Mathematics - Pure

A Computational Introduction to Number Theory and Algebra

Victor Shoup, New York University

This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory.

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(3 reviews)

A First Course in Linear Algebra

Robert A. Beezer, University of Puget Sound

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.

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(6 reviews)

A First Course in Linear Algebra

Ken Kuttler, Brigham Young University

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.

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(4 reviews)

A Gentle Introduction to the Art of Mathematics

Joseph E. Fields, Southern Connecticut State University

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction.

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(1 review)

Abstract Algebra: Theory and Applications

Thomas W. Judson, Stephen F. Austin State University

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.

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(2 reviews)

Active Calculus 2.0

David Austin, Grand Valley State University
Matt Boelkins, Grand Valley State University
Steve Schlicker, Grand Valley State University

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBW

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(4 reviews)

Active Calculus Multivariable

David Austin, Grand Valley State University
Matthew Boelkins, Grand Valley State University
Steve Schlicker, Grand Valley State University

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions.

(0 reviews)

Advanced Problems in Mathematics: Preparing for University

Stephen Siklos, Cambridge University

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). 

(0 reviews)

Algebra and Trigonometry

Multiple Authors , Openstax College

Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course.

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(5 reviews)

Algorithms and Data Structures With Applications to Graphics and Geometry

Jurg Nievergelt, ETH Zurich
Klaus Hinrichs, University of Muenster

An introductory coverage of algorithms and data structures with application to graphics and geometry.

 

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(1 review)

APEX Calculus

Brian Heinold, Mount St. Mary’s University
Dimplekumar Chalishajar, Virginia Military Institute
Gregory Hartman, Virginia Military Institute
Troy Siemers, Virginia Military Institute

APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

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(3 reviews)

Book of Proof

Dr. Richard Hammack, Virginia Commonwealth University

Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra.  Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

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(4 reviews)

Calculus

Gilbert Strang, MIT

Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a straightforward introductory calculus textbook available free online to educators and self-learners alike. It is covers single variable and multivariable calculus, including applications.

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(1 review)

Calculus for the Life Sciences: A Modeling Approach Volume 1

James L. Cornette, Iowa State University
Ralph A. Ackerman, Iowa State University

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.

(0 reviews)

Calculus for the Life Sciences: A Modeling Approach Volume 2

James L. Cornette, Iowa State University
Ralph A. Ackerman

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.

(0 reviews)

Calculus One

Multiple Authors, Mooculus

This text is based on David Guichard’s open-source calculus text which in turn is a modification and expansion of notes written by Neal Koblitz at the University of Washington.

(0 reviews)

Calculus Volume 1

Edwin Herman, University of Wisconsin-Stevens Point
Gilbert Strang, MIT

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning.

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(6 reviews)

Calculus Volume 2

Gilbert Strang, Massachusetts Institute of Technology

Calculus 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.

(0 reviews)

Calculus Volume 3

Gilbert Strang, Massachusetts Institute of Technology

Calculus 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.

(0 reviews)

Calculus: Early Transcendentals

David Guichard, Whitman College

Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses.

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(4 reviews)

College Algebra

Dr. Carl Stitz, Lakeland Community College
Dr. Jeff Zeager, Lorain County Community College

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 "Functions First," believing introducing functions first will help students understand new concepts more completely.

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(9 reviews)

College Algebra

Multiple Authors , Openstax College

College Algebra provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra course.

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(2 reviews)

College Trigonometry

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

Covers chapters 10-11 of Precalculus.

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(1 review)

Discrete Mathematics: An Open Introduction

Oscar Levin, University of Northern Colorado

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. 

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(2 reviews)

Elementary Algebra

John Redden, College of the Sequoias

Elementary Algebra, is an introductory text that focuses on the study of algebra at the beginning stages.  It assumes no prior algebraic experience and is intended for any student who needs build a strong algebraic foundation.  The book presents real world applications, setting a foundation for students to translate problems described in words into mathematical equations. The book illustrates the steps required to solve equations and interpret the results through the use of exercise sets and practice problems. The book stresses both the importance to solve problems correctly, and to learn to communicate those solutions to others.

