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College Algebra & Trigonometry
Richard Beveridge · Richard W. Beveridge · 2018
This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.
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Linear Algebra Done Right
Sheldon Axler · Springer · 2024
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
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Advanced Algebra
John Redden · 2012
Intermediate Algebra is the second part of a two-part course in Algebra. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of applications found in most disciplines. Used as a standalone textbook, it offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra clearly lays out the steps required to build the skills needed to solve a variety of 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, Intermediate Algebra was written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
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Basic Algebra with Applications
Ivan Zaigralin · Ivan G. Zaigralin · 2018
Basic Algebra with Applications
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Intermediate Algebra
Katherine Yoshiwara · Bruce Yoshiwara · 2020
Intermediate Algebra is a textbook for students who have some acquaintance with the basic notions of variables and equations, negative numbers, and graphs, although we provide a "Toolkit" to help the reader refresh any skills that may have gotten a little rusty. In this book we journey farther into the subject, to explore a greater variety of topics including graphs and modeling, curve-fitting, variation, exponentials and logarithms, and the conic sections. We use technology to handle data and give some instructions for using a graphing calculator, but these can easily be adapted to any other graphing utility.
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Elementary Algebra
Katherine Yoshiwara · Bruce Yoshiwara · 2019
This text introduces the basic skills and ideas of algebra.
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Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students
Jason Lachniet · Jason Lachniet · 2017
This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
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Linear Algebra with Applications
W. Keith Nicholson · Lyryx · 2023
The aim of this textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The content has enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners, whereas Chapters 5–9 contain a second semester course. The textbook is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
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Intermediate Algebra
Lynn Marecek; Andrea Mathis · OpenStax · 2017
Intermediate Algebra 2e is designed to meet the scope and sequence requirements of a one-semester intermediate 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. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses. 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 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.
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My Math GPS: Elementary Algebra Guided Problem Solving
Jonathan Cornick; Michael Guy; Karan Puri · CUNY Academic Works · 2016
My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.
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Elementary Algebra
Lynn Marecek; MaryAnne Anthony-Smith · OpenStax · 2017
Elementary 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.
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Introductory Algebra
Anne Gloag · Independent · 2012
Introductory Algebra provides a comprehensive introduction of variables, functionsand linear equations and gives students a solid foundation in algebra.
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Prealgebra
Lynn Marecek; MaryAnne Anthony-Smith · OpenStax · 2015
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.
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College Algebra
Jay Abramson · OpenStax · 2021
College Algebra 2e 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 addresses the needs of a variety of courses. College Algebra 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 College Algebra 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 College Algebra by OpenStax is available in web view here.
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Algebra and Trigonometry 2e
Jay Abramson · OpenStax · 2021
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.
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Abstract Algebra: Theory and Applications
Thomas Judson · University of Puget Sound · 2016
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
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A First Course in Linear Algebra
Ken Kuttler · Lyryx · 2023
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.
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Linear Algebra, Theory And Applications
Kenneth Kuttler · Saylor Foundation · 2012
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.
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Linear Algebra
David Cherney; Tom Denton; Andrew Waldon · University of California, Davis · 2016
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independen
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A Computational Introduction to Number Theory and Algebra
Victor Shoup · Cambridge University Press · 2009
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. There are a few sections that are marked with a “(∗),” indicating that the material covered in that section is a bit technical, and is not needed else- where. There are many examples in the text, which form an integral part of the book, and should not be skipped. There are a number of exercises in the text that serve to reinforce, as well as to develop important applications and generali