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Open Educational Resources: Mathematics

A guide to textbooks, course materials and multimedia which are free or or low cost for educational use. These resources were created with the intention of being widely used and are legal to use in courses with proper citation.

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Open Mathematics Textbooks

 

American Institute of Mathematics Approved Textbooks

This is a collection of openly licensed Math textbooks approved by the American Institute of Mathematics. Books span Liberal Arts Math, Precalculus, Linear Algebra, Discrete Structures, and Complex Analysis among others.

"To gain our seal of approval an open source mathematics textbook must be able to serve as the primary text in a mainstream mathematics course at the undergraduate level in U.S. colleges and universities. That means that we are not evaluating instructional modules, Java applets, supplementary lecture notes, or other materials that are designed for limited use within a course. Since the minimum length of a traditional course is 10 weeks with 30 hours of class instruction, the books we evaluate must have enough material for that, and most will have more since most college courses are 14 or 15 weeks in length with at least 40 hours of class time." Read More  -AIM

Editorial Board

David Austin, Mathematics, Grand Valley State University

George Jennings, Mathematics, California State University

Kent E. Morrison (chair), Mathematics, California Polytechnic State University

Frank Sottile, Mathematics, Texas A&M

Katherine Yoshiwara, Mathematics, Los Angeles Pierce College

Copyright rights vary within this collection; however, the American Institute of Mathematics recommend that books in the collection be openly licensed under a GNU Free Documentation License of a Creative Commons License. Check individual items for copyright status. 

 

College Algebra, College Trigonometry, Precalculus  -Carl Stitz and Jeff Zeager

The material [in these books] is presented at a level that de finitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in the text and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. As a contribution to the open-source community, all LaTeX files used to compile this book are available for free under a Creative Commons license at the author's website. -Stitz Zeager

 
 
 
 
 
Textbooks written by Stitz and Zeager are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Licenses
 

 

Calculus  -Gilbert Strang

Published in 1991, this book is a resource for educators and self-learners alike. It is well organized, covers single variable and multivariable Calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide. In addition to these text-based materials, Strang has developed a video playlist, the Big Picture of Calculus in which he explains the conceptual highlights of Calculus. 

Instructor:

Gilbert Strang, Ph. D., Massachusetts Institute of Technology, Mathematics

Use of the MIT OpenCourseWare site and materials is subject to their Creative Commons License and other terms of use.

 

 

Elementary Differential Equations with Boundary Value Problems  -William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. This text includes 1695 numbered exercises, many with several parts ranging in difficulty from routine to very challenging. Written informally, this book is mathematically accurate and is illustrated by appropriate graphics. This text is accompanied by its solution manual. -William F. Trench

Author:

William F. Trench, Ph. D., Trinity University, Mathematics

This text is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

 

Street-Fighting Mathematics -Sanjoy Mahajan

Street-Fighting Mathematics — the title refers to the fact that in a street fight, it’s better to have a quick and dirty answer than to stand there thinking about the right thing to do — is based on the premise that we can and should use rapid estimation techniques to get rough answers to difficult problems.  There are good reasons for preferring estimation over rigorous methods: the answer is arrived at quickly, the full set of input data may not be needed, and messy calculus-based or numerical techniques can often be avoided.  Perhaps more important, by avoiding a descent into difficult symbol pushing, a greater understanding of the problem’s essentials can sometimes be gained and a valuable independent check on rigorous — and often more error prone — methods is obtained. -John Regehr, Associate Professor of Computer Science at the University of Utah

Author:

Sanjoy Mahajan, Applied Science and Engineering, MIT

This text is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

 

Elementary Differential Equations  -Dr. Andrew Bennett

This is an online textbook by Dr. Andrew Bennett of the Kansas State Mathematics department.  This text was developed specifically for Dr. Bennett's class and is therefor a little more direct than a traditional textbook. 

Dr. Andrew Bennett has not CC licensed the content, but it is publicly available.  

