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# OER for COS

Open educational resources for UTSA's College of Science

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## Librarian

Charles Wu

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University of Texas at San Antonio

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## MAT 0203

### Basic Mathematics

- The Essence of Mathematics Through Elementary Problems by Tony GardinerISBN: 9781783747016Publication Date: 2019It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.
- Geometry with an Introduction to Cosmic Topology by Michael HitchmanISBN: 9781717134813Publication Date: 2018-06-08Motivated by questions in cosmology, the 2018 edition of Geometry with an Introduction to Cosmic Topology follows the Erlangen program to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text uses Mobius transformations in the extended complex plane to define and investigate these three candidate geometries, thereby providing a natural setting in which to express results common to them all, as well as results that encapsulate key differences. With these geometries in hand, the text then explores the interplay between the shape of a space and the type of geometry it admits. It is written to be suitable for a one semester course in geometry or as a guide to independent study, with over 200 exercises and several essays on topics such as the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.

## MAT 0213

### Intermediate Algebra

- College Algebra by OpenStax CollegeISBN: 1938168380Publication Date: 2020-02-12College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra 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.
- Elementary Algebra by OpenStaxISBN: 099862571XPublication Date: 2020-02-06Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on 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.
- Intermediate Algebra Textbook College of the RedwoodsPublication Date: 2017This textbook contains 9 chapters including exercises and solutions. Topics covered are: Number Systems, Solving Equations, Logic, Compound Inequalities, Functions, Linear Functions, Slope, Absolute Value Functions, Quadratic Functions, Polynomial Functions, Rational Functions, Exponential and Logarithmic Functions, and Radical Functions.
- Prealgebra by OpenStax CollegeISBN: 1938168992Publication Date: 2020-02-07Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra 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.

- American Institute of MathematicsA list of open textbooks by course title. All the books have been judged to meet the evaluation criteria set by the AIM editorial board.
- Intermediate Algebra Tutorials West Texas A&MThis site includes more than 40 tutorials in Intermediate Algebra topics with practice tests and answer keys. The site is designed to assist the user in preparing for math placement tests and the math portion of the GRE.
- MIT Open Courseware MathematicsMIT Open Courseware offers an extensive series of online courses. Courses generally include lecture videos, assignments, exams, and more for math.
- myOpenMathMyOpenMath is designed for mathematics, providing delivery of homework, quizzes, and tests with rich mathematical content. Students can receive immediate feedback on algorithmically generated questions with numerical or algebraic expression answers. And it can do so much more, providing a full course management system, including file posting, discussion forums, and a full gradebook, all designed with mathematics in mind.
- OpenStax Instructor Resources College AlgebraIncludes a getting started guide, sample syllabus language, instructor solution guide, supplemental test items, Powerpoint slides, iBooks comp copy assessment bank, and more. Must register for a faculty login to access.

## MAT 1023

### College Algebra with Applications

- College Algebra by OpenStax CollegeISBN: 1938168380Publication Date: 2020-02-12College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra 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.
- Elementary Algebra by OpenStaxISBN: 099862571XPublication Date: 2020-02-06Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on 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.

- American Institute of MathematicsA list of open textbooks by course title. All the books have been judged to meet the evaluation criteria set by the AIM editorial board.
- MIT Open Courseware MathematicsMIT Open Courseware offers an extensive series of online courses. Courses generally include lecture videos, assignments, exams, and more for math.
- myOpenMathMyOpenMath is designed for mathematics, providing delivery of homework, quizzes, and tests with rich mathematical content. Students can receive immediate feedback on algorithmically generated questions with numerical or algebraic expression answers. And it can do so much more, providing a full course management system, including file posting, discussion forums, and a full gradebook, all designed with mathematics in mind.
- OpenStax Instructor Resources College AlgebraIncludes a getting started guide, sample syllabus language, instructor solution guide, supplemental test items, Powerpoint slides, iBooks comp copy assessment bank, and more. Must register for a faculty login to access.

## MAT 1033

### Algebra with Calculus for Business

- Calculus Volume 1 by OpenStaxISBN: 193816802XPublication Date: 2020-02-18Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.
- College Algebra by OpenStax CollegeISBN: 1938168380Publication Date: 2020-02-12College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra 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.
- Elementary Algebra by OpenStaxISBN: 099862571XPublication Date: 2020-02-06Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on 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.
- Introduction to Financial Mathematics: Concepts and Computational Methods by Arash FahimPublication Date: 2019Introduction to Financial Mathematics: Concepts and Computational Methods serves as a primer in financial mathematics with a focus on conceptual understanding of models and problem solving. It includes the mathematical background needed for risk management, such as probability theory, optimization, and the like. The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis. In addition, it covers some areas which are outside the scope of mainstream financial mathematics textbooks. For example, it presents marginal account setting by the CCP and systemic risk, and a brief overview of the model risk. Inline exercises and examples are included to help students prepare for exams on this book.
- Math in Society by Lippman, DavidPublication Date: 2013This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.

