Faculty of Science
Department of Mathematics and Statistics
Actuarial Science
Risk Management for Enterprises and Individuals
This book provides a broad overview of risk management.
Includes: Key takeaways, discussion questions, review
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
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
Licence: CC BY 4.0
Mathematics
Active Calculus 2.0
This textbook is designed to create active learners, focusing on having students solve challenging problems. This textbook can be used along with Active Calculus Multivariable.
Includes: Interactive exercises and solutions, lab manual, other instructor resources.
Licence: CC BY-SA 4.0
Reviews: Available through the Open Textbook Library
Active Calculus Multivariable
This textbook is designed to create active learners, focusing on having students solve challenging problems. This textbook can be used along with Active Calculus 2.0.
Includes: Interactive exercises and solutions, lab manual, other instructor resources.
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
American Institute of Mathematics Open Textbook Initiative
Find more open textbooks through AIM’s Open Textbook Initiative.
Licence: Please refer to the individual licenses of the Open Textbooks. Licenses will vary.
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.
Includes: interactive graphics, exercises and solutions
Licence: CC BY-NC
Reviews: Available through the Open Textbook Library
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
Licence: CC BY
Book of Proof, 3rd Edition
This book is an introduction to the standard methods of proving mathematical theorems.
Includes: Instructor resources and workbook
Licence: CC BY-ND (Note: This is an open access text which restricts remixing and adapting).
Reviews: Available through the Open Textbook Library
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.
Includes: Instructor’s manual, a student study guide with exercises and select solutions, links to a calculus video series by the author
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
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.
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.)
Reviews: Available through the Open Textbook Library
Calculus: Volume 1
Concepts covered in this OpenStax volume with ancillary resources includes functions, limits, derivatives, and integration.
All volumes include: Exercises and answers, instructor resources, student resources.
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
Calculus: Volume 2
Concepts covered in this OpenStax volume with ancillary resources includes integration, differential equations, sequences and series, and parametric equations and polar coordinates.
All volumes include: Exercises and answers, instructor resources, student resources.
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
Calculus: Volume 3
Concepts covered in this OpenStax volume includes parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
All volumes include: Exercises and answers, instructor resources, student resources.
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
CLP-1 Differential Calculus
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 Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Licence: CC NC-SA
CLP-2 Integral Calculus
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 Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Licence: CC NC-SA
CLP-3 Multivariable Calculus
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 Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Licence: CC NC-SA
CLP-4 Vector Calculus
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 Feldman, Andrew 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 (LibreTexts)
This introduction to combinatorics available through LibreTexts discusses inclusion-exclusion, generating functions, and other topics.
Includes: Exercises, glossary
Licence: CC BY-NC-SA
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
Licence: CC BY-NC-SA 2.0
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.
Licence: CC BY-NC-SA
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.
Includes: Exercises
Licence: CC BY-NC-ND (Note the more restrictive licence does not allow any editing of the resource.)
Reviews: Available through the Open Textbook Library
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
Licence: CC BY
A Cool Brisk Walk Through Discrete Mathematics
This text covers sets, relations, probability, structures, counting, logic, and proof.
Includes: Videos, exercises
Licence: CC BY-SA
Reviews: Available through the Open Textbook Library
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.
Licence: CC BY-NC-SA
Differential Calculus: From Practice to Theory [New]
Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the foundational ideas (limits, continuity) are developed to replace infinitesimals, first intuitively then rigorously. This approach is more historically accurate than the usual development of calculus and, more importantly, it is pedagogically sound. The text also incorporates curated activities from the TRansforming Instruction in Undergraduate Mathematics Instruction via Primary Historical Sources (TRIUMPHS) project to provide students with ample opportunities to develop relevant competencies. [Description from resource].
Licence: CC BY-NC-SA
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.
Includes: Questions, answers, instructor resources upon request
Licence: CC BY-SA 4.0
Reviews: Available through the Open Textbook Library
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.
Includes: Exercises, hints
Licence: CC BY-SA
Reviews: Available through the Open Textbook Library
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.
Includes: Exercises, solutions, definitions
Licence: CC BY-NC
Reviews: Available through the Open Textbook Library
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.
Includes: Questions for essay prompts, exercises
Licence: CC BY-SA
Reviews: Available through the Open Textbook Library
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.
Includes: Code, exercises
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library and within the textbook
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. Supplementary materials are available.
Includes: Exercises, solutions, lab manual, lecture slides, videos
Licence: CC BY-SA
Reviews: Available through the Open Textbook Library and other sources
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.
Includes: Instructor resources: solution manual to exercises and lecture slides.
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
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.
Includes: Questions, answers, and instructor resources upon request
Licence: CC BY-NC-SA 3.0
Reviews: Available through the Open Textbook Library
Measure, Integration & Real Analysis
This textbook was written for a graduate level course and published by a traditional publisher.
Includes: Exercises
Licence: CC BY-NC
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.
Includes: Definitions
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
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.
Includes: Exercises, selected solutions
Licence: CC BY-NC-SA
Reviews: Available through the Open Textbook Library
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.
Includes: Exercises and answers
Licence: CC BY-NC-SA
Reviews: Available through the Open Library
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.
Includes: Key terms, chapter review, practice exercises, homework
Reviews: Available through the Open Textbook Library and BCcampus
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
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.
Includes: Learning outcomes, exercises, glossary, case studies
Licence: CC0, Public Domain
Reviews: Available through the Open Textbook Library
Intermediate Statistics with R
This textbook builds on the basic statistical thinking from an introductory course to explore a large number of statistical methods.
Includes: Case studies
Licence: CC BY-NC 4.0
Reviews: Available through the Open Textbook Library
OpenIntro Statistics, 4th Edition
OpenIntro is a nonprofit with some textbook offerings in statistics.
Includes: Videos, slides, labs, exercises, sample exams, data sets
Licence: CC BY-SA 3.0, CC BY-NC-SA 3.0
Reviews: Available through the Open Textbook Library
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.
Includes: Student resources, summaries, examples, problems, and real-world applications
Licence: CC BY-NC
Reviews: Available through the Open Textbook Library
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