57 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.
Approved Textbooks, a list of open textbooks by course titles that have been judged to meet the evaluation criteria set by the American Institute of Mathematics (AIM) editorial board.
3D Interactive Plots for Multivariate Calculus
Na Yu (Toronto Metropolitan University)
2022
Licence: CC BY-NC-SA 4.0
An open textbook created to improve both teaching and learning vital concepts and techniques in multivariable calculus, one of the fundamental courses across the undergraduate curriculum in science and engineering. The goals of this resource are to help learners develop their geometric intuition about abstract and complex mathematical concepts (e.g., partial derivatives, multiple integrals, vector fields), and train them to make connections between concepts visually (e.g., connecting “vectors” in mathematics with “magnitude” and “direction” in physics) in order to more fully understand engineering, physics and mathematical problems (e.g., differential equations) in their subsequent STEM coursework.
Format: Pressbooks webbook
Suggested for:
MAT 2122 Multivariable Calculus
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
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
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.
Format: PDF (under Download)
Includes: Interactive graphics, exercises, and solutions
Reviews: Open Textbook Library
Suggested for:
MAT 1320 Calculus I
MAT 1322 Calculus II
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
The Art of Analysis
Christopher Hammond (Connecticut College)
2022
Licence: CC BY-NC-ND (Note: assigning sections is permitted, but adaptations are not allowed without permission)
The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply a special case of integrability, with particular properties that are worth noting. This point of view has implications for the treatment of other topics, particularly continuity and differentiability.
Format: PDF
Suggested for:
MAT 2125 Elementary Real Analysis
Basic Probability
Mike Weimerskirch (University of Minnesota)
2022
Licence: CC BY-NC 4.0
This book provides a brief introduction to some common ideas in the study of probability. At the University of Minnesota, this material is included in a course on College Algebra designed to give students the basic skills to take an introductory statistics course. The material itself is basic, and should be within the grasp of students who have successfully completed a high school Algebra I course.
Formats: Pressbooks webbook, EPUB, PDF, and MOBI
Suggested for:
MAT 1372 Elements of Probability and Statistical Inference
Book of Proof – Third Edition∗
Richard Hammack (Virginia Commonwealth University)
2018
Licence: CC BY-NC-ND 4.0 (Note: assigning sections is permitted, but adaptations are not allowed without permission)
This book is an introduction to the standard methods of proving mathematical theorems.
Format: PDF
Includes: Instructor resources and workbook
Reviews: MAA – Open Textbook Library
Suggested for:
MAT 1362 Mathematical Reasoning and Proofs
Calculus Early Transcendentals: Integral & Multi-Variable Calculus for Social Sciences
Petra Menz and Nicola Mulberry (Simon Fraser University)
2018
Licence: CC BY-NC-SA 4.0
Calculus Early Transcendentals: Integral & Multi-Variable Calculus for Social Sciences has been redesigned in the Department of Mathematics at Simon Fraser University from Calculus Early Transcendentals by Lyryx. Substantial portions of the content, examples, and diagrams have been redeveloped to meet the needs of social science calculus. Additional contributions have been provided by an experienced and practicing instructor. The textbook is approachable, cohesive, and suitable for standard integral calculus courses offering a comprehensive treatment of the necessary calculus techniques and concepts.
Format: PDF
Suggested for:
MAT 1308 Introduction to Calculus
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 (Note: assigning sections is permitted, but adaptations are not allowed without permission)
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 (Note: assigning sections is permitted, but adaptations are not allowed without permission)
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
Calculus Volume 1∗
Gilbert Strang (Massachusetts Institute of Technology) 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 (Massachusetts Institute of Technology) (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 (Massachusetts Institute of Technology) (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
Collaborative Statistics
Barbara Illowsky and Susan Dean (De Anza College)
2012
Licence: CC BY 4.0
This book is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. The text is named Collaborative Statistics because students learn best by doing. In fact, they learn best by working in small groups. The old saying “two heads are better than one” truly applies here.
Format: Online and PDF
Reviews: Open Textbook Library
Suggested for:
MAT 2375 Introduction to Statistics
Contemporary Calculus
Dale Hoffman (Bellevue College) and Jeff Eldridge (Edmonds Community College)
2018
Licence: CC BY-SA 3.0 US
Chapters 0-3 cover differential calculus while chapters 4-8 cover integral calculus.
Formats: PDF and LaTeX
Suggested for:
MAT 1308 Introduction to Calculus
MAT 1320 Calculus I
MAT 1322 Calculus II
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
Differential Calculus for the Life Sciences∗
Leah Edelstein-Keshet (University of British Columbia)
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
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
forall x: An Introduction to Formal Logic
P.D. Magnus (SUNY Albany)
2012
Licence: CC BY-SA 4.0
forall x is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading.
