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.
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
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.
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 CalculusBrian 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).
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.
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 covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College
Covers chapters 10-11 of Precalculus.
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.
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.
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.
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.
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.
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.
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.
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..
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.
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.
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.
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.
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.
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
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.
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.
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.
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:
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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).
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.
Dan Sloughter, Furman University
This is a short introduction to the fundamentals of real analysis.