 

Calculus (in three semesters) -University of Wisconsin

At the link, there can be found all necessary course materials for three semesters of Calculus instruction.  The material is separated in a traditional way.  The textbooks available here can be downloaded with answers and without.  Latex and figure files are available for download and modification if desired.  Supplementary material is also included here including project files, tips on grading projects and condensed study material for students on topics including, basic Trig. properties, epsilon-delta definition of a limit, and when not to use L'Hopital's rule. 

Authors:


Sigurd B. Angenent, Mathematics, University of Wisconsin

Laurentiu Maxim, Mathematics, University of Wisconsin

Evan Dummit, Mathematics, University of Wisconsin

Joel Robbin, Mathematics, University of Wisconsin

This material is licensed under the terms of the GNU Free Documentation License, Version 1.2.

 

 

Linear Algebra -Jim Hefferon

This textbook takes a developmental approach to the standard topics of Linear Algebra, Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors.  This text can be downloaded in PDF form for viewing and TeX form for editing. 

Author:

Jim Hefferon, Mathematics, Saint Michael's College

This material is licensed under a Creative Commons Attribution-ShareAlike license.

Historical Math Monographs - Cornell University

The Cornell University Library Historical Mathematics Monographs is a collection of selected monographs with expired copyrights chosen from the mathematics field. These were monographs that were brittle and decaying and in need of rescue.  

Also check ou the University of Michigan Historical Mathematics Collection, a growing library of books selected from the University of Michigan mathematics collection that have been digitized to improve access and to preserve the content of these books. All of the books in this collection were published in the 19th or early 20th century. 

 

 

Abstract Algebra: Theory and Applications - Thomas Judson

This text was originally published by PWS Publishing Company in 1994; however, since then the copyright has been transferred back to its author who actively develops the book.  The book is formatted with MathBook XML whose full source is available for download and modification.  Periodically, PDF versions of thet including the most recent revisions are made available.  

Author:

Thomas Judson, Stephen F. Austin State University

This textbook is licensed under a GNU Free Documentation License


Abstract Algebra: The Basic Graduate Year

This is a complete Abstract Algebra textbook that contains exercises and solutions.   Each chapter is downloadable individually. 

Author:

Robert B. Ash, University of Illinois

This textbook may be copied both digitally or physically; however, all other rights are reserved by its author. 

 

Open Supplemental Material

Detexify

Anyone who works with LaTeX knows how time-consuming it can be to find a symbol that you cannot memorize the mark-up for.  Detexify is an attempt to simplify the search.  Users draw a symbol in a window on the page and Detexify matches it to its corresponding LaTeX markup. 

 

GeoGebra

GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package.  GeoGebra is a rapidly expanding community of millions of users located in just about every country.  GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning worldwide.

GeoGebra is licensed under the GeoGebra Non-Commercial License Agreement.

 

Sage

Sage is a free open-source mathematics software system licensed under the GNU General Public License.  It build on top of many existing open-source packages:  NumPy, SciPy, matplotlib, Sympy, GAP, FLINT, R, and many more.  Sage accesses the combined power of these through common, Python-based language or directly via interfaces or wrappers.  Tutorials and Documentation are available.

This software is licensed under the GNU General Public License. 

 

Online Interactive Graphing Application  -Desmos

Desmos is a math engine that can graph any equation, including derivatives and Fourier series.  Interactive sliders enable users to demonstrate function transformations.  The graphing calculator operates on any computer or tablet without requiring any downloads.  Desmos is completely free to use.  A free account is required to save plots and to export plots as images.

Desmos is subject to its terms of use.

"Desmos does not claim ownership of any formulae, information, data, text or other materials you submit for display... However, you grant to Desmos an irrevocable license ... to use, distribute, ... , [and] publicly display User Submissions."

 

MathCentre

Mathcentre provides support material for a variety of math classes.  Math centre is divided in classes and each class is separated into key topics featuring videos and reference sheets on topic specific material.

Material on mathcentre is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives License.

 

MyOpenMath

MyOpenMath is a free and open version of MyMathLab or WebAssign. Instructors can create randomized algorithmically generated problems for their students or choose from problems already created by other instructors. These problems will be automatically graded and are viewable from an instructor's account. Because of its open nature, MyOpenMath allows students to create free accounts that allow them access to randomized practice problems and the possibility of unlimited practice.