- American Institute of MathematicsA list of open textbooks by course title. All the books have been judged to meet the evaluation criteria set by the AIM editorial board.
- MIT Open Courseware MathematicsMIT Open Courseware offers an extensive series of online courses. Courses generally include lecture videos, assignments, exams, and more for math.
- myOpenMathMyOpenMath is designed for mathematics, providing delivery of homework, quizzes, and tests with rich mathematical content. Students can receive immediate feedback on algorithmically generated questions with numerical or algebraic expression answers. And it can do so much more, providing a full course management system, including file posting, discussion forums, and a full gradebook, all designed with mathematics in mind.
- OpenStax Instructor Resources College AlgebraIncludes a getting started guide, sample syllabus language, instructor solution guide, supplemental test items, Powerpoint slides, iBooks comp copy assessment bank, and more. Must register for a faculty login to access.

## MAT 1043

### Introduction to Mathematics

- Geometry with an Introduction to Cosmic Topology by Michael HitchmanISBN: 9781717134813Publication Date: 2018-06-08Motivated by questions in cosmology, the 2018 edition of Geometry with an Introduction to Cosmic Topology follows the Erlangen program to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text uses Mobius transformations in the extended complex plane to define and investigate these three candidate geometries, thereby providing a natural setting in which to express results common to them all, as well as results that encapsulate key differences. With these geometries in hand, the text then explores the interplay between the shape of a space and the type of geometry it admits. It is written to be suitable for a one semester course in geometry or as a guide to independent study, with over 200 exercises and several essays on topics such as the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
- An Introduction to the Theory of Numbers by Leo MoserISBN: 9781931705011Publication Date: 2004-01-01This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.
- A Spiral Workbook for Discrete Mathematics 2nd ed by Harris KwongISBN: 9781956862010Publication Date: 2024-03-25A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.

## MAT 1053

### Mathematics for Business

- Introduction to Financial Mathematics: Concepts and Computational Methods by Arash FahimPublication Date: 2019Introduction to Financial Mathematics: Concepts and Computational Methods serves as a primer in financial mathematics with a focus on conceptual understanding of models and problem solving. It includes the mathematical background needed for risk management, such as probability theory, optimization, and the like. The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis. In addition, it covers some areas which are outside the scope of mainstream financial mathematics textbooks. For example, it presents marginal account setting by the CCP and systemic risk, and a brief overview of the model risk. Inline exercises and examples are included to help students prepare for exams on this book.
- A Spiral Workbook for Discrete Mathematics 2nd ed by Harris KwongISBN: 9781956862010Publication Date: 2024-03-25A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.

## MAT 1073

### Algebra for Scientists and Engineers

- ISBN: 1938168380Publication Date: 2020-02-12

## MAT 1093, 1214, & 1224

### Precalculus, Calculus I & Calculus II

- Calculus Volume 1 by OpenStaxISBN: 193816802XPublication Date: 2020-02-18Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.
- Calculus Volume 2 by OpenStaxISBN: 1938168062Publication Date: 2020-02-14Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
- Calculus Volume 3 by OpenStaxISBN: 1938168070Publication Date: 2020-01-16Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
- Precalculus by OpenStax CollegeISBN: 1938168348Publication Date: 2020-02-12Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives, and includes worked examples that demonstrate problem-solving approaches in an accessible way.

## MAT 3123

### Essentials of Geometry

- Geometry with an Introduction to Cosmic Topology by Michael HitchmanISBN: 9781717134813Publication Date: 2018-06-08Motivated by questions in cosmology, the 2018 edition of Geometry with an Introduction to Cosmic Topology follows the Erlangen program to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text uses Mobius transformations in the extended complex plane to define and investigate these three candidate geometries, thereby providing a natural setting in which to express results common to them all, as well as results that encapsulate key differences. With these geometries in hand, the text then explores the interplay between the shape of a space and the type of geometry it admits. It is written to be suitable for a one semester course in geometry or as a guide to independent study, with over 200 exercises and several essays on topics such as the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.

## MAT 3633

### Numerical Analysis

- First Semester in Numerical Analysis with Julia by Giray ÖktenPublication Date: 2019First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.
- Tea Time Numerical Analysis by Leon BrinPublication Date: 2016This textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics. The ultimate goal of Tea Time Numerical Analysis is to be a complete, one-semester, single-pdf, downloadable textbook designed for mathematics classes. Now includes differential equations.

## MAT 4213 & 4223

### Real Analysis I & II

- Mathematical Analysis I by Elias ZakonISBN: 978193170502XPublication Date: 2004This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.