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Open Educational Resources: Mathematics

Library Resources for Mathematics

We provide access to content such as online books, journals and image collections that can be used to lower or remove student textbook costs for students.  To learn more, see the following:

Lecture Videos

Khan Academy

Khan Academy offers a number of video tutorials spanning, Algebra Trigonometry, Calculus, Differential Equations, Linear Algebra, and Statistics. Most videos are on the order of a few minutes long and are primarily example and intuition-based rather than proof-based.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

CC BY-NC-SA

Mathematics Courseware  -Massachusetts Institute of Technology

MIT has provided many Math classes complete with video lectures, homework problems, and lecture notes. 

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

Attribution-NonCommercial-ShareAlike 3.0 United States

Vi Hart

Unconventional from an instructional perspective, Vi Hart's videos are more inspiring and attention-grabbing than they are formally educational. These videos put math concepts in terms of silly characters and put topics such as Fibonacci numbers, fractals and pi in a recreational light.

Vi Hart videos are available for download at her website and can be viewed on YouTube. These videos are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike license.

Attribution-NonCommercial-ShareAlike 4.0 International

Mathematics

On this page you will find several open Mathematics textbooks along with supplemental material and a few lecture videos.  

The purpose of these discipline specific pages is to showcase content that might be of interest to faculty who are considering adopting open educational resources for use in their classes. This list of content is by no means exhaustive.  The nature of open educational resources is very collaborative and it is in that spirit that we encourage any comments about the content featured on this page or recommendations of content that are not already listed here. 

Content on this page that is highlighted in crimson and cream was created or is being used by an OU faculty member and is being given special attention as such.

 

Creative Commons

Textbooks

Calculus eBook  -Dr. Kurt Gramoll

This Calculus eBook written by OU professor, Dr. Kurt Gramoll, features all of the main topics of Calculus. Each topic is divided into a number of sub-categories that broadens the user's understanding as well as supports the main concepts of Calculus.  Each sub-category is further divided into a case introduction, theory, case solution, and a simulation which the user can manipulate, giving the opportunity to enhance the user's understanding of the material.

Author:

Dr. Kurt Gramoll, University of Oklahoma

The contents of eCourses are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike license.

CC BY-NC-ND 3.0

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."  -AIM Read More about AIM evaluation criteria

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

In addition to our own two schools, we learned that 26 institutions across the US (and some abroad!) have taken our materials, put in their own hard work, and made it into something for their students to use! We've helped roughly 7500 students save a collective $780,000! (If the stats from our own schools are included, those numbers soar to roughly 13,000 students and $1.2 million!)

Authors

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

CC BY-NC-SA 3.0

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.

CC BY-BC-SA 3.0 US

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.

CC BY-NC-SA

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.
CC BY-SA

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.

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:

Thomas Judson, Stephen F. Austin State University

This textbook is licensed under a GNU Free Documentation License

Open Textbook Collections

Supplemental Materials

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.

CC BY-NC-ND

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. 

License

All original content on this page is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. All linked-to content adheres to its respective license.

Creative Commons License