# Mathematics

## 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.

(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.

(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.

(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.

(1 review)

## A Primer of Real Analysis

Dan Sloughter, Furman University

This is a short introduction to the fundamentals of real analysis.

(0 reviews)

## 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.

(2 reviews)

## Active Calculus

David Austin, Grand Valley State University

Matt Boelkins, Grand Valley State University

Steve Schlicker, Grand Valley State University

In *Active Calculus*, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore.

(4 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.

(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.

(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).

(3 reviews)

## Applied Combinatorics

Mitchel T. Keller, Washington and Lee University

William T. Trotter, Georgia Institute of Technology

*Applied Combinatorics* is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics.

(0 reviews)

## Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell

Kenneth Levasseur, University of Massachusetts Lowell

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

(2 reviews)

## Applied Finite Mathematics

*Applied Finite Mathematics *covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.

(0 reviews)

## Applied Probability

Paul Pfeiffer, Rice University

In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand alone exposition as well as a supplement to any of several current textbooks. Some key contributors are acknowledged.

(0 reviews)

## Basic Analysis: Introduction to Real Analysis

Jirí Lebl, Oklahoma State University

This free online textbook (e-book in webspeak) is a one semester course in basic analysis.

(2 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.

(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.

(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.

(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.

(4 reviews)

## Collaborative Statistics

Barbara Illowsky, De Anza College

Susan Dean, De Anza College

*Collaborative Statistics* was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.

(9 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.

(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.

(2 reviews)

## College Trigonometry

Carl Stitz, Lakeland Community College

Jeff Zeager, Lorain County Community College

Covers chapters 10-11 of Precalculus.

(1 review)

## Combinatorics Through Guided Discovery

Kenneth P. Bogart, Dartmouth College

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems.

(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.

(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.

(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.

(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.

(5 reviews)

## How We Got from There to Here: A Story of Real Analysis

Eugene Boman, The Pennsylvania State University

Robert Rogers, State University of New York

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.

(2 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.

(1 review)

## Introduction to Mathematical Analysis I

Beatriz Lafferriere, Portland State University

Gerardo Lafferriere, Portland State University

Mau Nam Nguyen, Portland State University

Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

(0 reviews)

## Introduction to Probability

Charles M. Grinstead, Swarthmore College

J. Laurie Snell, Dartmouth College

This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a firm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.

(4 reviews)

## Introduction to Real Analysis

William F. Trench, Trinity University

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

(0 reviews)

## Introduction to Statistics

David Lane, Rice University

*Introduction to Statistics* is a resource for learning and teaching introductory statistics.

(1 review)

## Introductory Business Statistics

Thomas K. Tiemann, Elon University

The book "*Introductory Business Statistics*" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions.

(1 review)

## Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition

Mohammad Mahbobi, Thompson Rivers University

Thomas K. Tiemann, Elon University

Introductory Business Statistics with Interactive Spreadsheets - 1st Canadian Edition is an adaptation of Thomas K. Tiemann's book, Introductory Business Statistics. This new edition also allows readers to learn the basic and most commonly applied statistical techniques in business in an interactive way -- when using the web version -- through interactive Excel spreadsheets. All information has been revised to reflect Canadian content.

(0 reviews)

## Introductory Statistics

Douglas S. Shafer, University of North Carolina

Zhiyi Zhang, University of North Carolina

Shafer and Zhang wrote* Introductory Statistics *by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students’ maturity level.

(7 reviews)

## Introductory Statistics

Multiple Authors, Openstax College

*Introductory Statistics* follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering.

(11 reviews)

## 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.

(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.

(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.

(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.

(1 review)

## Math in Society

David Lippman, Pierce College

*Math in Society* is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors.

(4 reviews)

## Mathematical Reasoning: Writing and Proof

Ted Sundstrom, Grand Valley State University

*Mathematical Reasoning: Writing and Proof* is designed to be a text for the first 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.

(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.

(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)

## OpenIntro Statistics

Christopher D. Barr, Harvard School of Public Health

David M. Diez, Harvard School of Public Health

Mine Cetinkaya-Rundel, Duke University

*OpenIntro Statistics 3rd Edition* strives to be a complete introductory textbook of the highest caliber. Its core derives from the classic notions of statistics education and is extended by recent innovations. The textbook meets high quality standards and has been used at Princeton, Vanderbilt, UMass Amherst, and many other schools. We look forward to expanding the reach of the project and working with teachers from all colleges and schools.

(10 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.

(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.

(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.

(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.

(3 reviews)

## Principles of Business Statistics

This textbook provides a brief introduction to the field of statistics, including examples of how these topics shows up in a variety of real-life examples.

(1 review)

## 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..

(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.

(2 reviews)

## Statistical Inference For Everyone

Brian Blais, Bryant University

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic.

(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.

(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)