Faculty of Science

Department of Mathematics and Statistics

Mathematics

American Institute of Mathematics Open Textbook Initiative 

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

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.

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

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

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

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

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.

Includes: Exercises, solutions to select problems, MATLAB exercises.

Licence: CC BY-NC-ND (Note: this more restrictive licence does not allow any editing of the resource.)

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.

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. The authors are three UBC Mathematics Department faculty, Joel FeldmanAndrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.

Licence: CC NC-SA

Combinatorics and Graph Theory

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

Includes: Exercises, glossary

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

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.

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. Reviews are available.

Includes: Exercises

Licence: CC BY-NC-ND (Note the more restrictive licence does not allow any editing of the resource.)

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

A Cool Brisk Walk Through Discrete Mathematics

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

Includes: Videos, exercises

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.

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

Elementary Differential Equations

This book was published previously by Brooks/Cole Thomson Learning, 2001. This free edition is made available in the hope that it will be useful as a textbook or reference. Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

Licence: CC-NC-SA

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

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

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

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.

Includes: Exercises, chapter reviews

Licence: CC BY-NC-ND (Note the more restrictive licence does not allow any editing of the resource.)

Introduction to the Modeling and Analysis of Complex Systems

This textbook introduces students to mathematical/computational modelling 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

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

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.

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

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

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

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

Statistics

Introductory Statistics: Saylor

This peer reviewed textbook was written for an introductory statistics course, and focuses on core statistical concepts rather than introducing broader concepts. A review is available.

Includes: Exercises and answers

Introductory Statistics

Introductory Statistics is a peer reviewed text that follows the scope of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. It focuses on the applications of statistical knowledge rather than the theory behind it. Reviews can be found through the Open Textbook Library and BCcampus.

Includes: Key terms, chapter review, practice exercises, homework

Introduction to Probability, Statistics and Random Processes

This peer reviewed textbook is intended for undergraduate courses in probability, statistics, and random processes.

Includes: Exercises, solutions, and code

Licence: CC BY-NC-ND (Note: due to the more restrictive licence, editing this resource is not permitted.)

Introduction to Statistics

This textbook from 2003 is in the Public Domain. Many reviews are available through the Open Textbook Library.

Includes: Learning outcomes, exercises, glossary, case studies

Intermediate Statistics with R, v. 3

This textbook builds on the basic statistical thinking from an introductory course to explore a large number of statistical methods. Reviews are available through the Open Textbook Library.

Includes: Case studies

OpenIntro Statistics, 4th ed.

OpenIntro is a nonprofit with some textbook offerings in statistics. Many reviews are available on the Open Textbook Library.

Includes: Videos, slides, labs, exercises, sample exams, data sets

Think Bayes: Bayesian Statistics Made Simple

This statistics text has been positively reviewed. It covers introductory concepts in Bayesian statistics, from computational statistics to dimensions. Reviews can be found through the Open Textbook Library.

Includes: Student resources, summaries, examples, problems, and real-world applications

Actuarial Science

Risk Management for Enterprises and Individuals

This book provides a broad overview of risk management. Reviews are available through the Open Textbook Library.

Includes: Key takeaways, discussion questions, review

Loss Data Analytics

This open textbook is the first product of the Open Actuarial Textbooks Project and created by the actuarial community.

Includes: Case studies, exercises, R code

Data Science

No suggested OER at this time.


Your Subject Librarians in the Department of Mathematics and Statistics are James Murphy and Bronte Chiang.


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License

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OER by Discipline Guide: University of Calgary by editors Sarah Adams and Ramina Mukundan with Libraries and Cultural Resources is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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