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

**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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