Open Educational Resources (OER): Mathematics

This site provides a list of open textbooks approved for use by the American Institute of Mathematics.

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates.

Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles.

Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles.

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses.

Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. Topics covered include: pre-algebra review, solving linear equations, graphing linear equations, inequalities, systems of linear equations, polynomials, factoring, rational expressions and equations, radicals, quadratics, and functions including exponential, logarithmic and trigonometric.

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. Volume 1 covers functions, limits, derivatives, and integration.

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.

Since August 2012, Active Calculus has been available as a free, open-source calculus text. I undertook the project to provide an activity-driven text in a format that is freely accessible to students. The 2016 and 2017 editions of the text are now available online.

An early transcendentals book covering single variable calculus, infinite series, and multivariable calculus.

An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that text.

Written by James Cornette & Ralph Ackerman, Iowa State University

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory.

Learning Statistics with R covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing.

This is a series of lesson plans based upon the OpenStax Introductory Statistics Textbooks. It contains sections on Sampling and Data, Descriptive Statistics, Probability, Discrete Random Variables, Continuous Random Variables, Distributions, The Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Linear Regression and Correlation.

We organized this course around the Big Picture of Statistics. As we learn new material, we will always look at how these new ideas relate to the Big Picture.

"This book starts by presenting an overview of the statistical thought process. By the end of chapter 2, students are already familiar with concepts such as hypotheses, level of significance, p-values, errors. Normally these topics are not introduced until after a discussion of probability and sampling distributions."

The mission of OpenIntro is to make educational products that are free, transparent, and lower barriers to education. OpenIntro Statistics includes a free textbook, labs, videos, and additional resources.

The goal of this tool is to make statistics more accessible through interactive visualizations. The authors of the site are also currently producing a textbook. These resources are free to access online but not open.

Combinatorics provides an introduction to enumeration, graph theory, and design theory. It is aimed at upper-level undergraduate students and the exercises expect some mathematical sophistication, including a reasonable ability to construct proofs. The text is designed to be used in an undergraduate course, but could be suitable for independent study by a student with some mathematical background and understanding of proofs.

Are you an instructor who wants to adopt an open textbook, who feels online interactive homework is valuable, but doesn't want their students to have to pay an additional fee? Then read more about using MyOpenMath in the classroom.

Designed by educators, Lumen Online Homework Manager (OHM) draws from thousands of interactive assessment questions to help students master math and other quantitative skills.

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.

Desmos includes multiple tools for use in mathematics courses, including the HTML5 Desmos graphing calculator, which millions of students around the world use for free, including students who are blind or visually-impaired. They also provide teaching activities and an activity builder for instructors using the platform.

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.