tag:open.umn.edu,2005:/opentextbooks/textbooks?commit=Go&page=19&term=mathOpen Textbook Library - Search results for "math"2018-09-07T17:21:50Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png2332018-09-07T17:21:50Z2024-01-22T14:52:19ZIntroduction to the Modeling and Analysis of Complex Systems<img alt="Read more about Introduction to the Modeling and Analysis of Complex Systems" title="Introduction to the Modeling and Analysis of Complex Systems cover image" class="cover " width="717" height="717" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTg5LCJwdXIiOiJibG9iX2lkIn19--a45bf6a9790a75b1ba3f7fb05c39d5df5f5b687b/9781942341093.png" />Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.2232018-09-07T17:21:49Z2024-01-22T14:51:47ZBeyond Lean: Simulation in Practice - Second Edition<img alt="Read more about Beyond Lean: Simulation in Practice - Second Edition" title="Beyond Lean: Simulation in Practice - Second Edition cover image" class="cover " width="815" height="1051" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTgxLCJwdXIiOiJibG9iX2lkIn19--ba700b633320739e91137d66767aa589afe95d6b/0000BeyLeSiPr.png" />Lean thinking, as well as associated processes and tools, have involved into a ubiquitous perspective for improving systems particularly in the manufacturing arena. With application experience has come an understanding of the boundaries of lean capabilities and the benefits of getting beyond these boundaries to further improve performance. Discrete event simulation is recognized as one beyond-the-boundaries of lean technique. Thus, the fundamental goal of this text is to show how discrete event simulation can be used in addition to lean thinking to achieve greater benefits in system improvement than with lean alone. Realizing this goal requires learning the problems that simulation solves as well as the methods required to solve them. The problems that simulation solves are captured in a collection of case studies. These studies serve as metaphors for industrial problems that are commonly addressed using lean and simulation.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.2192018-09-07T17:21:49Z2024-01-22T14:51:48ZChemistry - 2e<img alt="Read more about Chemistry - 2e" title="Chemistry - 2e 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/eyJfcmFpbHMiOnsiZGF0YSI6NjQ2LCJwdXIiOiJibG9iX2lkIn19--95956fd5ea634eff72eeabb52a25704a2e5ec52c/9781947172616.png" />Chemistry 2e is designed to meet the scope and sequence requirements of the two-semester general chemistry course. The textbook provides an important opportunity for students to learn the core concepts of chemistry and understand how those concepts apply to their lives and the world around them. The book also includes a number of innovative features, including interactive exercises and real-world applications, designed to enhance student learning. The second edition has been revised to incorporate clearer, more current, and more dynamic explanations, while maintaining the same organization as the first edition. Substantial improvements have been made in the figures, illustrations, and example exercises that support the text narrative.2182018-09-07T17:21:49Z2024-03-18T13:05:11ZJava, Java, Java: Object-Oriented Problem Solving<img alt="Read more about Java, Java, Java: Object-Oriented Problem Solving" title="Java, Java, Java: Object-Oriented Problem Solving cover image" class="cover " width="526" height="648" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTc4LCJwdXIiOiJibG9iX2lkIn19--bd4faba467e42bc38e41c9bec482bf03658fcc23/0000JavaJavaJ.png" />We have designed this third edition of Java, Java, Java to be suitable for a typical Introduction to Computer Science (CS1) course or for a slightly more advanced Java as a Second Language course. This edition retains the “objects first” approach to programming and problem solving that was characteristic of the first two editions. Throughout the text we emphasize careful coverage of Java language features, introductory programming concepts, and object-oriented design principles. The third edition retains many of the features of the first two editions, including: Early Introduction of Objects Emphasis on Object Oriented Design (OOD) Unified Modeling Language (UML) Diagrams Self-study Exercises with Answers Programming, Debugging, and Design Tips. From the Java Library Sections Object-Oriented Design Sections End-of-Chapter Exercises Companion Web Site, with Power Points and other Resources The In the Laboratory sections from the first two editions have been moved onto the book's Companion Web Site. Table 1 shows the Table of Contents for the third edition.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.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.2002018-09-07T17:21:48Z2024-01-22T14:51:48ZHow We Got from There to Here: A Story of Real Analysis<img alt="Read more about How We Got from There to Here: A Story of Real Analysis" title="How We Got from There to Here: A Story of Real Analysis cover image" class="cover " width="717" height="717" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTYzLCJwdXIiOiJibG9iX2lkIn19--17e815786017b12881b24c7f11e48c2c7028e6ed/9780989722667.png" />The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
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