tag:open.umn.edu,2005:/opentextbooks/subjects/36?page=6Open Textbook Library - Pure Textbooks2018-09-07T17:21:50Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png2412018-09-07T17:21:50Z2024-01-22T14:51:48ZPrealgebra - 2e<img alt="Read more about Prealgebra - 2e" title="Prealgebra - 2e cover image" class="cover " width="404" height="519" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTQ4OSwicHVyIjoiYmxvYl9pZCJ9fQ==--af1e302e61cb8a534719d9238954362a99e6380f/PreAlg.PNG" />Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra or basic math course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty. The first edition of Prealgebra by OpenStax is available in web view in the ancillaries.2392018-09-07T17:21:50Z2024-01-22T14:52:31ZAlgebra and Trigonometry 2e<img alt="Read more about Algebra and Trigonometry 2e" title="Algebra and Trigonometry 2e cover image" class="cover " width="824" height="1060" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzcwNSwicHVyIjoiYmxvYl9pZCJ9fQ==--a7fde398cfa52fa9a6ff2a9081f4a4b290008235/Screen%20Shot%202022-05-27%20at%2011.39.02%20AM.png" />Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. The Algebra and Trigonometry 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text. The first edition of Algebra and Trigonometry by OpenStax is available in web view here.2102018-09-07T17:21:49Z2024-01-22T18:50:43ZLinear Algebra, Theory And Applications<img alt="Read more about Linear Algebra, Theory And Applications" title="Linear Algebra, Theory And Applications cover image" class="cover " width="652" height="848" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjQwLCJwdXIiOiJibG9iX2lkIn19--359176ec3811266b5049f7fc4e360a9cb63f7cb4/0000LinTheApp.png" />This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.2252018-09-07T17:21:49Z2023-08-31T14:09:59ZMathematical Reasoning: Writing and Proof, Version 2.1<img alt="Read more about Mathematical Reasoning: Writing and Proof, Version 2.1" title="Mathematical Reasoning: Writing and Proof, Version 2.1 cover image" class="cover " width="115" height="150" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTgzLCJwdXIiOiJibG9iX2lkIn19--907d5a846812bc61f3ee1f754f50935da20ec20e/9781492103851.png" />Mathematical Reasoning: Writing and Proofis designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples. Develop the ability to read and understand written mathematical proofs. Develop talents for creative thinking and problem solving. Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics. Better understand the nature of mathematics and its language. This text also provides students with material that will be needed for their further study of mathematics.2202018-09-07T17:21:49Z2024-01-22T14:51:47ZCalculus One<img alt="Read more about Calculus One" title="Calculus One cover image" class="cover " width="2550" height="3300" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTc5LCJwdXIiOiJibG9iX2lkIn19--6a1ceaeb0591697989df678062a7ace17b12b4d8/0000MooCalcul.png" />Calculus is about the very large, the very small, and how things change—the surprise is that something seemingly so abstract ends up explaining the real world. This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course is based around doing practice problems.2172018-09-07T17:21:49Z2024-01-22T14:52:23ZAbstract Algebra: Theory and Applications<img alt="Read more about Abstract Algebra: Theory and Applications" title="Abstract Algebra: Theory and Applications cover image" class="cover " width="188" height="300" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTc3LCJwdXIiOiJibG9iX2lkIn19--b17c33718c99e58389eb09bf61f578850bc1132d/9781944325022.png" />This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly. Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation. This text contains more material than can possibly be covered in a single semester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester course might cover groups and rings while briefly touching on field theory, using Chapters 1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters 1 through 6, 9, 10, 11, 13 through 18, 20, 21, 22 (the first part), and 23. On the other hand, if applications are to be emphasized, the course might cover Chapters 1 through 14, and 16 through 22. In an applied course, some of the more theoretical results could be assumed or omitted. A chapter dependency chart appears below. (A broken line indicates a partial dependency.)2132018-09-07T17:21:49Z2024-01-22T14:52:06ZA First Course in Linear Algebra<img alt="Read more about A First Course in Linear Algebra" title="A First Course in Linear Algebra cover image" class="cover " width="612" height="792" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MjE5OSwicHVyIjoiYmxvYl9pZCJ9fQ==--dc2d72d6dd3dbe074def2d106812481f21adc328/Kuttler-LinearAlgebra-2021A-Thumbnail.png" />This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.2112018-09-07T17:21:49Z2024-01-22T18:48:39ZNotes on Diffy Qs: Differential Equations for Engineers<img alt="Read more about Notes on Diffy Qs: Differential Equations for Engineers" title="Notes on Diffy Qs: Differential Equations for Engineers cover image" class="cover " width="244" height="320" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTcyLCJwdXIiOiJibG9iX2lkIn19--6e55ba7843506ce7165e1d6b24ac6f2fc037b18f/9781505698190.png" />A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.1972018-09-07T17:21:48Z2024-01-22T14:52:20ZPrecalculus<img alt="Read more about Precalculus" title="Precalculus cover image" class="cover " width="202" height="260" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTYwLCJwdXIiOiJibG9iX2lkIn19--2265de6d63e5cbfb172054bdf49d88fef61fc945/9781938168345.png" />Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing College Algebra and Algebra and Trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.1982018-09-07T17:21:48Z2024-01-22T14:51:47ZAPEX Calculus<img alt="Read more about APEX Calculus" title="APEX Calculus cover image" class="cover " width="300" height="396" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjE4LCJwdXIiOiJibG9iX2lkIn19--90a3f177408880ae700d4fec966ace7f575f2f7b/9781514225158.png" />This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14. More information, including free downloads of .pdf versions of the text, is available at www.apexcalculus.com.
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