Research Guides: Mathematics: Learning Tools & Open Educational Resources

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Learning Tool Resources

PrepSTEP
This resource offers skill-building materials in English, math, and sciencefor use in self-directed study or as supplemental materials for developmental programs.
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AccessEngineering
Engineering and technical reference ebooks, including handbooks, manuals, subject overviews and videos explaining key engineering concepts.

Center for Research Data and Digital Scholarship The Center for Research Data and Digital Scholarship (CRDDS) is a collaboration between Research Computing and University Libraries, offering a full range of data services and support to the university and community. In addition to the offerings on our website, we have a seminar and consulting space in Room E206 of Norlin Library. We look forward to working with you on your research efforts and welcome opportunities for ongoing collaborations.

Finding and Evaluating Data
by Elizabeth Novosel Last Updated Jul 22, 2024 121 views this year

Statistics Through an Equity Lens by Yvonne Anthony This Open Educational Resource (OER) carries a significant responsibility by presenting statistics through an equity lens. The metaphor of a lens is used intentionally–as the glasses one wears can have a profound effect on what one sees. The book encourages further inspection of the ways in which data is collected, interpreted, and analyzed on a variety of social justice issues, such as health disparities, hunger and food insecurity, homelessness, behavioral health (mental health and substance use), and incarceration of males of color. It also attempts to reveal how the misuse of data can reinforce inequities, for example, by stigmatizing people and labeling neighborhoods as high poverty, violent, and having poor educational opportunities. Whether an intended or unintended consequence, irresponsible data use can contribute to racist impressions of people and communities. "The statistical expertise/prowess of the author, coupled with the examples chosen to highlight and bring to life how one can use data to bring light to disparities and then drive change to mitigate them, is meritorious."--Dr. Marianne Pugatch
OER Commons: Math Textbooks Search the OER (Open Educational Resource) Commons (https://oercommons.org/) to find textbooks on any topic.
American Institute of Mathematics List of Approved Open Textbooks
These books have met the criteria set by the AIM editorial board.
Open Textbook Library: Mathematics Textbooks in the Open Textbook Library are considered open because they are free to use and distribute, and are licensed to be freely adapted or changed with proper attribution.
LibreTexts: Mathematics his central Bookshelves area in this LibreTexts Library holds texts that are curated by the LibreTexts Development team and can be used either directly or as content for building customized remixes (i.e., texts that are generated from existing content often with customized editing and/or content interspersed) for use in Course Shells housed in Campus Bookshelves. There are two classes of texts found in the Bookshelves: "Textbooks" and "Textmaps". Textbooks are the central spot for integrated content into our library and are identified by "Book:" in their titles. Textmaps are specialized remixes that are constructed to follow the organization of existing commercial textbooks. Textmaps facilitate adoption by faculty that are unable to switch from a commercial textbook to an OER alternative; these texts are identified by "Map:" in their titles. For details on how to have a text added to the bookshelves or how to remix content into your customized remix contact us at info@libretexts.org.
Contemporary Calculus 1 (differential calculus) This is a textbook for differential calculus with explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Topics are typically introduced by way of applications, and the text contains the usual theorems and techniques of a first course in calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of differential calculus. This is the first of a three-part calculus series. The others are available on the author's website
Basic Analysis: Introduction to Real Analysis This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces. By Jirí Lebl, Assistant Professor, Department of Mathematics, Oklahoma State University.
Combinatorics Through Guided Discovery by Kenneth P. Bogart 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. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on. There are six chapters as well as an appendix with three additional topics: What is Combinatorics? Applications of Induction and Recursion in Combinatorics and Graph Theory Distribution Problems Generating Functions The Principle of Inclusion and Exclusion Groups Acting on Sets The three supplemental sections deal with relations, mathematical induction, and exponential generating functions. Many of problems have hints, which can be found in the back of the book (for the pdf and print versions) or linked directly from the problem (in the online version).

Sage Math SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
MyOpenMath Here are the courses offered: - Prealgebra, using the College of Redwoods textbook - Beginning and Intermediate Algebra, using the Tyler Wallace textbook - Precalculus 1 (College Algebra), using the Lippman/Rasmussen textbook - Precalculus 2 (Trigonometry), using the Lippman/Rasmussen textbook - Trigonometry, using the CK12/Sousa textbook
Grasple Find high quality curated open exercises and lessons on math & stats created by the community.
MIT Mathlets Here you will find a suite of dynamic Javascript "Mathlets" for use in learning about differential equations and other mathematical subjects, along with examples of how to use them in homework, group work, or lecture demonstration, and some of the underlying theory. There are also voice-over animated demos.
GeoGebra Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more
Math Insight The Math Insight web site contains both narrative pages and interactive applets focusing on the concepts underlying a few topics in mathematics. It has the largest coverage of multivariable calculus, as its origins are from the CSE Multivariable Calculus and Vector Analysis course at the University of Minnesota. Although no effort has been made to turn this into a comprehensive source of information on any topic, the goal is to provide some depth on selected topics, so readers can explore mathematical concepts at different levels, depending on their preparation or interest. One can view these pages more like a lecture than a textbook. They are not a replacement for a mathematics textbook because they don't cover all the theoretical details behind the main ideas. For the same reason, they should be easier to understand than a textbook.
Desmos Math Tools (Graphing Calculator App!)
WeBWork Open Problem Library (OPL) The WeBWorK Open Problem Library (OPL) contains problems contributed by faculty from many institutions that have used WeBWorK. Currently, there are approximately 35,000 problems in the OPL, and new problems are added regularly. The OPL was initially formed from several of the original File Based Problem Libraries, and includes all of the problems from the Arizona State, Rochester, California State-Long Beach, and the University of Virginia libraries. It also contains most, if not all, of the problems from Union College, the College of New Jersey, Dartmouth, Ohio State, Northern Arizona University, and Indiana University. Once known as the National Problem Library (NPL), the Open Problem Library (OPL) naming convention was adopted in the summer of 2012 to accommodate the increasing internationalization of WeBWorK and the possible inclusion of problem libraries from textbook publishers. In addition to merging problem collections from multiple institutions into a single collection, WeBWorK provides a different interface to these problems. Problems in the OPL are marked internally with metadata, and instructors can search for problems on the basis of this data. This mechanism is built into WeBWorK's library browser. In particular, one can search hierarchically by course, chapter, or section. To a limited extent, problems have been indexed against sections of textbooks, in which case instructors can also search for problems on that basis. WeBWorK stores this information in a database, so part of the installation involves loading metadata into the database.
OpenStax Calculus 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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.