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(8 reviews)

Elementary Algebra

Denny Burzynski, College of Southern Nevada
Wade Ellis, West Valley Community College

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative skills.

(0 reviews)

Elementary Algebra

Lynn Marecek, Santa Ana College
MaryAnne Anthony-Smith, Santa Ana College

Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course.

(0 reviews)

Elementary Differential Equations with Boundary Value Problems

William F. Trench, Trinity University

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

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(1 review)

Euclidean plane and its relatives

Anton Petrunin, Penn State

This book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.

(0 reviews)

Fundamentals of Mathematics

Denny Burzynski, College of Southern Nevada
Wade Ellis, West Valley Community College

Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra.

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(5 reviews)

Intermediate Algebra

John Redden, College of the Sequoias

Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. 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 in applications found in most disciplines.

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(1 review)

Linear Algebra

Jim Hefferon, Saint Michael's College

This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications.

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(3 reviews)

Linear Algebra

Andrew K. Waldon, UC Davis
David Cherney, UC Davis
Tom Denton, The Fields Institute and York University

This book is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors.

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(1 review)

Linear Algebra, Theory And Applications

Kenneth Kuttler, Bringham Young University

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.

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(1 review)

Linear Regression Using R: An Introduction to Data Modeling

David J. Lilja, University of Minnesota

Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style.

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(1 review)

Mathematical Reasoning: Writing and Proof, Version 2.1

Ted Sundstrom, Grand Valley State University

Mathematical Reasoning: Writing and Proof is 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

    (0 reviews)

My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition)

Jonathan Cornick, Queensborough Community College
Karan Puri
Michael Guy, Queensborough Community College

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). 

(0 reviews)

Notes on Diffy Qs: Differential Equations for Engineers

Jirí Lebl, Oklahoma State University

A one semester first course on differential equations, aimed at engineering students.

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(1 review)

Open Logic Project

Andrew Arana, University of Paris
Audrey Yap, University of Victoria
Gillian Russell, University of North Carolina
Jeremy Avigad, Carnegie Mellon University
Nicole Wyatt, University of Calgary
Richard Zach, University of Calgary
Walter Dean, University of Warwick

The Open Logic Project is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments. 

(0 reviews)

Prealgebra

Multiple Authors, Openstax College

Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on. The organization makes it easy to adapt the book to suit a variety of course syllabi.

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(9 reviews)

Precalculus

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

A casual glance through the Table of Contents of most of the major publishers’ College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.

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(1 review)

Precalculus

Multiple Authors, Openstax College

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.

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(1 review)

Precalculus

Holly Carley, NYC College of Technology
Thomas Tradler, NYC College of Technology

These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems.

(0 reviews)

Precalculus: An Investigation of Functions

David Lippman, Pierce College
Melonie Rasmussen, Pierce College

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry.

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(3 reviews)

Proofs and Concepts: The Fundamentals of Abstract Mathematics

Dave Witte Morris, University of Lethbridge
Joy Morris, University of Lethbridge

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. 

(0 reviews)

Single Variable Calculus I: Early Transcendentals

David Guichard, Whitman College

The original version of the text was written by David Guichard. The single variable material is a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original. The text also includes some exercises and examples from Elementary Calculus: An Approach Using Infinitesimals, by H. Jerome Keisler under a Creative Commons license. In addition, the chapter on differential equations and the section on numerical integration are largely derived from the corresponding portions of Keisler’s book. Albert Schueller, Barry Balof, and Mike Wills have also contributed additional material..

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(1 review)

Spiral Workbook for Discrete Mathematics

Harris Kwong, State University of New York (SUNY) Fredonia

This is a text that 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. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final 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 different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

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(2 reviews)

Trigonometry

Steven Schlicker, Grand Valley State University
Ted Sundstrom, Grand Valley State University

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them.

(0 reviews)

Vector Calculus

Michael Corral, Schoolcraft College

 This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

(0 reviews)

Whitman Calculus

Dr David Guichard, Whitman College

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.

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(6 reviews)

Yet Another Calculus Text

Dan Sloughter, Furman University

This book is an introduction to calculus based on the hyperreal number system.

(0 reviews)