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Open Educational Resources

Calculus

 

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.

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

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.

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).

 

Jurg Nievergelt, ETH Zurich
Klaus Hinrichs, University of Muenster

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

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).

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.

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.

 

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.

 

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.

Basic Analysis: Introduction to Real Analysis

Jirí Lebl, Oklahoma State University

This free online textbook is a one semester course in basic analysis.

 

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

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.

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.

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.

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.

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.

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.

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.

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.

 

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.

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.

 

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.

College Trigonometry

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

Covers chapters 10-11 of Precalculus.

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.

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.

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.

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.

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.

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.

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.

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..

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.

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.

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.

Other

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.

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.

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

Introduction to Mathematical Analysis I - Second Edition

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.

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.

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.

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

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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).

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.

A Primer of Real Analysis

Dan Sloughter, Furman University

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