This book treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven.
See also forall x: Calgary (Fall 2020)
Formats: PDF and LaTeX
Includes: Practice exercises, solutions to selected exercises
Reviews: Open Textbook Library – BCcampus
Suggested for:
MAT 3361 Introduction to Mathematical Logic
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
Fundamental Methods of Logic
Matthew Knachel (University of Wisconsin-Milwaukee)
2017
Licence: CC BY 4.0
Fundamental Methods of Logic is suitable for a one-semester introduction to logic/critical reasoning course. It covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill’s Methods. Chapter Six covers basic probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.
Format: PDF
Reviews: Open Textbook Library
Suggested for:
MAT 1362 Mathematical Reasoning and Proofs
MAT 3361 Introduction to Mathematical Logic
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
Introduction to Linear, Time-Variant, Dynamic Systems for Students of Engineering
William L. Hallauer Jr. (Virginia Tech)
2016
Licence: CC BY-NC 4.0
The book is intended to enable students to:
- Solve first-, second-, and higher-order, linear, time-invariant (LTI) ordinary differential equations (ODEs) with initial conditions and excitation, using both time-domain and Laplace-transform methods;
- Solve for the frequency response of an LTI system to periodic sinusoidal excitation and plot this response in standard form;
- Explain the role of the time constant in the response of a first-order LTI system, and the roles of natural frequency, damping ratio, and resonance in the response of a second-order LTI system;
- Derive and analyze mathematical models (ODEs) of low-order mechanical systems, both translational and rotational, that are composed of inertial elements, spring elements, and damping devices;
- Derive and analyze mathematical models (ODEs) of low-order electrical circuits composed of resistors, capacitors, inductors, and operational amplifiers;
- Derive (from ODEs) and manipulate Laplace transfer functions and block diagrams representing output-to-input relationships of discrete elements and of systems;
- Define and evaluate stability for an LTI system; -Explain proportional, integral, and derivative types of feedback control for single-input, single-output (SISO), LTI systems;
- Sketch the locus of characteristic values, as a control parameter varies, for a feedback-controlled SISO, LTI system;
- Use MATLAB as a tool to study the time and frequency responses of LTI systems.
Format: PDF
Includes: homework problems
Suggested for:
MAT 3320 Mathematics for Engineers
Introduction to Mathematical Analysis I – Second Edition
Beatriz Lafferriere, Gerardo Lafferriere, and Nguyen Mau Nam (Portland State University)
2018
Licence: CC BY-NC 4.0
Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.
Format: PDF
Includes: Video lectures explaining problem-solving strategies, exercises
Suggested for:
MAT 2125 Elementary Real Analysis
MAT 3120 Real Analysis
Introduction to Modern Statistics
Open Intro
Licence: CC BY-SA 3.0
Introduction to Modern Statistics is a re-imagining of a previous title, Introduction to Statistics with Randomization and Simulation. The new book puts a heavy emphasis on exploratory data analysis (specifically exploring multivariate relationships using visualization, summarization, and descriptive models) and provides a thorough discussion of simulation-based inference using randomization and bootstrapping, followed by a presentation of the related Central Limit Theorem based approaches.
Other highlights include: While the main text of the book is agnostic to statistical software and computing language, each part features 4-8 interactive R tutorials (for a total of 32 tutorials) that walk you through the implementation of the part content in R with the tidyverse for data wrangling and visualization and the tidyverse-friendly infer package for inference. The self-paced and interactive R tutorials were developed using the learnr R package, and only an internet browser is needed to complete them. Each part also features 1-2 R based labs. The labs consist of data analysis case studies and they also make heavy use of the tidyverse and infer packages. Datasets used in the book are marked with a link to where you can find the raw data. The majority of these point to the openintro package. You can install the openintro package from CRAN or get the development version on GitHub.
Formats: Online and PDF
Suggested for:
MAT 2375 Introduction to Statistics
Introduction to Probability, Statistics and Random Processes∗
Hossein Pishro-Nik (University of Massachusetts Amherst)
2014
Licence: CC BY-NC-ND 3.0 (Note: assigning sections is permitted, but adaptations are not allowed without permission)
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.
