# 31 Mathematics and Statistics

# Mathematics (MAT)

See also Open Access Texts, a list of open textbooks for undergraduate mathematics curated by Professor Alistair Savage, Department of Mathematics and Statistics, University of Ottawa.

### Applied Calculus∗

Shana Calaway (Shoreline Community College), Dale Hoffman (Bellevue College), and David Lippman (Pierce College Ft Steilacoom)

2014

Licence: CC BY 3.0

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

Format: PDF

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

###### Suggested for:

###### MAT 1300 Mathematical Methods I

###### MAT 1308 Introduction to Calculus

### Calculus Volume 1∗

Gilbert Strang (MIT) and Edwin Herman (University of Wisconsin-Stevens Point) (OpenStax)

2016

Licence: CC BY-NC-SA 4.0

*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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.

Formats: Online and PDF; online LibreTexts version

Includes: Exercises and answers

Reviews: Open Textbook Library – BCcampus – eCampusOntario Open Library

###### Suggested for:

###### MAT 1320 Calculus I

###### MAT 1321 Intensive Calculus I

###### MAT 1329 Intensive Mathematical Methods I

### Calculus Volume 2∗

Gilbert Strang (MIT) (Open Stax)

2016

Licence: CC BY-NC-SA 4.0

*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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

Formats: Online and PDF; online LibreTexts version

Includes: Exercises and answers

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1321 Intensive Calculus I

###### MAT 1322 Calculus II

###### MAT 1329 Intensive Mathematical Methods I

### Calculus Volume 3∗

Gilbert Strang (MIT) (Open Stax)

2016

Licence: CC BY-NC-SA 4.0

*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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Formats: Online and PDF; online LibreTexts version

Includes: Exercises and answers

Reviews: Open Textbook Library – BCcampus

###### Suggested for:

###### MAT 1322 Calculus II

Matt Boelkins, David Austin, and Steve Schlicker (Grand Valley State University)

2017

Licence: CC BY-NC-SA 4.0

*Active Calculus* (2017 edition) may be used as a stand-alone textbook for a standard first-semester college calculus course or as a supplement to a more traditional text. Chapters 1–4 address the typical topics for differential calculus, while Chapters 5–8 provide the standard topics of integral calculus, including a chapter on differential equations (Chapter 7) and on infinite series (Chapter 8). In *Active Calculus*, 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. We pose problems or situations, consider possibilities, and then ask students to investigate and explore. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true.

Formats: Online and PDF

Includes: Interactive exercises and graphics in online version

Reviews: Open Textbook Library – eCampusOntario Open Library

###### Suggested for:

###### MAT 1300 Mathematical Methods I

###### MAT 1308 Introduction to Calculus

###### MAT 1320 Calculus I

###### MAT 1322 Calculus II

### Active Calculus Multivariable∗

Steve Schlicker, David Austin, and Matthew Boelkins (Grand Valley State University)

2017

Licence: CC BY-NC-SA 4.0

*Active Calculus Multivariable* is the continuation of *Active Calculus *to multivariable functions. 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. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer plausibility arguments for such results, rarely do we include formal proofs. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true

Formats: Online, PDF, and LaTex

Includes: Exercises and solutions

Reviews: Open Textbook Library – BCcampus

###### Suggested for:

###### MAT 1320 Calculus I

###### MAT 1322 Calculus II

###### MAT 1329 Intensive Mathematical Methods I

### APEX Calculus∗

Gregory Hartman (Virginia Military Institute), Brian Heinold (Mount St. Mary’s University), Troy Siemers (Virginia Military Institute), Dimplekumar Chalishajar (Virginia Military Institute), and Jennifer Bowen (The College of Wooster)

2014

Licence: CC BY-NC 4.0

This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14.

Formats: PDF (under Download)

Includes: Interactive graphics, exercises, and solutions

Reviews: Open Textbook Library

##### Suggested for:

##### MAT 1320 Calculus I

##### MAT 1322 Calculus II

### Precalculus∗

Jay Abramson (Arizona State University), Valeree Falduto (Palm Beach State College), and Rachael Gross (Towson State University) (OpenStax)

2014

Licence: CC BY 4.0

*Precalculus *is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text.

