Library Homepage: Open Educational Resources: Mathematics

Mathematics Repositories & Collections

American Institute of Mathematics (AIM)
Includes AIM-approved texts and learning materals
LibreTexts Bookshelf - Mathematics
Open Textbook Library - Mathematics

Homework Systems and Ancillaries

MyOpenMath
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.
Sage
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.
Grasple
An online platform for instructors to collaboratively create and share open exercises and lessons for Math and Statistics. Includes interactive exercises for Prealgebra, Calculus, Linear Algebra, and Statistics.
Lumen Online Homework Manager
Designed by educators, Lumen Online Homework Manager (OHM) draws from thousands of interactive assessment questions to help students master math and other quantitative skills.
MIT Mathlets
The MIT Mathlets constitute a suite of carefully designed and highly interactive Javascript applets designed to enhance selected university level STEM classes.
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.
Desmos
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.
Math Insight
The Math Insight web site is a collection of pages and applets designed to shed light on concepts underlying a few topics in mathematics. The focus is on qualitative description rather than getting all technical details precise.
WebWork Open Problem Library
The WeBWorK Open Problem Library (OPL) contains problems contributed by faculty from many institutions that have used WeBWorK, an open-source online homework system for math and sciences courses. WeBWorK is supported by the MAA and the NSF. Currently, there are approximately 35,000 problems in the OPL, and new problems are added regularly.

Introductory Mathematics

Book of Proof
This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.
A Gentle Introduction to the Art of Mathematics
A Gentle Introduction to the Art of Mathematics (GIAM for short) is a textbook for a "transitions" course. Transitions courses (also known as "foundations" or "intro to proofs" courses) are typically taken after the Calculus sequence and before upper-division coursework in the mathematics major. Their purpose is to acclimatize the student to some of the culture and terminology of mathematics and to begin developing in them a proficiency at reading and writing mathematical proofs.
Mathematics for the Liberal Arts
This course was originally developed for the Open Course Library project. The text used is Math in Society, edited by David Lippman, Pierce College. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.
Quantitative Problem Solving in Natural Resources
Funded through the ISU Miller Open Education Mini-Grant Program, this text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and professional internships.

Algebra

OpenStax College Algebra, 2nd edition
OpenStax Algebra and Trigonometry, 2nd edition
Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.
OpenStax Prealgebra, 2nd edition
Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on. The organization makes it easy to adapt the book to suit a variety of course syllabi.
OpenStax Elementary Algebra, 2nd edition
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.
OpenStax Intermediate Algebra, 2nd edition
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.

Linear Algebra

A First Course in Linear Algebra
This text, originally by Ken Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems.
Linear Algebra with Applications
The aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.
Linear Algebra with Applications: An adaptation for MAT223 UTM
This open textbook is an adaptation of Linear Algebra with Applications by W. Keith Nicholson. The original book can be found and downloaded from Lyryx.com. Five topics are covered here: system of linear equations, matrix algebra, determinants and diagonalization, vector geometry and vector space. It's suitable for beginners who are interested in learning linear algebra.

Calculus

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. Volume 1 covers functions, limits, derivatives, and integration.
Contemporary Calculus I
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.
Applied 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.
Active Calculus Multivariable
In Active Calculus Multivariable, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore.
Community Calculus
An early transcendentals book covering single variable calculus, infinite series, and multivariable calculus.
Calculus: Early Transcendentals
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. To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions.

Other Textbooks

Basic Analysis: Introduction to Real Analysis
This is exactly the material that a student needs to see in their first two semesters of introductory analysis. It can be used as a first proof-based course coming after a linear algebra or possibly concurrently. Different people will find it fitting their curriculum differently. But this book provides a very nice two semester course that starts by introducing set theory and induction for the first time and ends with students ready for topology, measure theory, or more advanced calculus.
Elementary Differential Equations with Boundary Value Problems
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra.
Spiral Workbook for Discrete Mathematics
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.
OpenStax Introductory Statistics, 2nd edition
Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others.
Combinatorics Through Guided Discovery
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. Above all, this book is dedicated to the principle that doing mathematics is fun.