68 Mathematics

Linear Algebra with Applications: Lyryx

The first version of this book was published in 1986 as a traditionally published textbook. The current version from 2018 was published as an open educational resource for a traditional or advanced introduction to the topics within linear algebra. Reviews are available.

Includes: Instructor resources: solution manual to exercises and lecture slides.

Linear Algebra

This text covers linear systems and Gauss’s Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. Reviews from multiple sources and supplementary materials are available.

Includes: Exercises, solutions, lab manual, lecture slides, videos

Fundamentals of Matrix Algebra

This text deals with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. It has been reviewed.

Includes: Exercises, solutions, definitions

Differential Calculus for the Life Sciences

This textbook was written by a math professor at the University of British Columbia and is currently used as a textbook for introductory calculus courses for life sciences undergraduates.

Includes: Exercises and solutions to selected problems

Calculus for the Life Sciences: A Modelling Approach Volume 1

This textbook was written by two professors at Iowa State University with the goal introducing students to scientific modeling. This course aims to teach students the necessary skills and concepts from a traditional physical sciences course, while explaining the applications of calculus to the life sciences. It has been reviewed. Please note the more restrictive CC-BY NC ND license does not allow any editing of the resource.

Includes: Exercises, solutions to select problems, MATLAB exercises

CLP Calculus Textbooks

The CLP calculus textbooks and problem books were written for standard university Calculus 1, 2, 3 and 4 courses at the Department of Mathematics, UBC.

Calculus: Volumes 1-3 (OpenStax)

Volume 1: Concepts covered in this volume include functions, limits, derivatives, and integration. This volume has been reviewed, and has ancillary resources.

Volume 2: Concepts covered in this volume include integration, differential equations, sequences and series, and parametric equations and polar coordinates. Volume 2 has been reviewed and has ancillary resources.

Volume 3: Concepts covered in this volume include parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations. This volume has been reviewed.

All volumes include: Exercises and answers, instructor resources, student resources

Active Calculus 2.0, and Active Calculus Multivariable

These complementary textbooks are designed to create active learners, focusing on having students solve challenging problems. Reviews are available for the single variable and multivariable books.

Includes: Interactive exercises and solutions, lab manual, other instructor resources

Community Calculus (Single, Multivariable)

This online compilation of four calculus textbooks is frequently updated and has been used in courses. It has been positively reviewed by the Mathematical Association of America. It also covers early and late transcendentals.

Includes: Exercises, solutions, and WeBWorK problem sets

APEX Calculus

This text, or portions of it, has been adopted at a considerable number of American institutions to, according to their website. These institutions include the Virginia Military Institute, where the author is an associate professor of mathematics. Reviews are available.

Includes: interactive graphics, exercises and solutions

Elementary Differential Equations

This textbook is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

Includes: Exercises

Contemporary Calculus

This textbook was created as part of the Washington State Colleges’ Open Course Library Project, which received funding through the Gates Foundation.

Includes: Exercises, solutions to odd-numbered problems

Calculus

Originally published through traditional means, this textbook is now available as an open educational resource. This text includes single and multivariable calculus and was written by a professor of mathematics at the Massachusetts Institute of Technology. Reviews are available.

Includes: Instructor’s manual, a student study guide with exercises and select solutions, links to a calculus video series by the author

Applied Calculus

This text covers all of the concepts of first-year calculus with a balance of application and theory.

Includes: Problem-solving guides, examples on MyOpenMath, videos, applications, problems, selected solutions, summaries

Discrete Mathematics: An Open Introduction

Approved by the American Institute of Mathematics, this textbook grew out of a discrete mathematics course at the University of Northern Colorado. Reviews are available.

Includes: Questions, answers, instructor resources upon request

Book of Proof, 3rd ed.

This book is an introduction to the standard methods of proving mathematical theorems. Reviews are available.

Includes: Instructor resources and workbook

Mathematical Reasoning: Writing and Proof

This textbook is designed for the first course in a mathematics curriculum that introduces students to the processes of constructing and writing proofs. It focuses on the formal development of mathematics. Reviews are available.

Includes: Questions, answers, and instructor resources upon request

A 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. Reviews are available.

Includes: Exercises, selected solutions

Euclidean plane and its relatives

The book is a minimalist introduction to the Euclidean plane, intended for upper-level students. Reviews are available.

Includes: Exercises, hints

A Cool Brisk Walk Through Discrete Mathematics

This text covers sets, relations, probability, structures, counting, logic, and proof. Reviews are available.

Includes: Videos, exercises

Combinatorics and Graph Theory

This introduction to combinatorics discusses inclusion-exclusion, generating functions, and other topics.

Includes: Exercises, glossary

A Computational Introduction to Number Theory and Algebra

The mathematical material covered includes the basics of number theory and of abstract algebra. It also includes an introduction to discrete probability theory. Please note the more restrictive CC-BY NC ND license does not allow any editing of the resource. Reviews are available.

Includes: Exercises

An Introduction to Set Theory and Topology

These notes are an introduction to set theory and topology. They are the result of teaching a two-semester course sequence on these topics at Washington University in St. Louis. Please note the more restrictive CC-BY NC ND license does not allow any editing of the resource.

Includes: Exercises, chapter reviews

Proofs and Concepts: The Fundamentals of Abstract Mathematics

This textbook has been created and used at the University of Lethbridge. It provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. Reviews can be found through the Open Textbook Library.

Includes: Definitions

Introduction to the Modeling and Analysis of Complex Systems

This textbook introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Reviewer’s notes are included, and another review is available.

Includes: Code, exercises

Introduction to Game Theory: a Discovery Approach

This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. The questions in each of these sections are intended to serve as essay prompts for writing assignments. Reviews can be found on the Open Textbook Library.

Includes: Questions for essay prompts, exercises

Combinatorics: An Upper-Level Introductory Course in Enumeration, Graph Theory, and Design Theory, v.2

This textbook is used for a written by a math professor at the University of Lethbridge for a third year course.

Includes: Exercises and solutions, biographical briefs

Measure, Integration & Real Analysis

This textbook was written for a graduate level course and published by a traditional publisher. The online version was last updated in 2022.

Includes: Exercises

Cree Dictionary of Mathematical Terms with Visual Examples and Sound, 3rd Ed.

The third edition of the dictionary provides 176 mathematical terms, and includes both visual examples and audio pronunciations. Published by the First Nations University of Canada and University of Regina, it was reviewed by Elders, Indigenous Knowledge Keepers and Cree-speaking educators.

American Institute of Mathematics Open Textbook Initiative 

Find more open textbooks through AIM’s Open Textbook Initiative.