Formats: Online and PDF; online LibreTexts version

Includes: Key terms, key equations, key concepts, review exercises, and practice tests

Reviews: Open Textbook Library – BCcampus

###### Suggested for:

###### MAT 1318 Functions

### Linear Algebra with Applications∗

W. Keith Nicholson (University of Calgary) (Lyryx)

2018

Licence: CC BY-NC-SA 4.0

Overall, 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.

The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate

Format: PDF

Includes: Solution manual to exercises and lecture slides

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1341 Introduction to Linear Algebra

### Linear Algebra∗

Jim Hefferon (St. Michael’s College)

2016 (updated 2020)

Licences: GNU Free Documentation License or CC BY-SA 2.5

This text covers the standard material for a US undergraduate first course: 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. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.

Includes: Exercises, solutions, lab manual, lecture slides, and applications of linear algebra

Reviews: MAA – Open Textbook Library

###### Suggested for:

###### MAT 1341 Introduction to Linear Algebra

### Book of Proof – Third Edition∗

Richard Hammack (Virginia Commonwealth University)

2018

Licence: CC BY-NC-ND 4.0

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

Formats: PDF

Includes: Instructor resources and workbook

Reviews: MAA – Open Textbook Library

###### Suggested for:

###### MAT 1362 Mathematical Reasoning and Proofs

### Mathematical Reasoning: Writing and Proof∗

Ted Sundstrom (Grand Valley State University)

2014

Licence: CC BY-NC-SA 3.0

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.

Format: PDF

Includes: Questions, answers, and instructor resources upon request

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1362 Mathematical Reasoning and Proofs

### Calculus for the Life Sciences: A Modeling Approach Volume 1∗

James L. Cornette and Ralph A. Ackerman (Iowa State University)

2011

Licence: CC BY-NC-ND 3.0

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. (Note: clickable table of contents in PDF does not work)

Formats: PDF and EPUB

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

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1327 Intensive Calculus for the Life Sciences I

###### MAT 1330 Calculus for the Life Sciences I

### Calculus for the Life Sciences: A Modeling Approach Volume 2∗

James L. Cornette and Ralph A. Ackerman (Iowa State University)

2013

Licence: CC BY-NC-ND 3.0

This textbook was written by two professors at Iowa State University with the goal of 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. (Note: clickable table of contents in PDF does not work)

Formats: PDF and EPUB

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

###### Suggested for:

###### MAT 1327 Intensive Calculus for the Life Sciences I

###### MAT 1330 Calculus for the Life Sciences I

###### MAT 1332 Calculus for the Life Sciences II

### Differential Calculus for the Life Sciences∗

Leah Edelstein-Keshet (UBC)

2017

Licence: CC BY-NC-SA 4.0

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.

Format: PDF

Includes: Exercises and solutions to selected problems

###### Suggested for:

###### MAT 1330 Calculus for the Life Sciences I

### Discrete Mathematics: An Open Introduction∗

Oscar Levin (University of Northern Colorado)

2016

Licence: CC BY-SA 4.0

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

Formats: Online, PDF, and LaTex

Includes: Questions, answers, and instructor resources upon request

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1348 Discrete Mathematics for Computing

### Introductory Statistics∗

Douglas S. Shafer and Zhiyi Zhang (University of North Carolina) (Saylor Foundation)

2012

Licence: CC BY-NC-SA 3.0

This peer-reviewed resource introduces statistical concepts, including: descriptive statistics, basic concepts of probability, discrete random variables, continuous random variables, sampling distributions, estimation, testing hypotheses, two-sample problems, correlation and regression, and chi-square and f-tests.

Formats: Online and PDF

Includes: Exercises

Reviews: Open Textbook Library – BCcampus – eCampusOntario Open Library

###### Suggested for:

###### MAT 1371 Descriptive Statistics

###### MAT 1372 Elements of Probability and Statistical Inference

### Introductory Statistics∗

Barbara Illowsky (De Anza College), Susan Dean (De Anza College), and Laurel Chiappetta (University of Pittsburgh) (OpenStax)

2013

Licence: CC BY 4.0

*Introductory Statistics* follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it.

