serve to motivate the more abstractcontinuous probability discussions. For use in a discrete probability course, studentsshould have taken one term of calculus as a prerequisite. Very little computing background is assumed or necessary in order to obtain fullbenefits from the use of the computing material and examples in the text. All ofthe programs that are used in the text have been written in each of the languagesTrueBASIC, Maple, and Mathematica.</content> </entry> <entry> <id>24</id> <published>2018-09-07T17:21:39Z</published> <updated>2024-08-19T13:05:42Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/linear-algebra"/> <title>Linear Algebra</title> <content type="html"><img alt="Read more about Linear Algebra" title="Linear Algebra cover image" class="cover " width="748" height="909" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTkwNSwicHVyIjoiYmxvYl9pZCJ9fQ==--4b93dd1f67a95b84a76c80332e51e824a93f51d3/cover.png" />This text covers the standard material for a US undergraduate first course: linear systems and Gauss&#39;s Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.</content> </entry> <entry> <id>52</id> <published>2018-09-07T17:21:40Z</published> <updated>2024-12-02T14:00:44Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/whitman-calculus"/> <title>Whitman Calculus</title> <content type="html"><img alt="Read more about Whitman Calculus" title="Whitman Calculus cover image" class="cover " width="195" height="258" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDIsInB1ciI6ImJsb2JfaWQifX0=--61716c549de596e9a943eea357bdc7aec95393bc/0000WhitCalc.png" />An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at: Boise State University, Claremont McKenna College, University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.</content> </entry> <entry> <id>57</id> <published>2018-09-07T17:21:40Z</published> <updated>2024-09-23T13:00:26Z</updated> <link rel="alternate" type="text/html" href="https://open.umn.edu/opentextbooks/textbooks/college-trigonometry"/> <title>College Trigonometry</title> <content type="html"><img alt="Read more about College Trigonometry" title="College Trigonometry cover image" class="cover " width="239" height="315" data-controller="common--cover" data-placeholder="/assets/common/placeholder-f8e123f91b7e13ad321132c609842fdd40121f691ee7db391b88763bc42be6a0.webp" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDUsInB1ciI6ImJsb2JfaWQifX0=--5e07daa661a62ff1d4004152c5436f5e74162641/0000CollegeTr.png" />Covers chapters 10-11 of Precalculus.</content> </entry> <link rel="next">https://open.umn.edu/opentextbooks/subjects/mathematics?page=2</link> </feed>