Formats: Online and PDF; online LibreTexts version

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

Reviews: Open Textbook Library – BCcampus

###### Suggested for:

###### MAT 1371 Descriptive Statistics

###### MAT 1372 Elements of Probability and Statistical Inference

### Think Bayes: Bayesian Statistics Made Simple∗

Allen B. Downey (Franklin W. Olin College of Engineering)

2012

Licence: CC BY-NC-SA 4.0

This statistics text has been positively-reviewed. It covers introductory concepts in Bayesian statistics, from computational statistics to dimensions.

Formats: Online, PDF, and LaTex

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

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 2371 Introduction to Probability

###### MAT 3373 Methods of Machine Learning

###### MAT 4171 Probability Theory II

### Introduction to Probability, Statistics and Random Processes∗

Hossein Pishro-Nik (University of Massachusetts Amherst)

2014

Licence: CC BY-NC-ND 3.0

This textbook is intended for undergraduate and first-year graduate-level courses in probability, statistics, and random processes. This probability textbook can be used by both students and practitioners in engineering, mathematics, finance, and other related fields.

Formats: Online

Includes: Exercises, solutions, and code

###### Suggested for:

###### MAT 2371 Introduction to Probability

###### MAT 2377 Probability and Statistics for Engineers

### Introduction to Game Theory: a Discovery Approach∗

Jennifer Firkins Nordstrom (Linfield College)

Last updated: 2020

Licence: CC BY-SA 4.0

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! 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. It suggests films, television shows, and novels with themes from game theory. The questions in each of these sections are intended to serve as essay prompts for writing assignments.

Formats: Online and PDF

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1374 Probability and Games of Chance: Poker 101

### Measure, Integration & Real Analysis

Sheldon Axler (San Francisco State University)

Last updated: 2021

Licence: CC BY-NC 4.0

This book seeks to provide students with a deep understanding of the definitions, examples, theorems, and proofs related to measure, integration, and real analysis. The content and level of this book fit well with the first-year graduate course on these topics at most American universities. This textbook features a reader-friendly style and format that will appeal to today’s students.

Format: PDF

Includes: Supplement with exercises

Reviews:

###### Suggested for:

###### MAT 2125 Elementary Real Analysis

###### MAT 3120 Real Analysis

###### MAT 4124 Introduction to Functional Analysis

### Delftse Foundations of Computation∗

Stefan Hugtenburg and Neil Yorke-Smith (Delft University of Technology)

2018

Licence: CC BY-NC-SA 4.0

The textbook is designed for an introductory course in theoretical computer science. It includes topics from propositional and predicate logic, proof techniques, set theory and the theory of computation, along with practical applications to computer science.

Format: PDF

Includes: Exercises

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1348 Discrete Mathematics for Computing

### Foundations of Computation∗

Carol Critchlow and David Eck (Hobart and William Smith Colleges)

2011

Licence: CC BY-NC-SA 4.0

The textbook is designed for a one-semester course in theoretical computer science.

Format: PDF

Includes: Exercises

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 1348 Discrete Mathematics for Computing

### Elementary Differential Equations with Boundary Value Problems∗

William F. Trench (Trinity University)

2013

Licence: CC BY-NC-SA 3.0

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

Formats: PDF and LaTex

Includes: Exercises, LaTex source code, and student solutions manual (under Additional Resources)

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 2324 Ordinary Differential Equations and the Laplace Transform

###### MAT 2384 Ordinary Differential Equations and Numerical Methods

###### MAT 3320 Mathematics for Engineers

Notes on Diffy Qs: Differential Equations for Engineers∗

Jirí Lebl (Oklahoma State University)

2014, last updated 2020

Licence: CC BY-NC-SA 4.0

This textbook is designed for a one-semester first course on differential equations, aimed at engineering students.

Formats: Online, PDF, and LaTex

Includes: Exercises and solutions, figures as PDF, and WeBWorK online homework problems (under Supplementary materials)

Reviews: Open Textbook Library

###### Suggested for:

###### MAT 2324 Ordinary Differential Equations and the Laplace Transform

###### MAT 2384 Ordinary Differential Equations and Numerical Methods