Format: Online
Includes: Exercises, solutions, and code
Suggested for:
MAT 2371 Introduction to Probability
MAT 2377 Probability and Statistics for Engineers
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
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 for Life and Biomedical Sciences
Open Intro
Licence: CC BY-SA 3.0
Introduction to Statistics for the Life and Biomedical Sciences has been written to be used in conjunction with a set of self-paced learning labs. These labs guide students through learning how to apply statistical ideas and concepts discussed in the text with the R computing language.
The text discusses the important ideas used to support an interpretation (such as the notion of a confidence interval), rather than the process of generating such material from data (such as computing a confidence interval for a particular subset of individuals in a study). This allows students whose main focus is understanding statistical concepts to not be distracted by the details of a particular software package. In our experience, however, we have found that many students enter a research setting after only a single course in statistics. These students benefit from a practical introduction to data analysis that incorporates the use of a statistical computing language. In a classroom setting, we have found it beneficial for students to start working through the labs after having been exposed to the corresponding material in the text, either from self-reading or through an instructor presenting the main ideas. The labs are organized by chapter, and each lab corresponds to a particular section or set of sections in the text. There are traditional exercises at the end of each chapter that do not require the use of computing. More complicated methods, such as multiple regression, do not lend themselves to hand calculation and computing is necessary for gaining practical experience with these methods. The lab exercises for these later chapters become an increasingly important part of mastering the material. An essential component of the learning labs are the “Lab Notes” accompanying each chapter. The lab notes are a detailed reference guide to the R functions that appear in the labs, written to be accessible to a first-time user of a computing language. They provide more explanation than available in the R help documentation, with examples specific to what is demonstrated in the labs. The notes cover topics such as constructing histograms, writing loops, and running regression models.
Formats: PDF and LaTeX
Suggested for:
MAT 2379 Introduction to Biostatistics
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.
Formats: PDF and LaTeX
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
Linear Algebra I: Skills, Concepts and Applications
Gregg Waterman (Oregon Institute of Technology)
2016
Licence: CC BY 4.0
Systems of linear equations, Euclidean spaces and victors, matrices and vectors, vector spaces and subspaces, linear transformations.
Format: PDF
Includes: Exercises and solutions
Suggested for:
MAT 1341 Introduction to Linear Algebra
Linear Algebra with Applications∗
W. Keith Nicholson (University of Calgary) (Lyryx)
2018, updated 2021
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
Math 679 – Elliptic Curves
Andrew Snowden (University of Michigan)
Revised June 2015
Licence: CC BY 3.0
Math 679 is a graduate-level mathematics course whose purpose is to prove Mazur’s theorem. Mazur’s theorem is a well-known and important result, however it is not often taught in classroom settings. The course is divided into three parts: elliptic curves and abelian varieties, moduli of elliptic curves, and proof of Mazur’s theorem.
Formats: PDF and video
Suggested for:
MAT 5160 Mathematical Cryptography
Mathematical Python
Patrick Walls (University of British Columbia)
2019
Licence: CC BY-NC-SA 4.0
Mathematical Python is an introduction to mathematical computing including:
- Jupyter notebooks, markdown and LaTeX
- Basic Python programming: datatypes, logic, loops and functions
- Scientific computing with NumPy, SciPy and Matplotlib
- Applications in calculus, linear algebra and differential equations
Format: Online
Suggested for:
MAT 1373 Data Analysis By Computer
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
Mathematical Statistics
Gregg Waterman (Oregon Institute of Technology)
2015
Licence: CC BY-NC-SA 3.0
The title of this book is perhaps misleading, as there is no statistics within. It is instead a fairly straightforward introduction to mathematical probability, which is the foundation of mathematical statistics. One could follow this course with a rigorous treatment of statistics, beyond that usually seen in most introductory statistics courses.
Format: PDF
Suggested for:
MAT 1372 Elements of Probability and Statistical Inference
MAT 2371 Introduction to Probability
Matrix Algebra with Computational Applications
Dirk Colbry (Michigan State University)
2021
Licence: CC BY-NC 4.0
Matrix Algebra with Computational Applications is a collection of OER materials designed to introduce students to the use of Linear Algebra to solve real-world problems. These materials were developed specifically for students and instructors working in a “flipped classroom” model that emphasizes hands-on problem-solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom.
Format: Pressbooks webbook
Suggested for:
MAT 1302 Mathematical Methods II
MAT 1332 Calculus for the Life Sciences II
MAT 2342 Introduction to Applied Linear Algebra
MAT 3341 Applied Linear Algebra
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: Open Textbook Library
Suggested for:
MAT 2125 Elementary Real Analysis
MAT 3120 Real Analysis
MAT 4124 Introduction to Functional Analysis
Modelling with Differential and Difference Equations
Bernardo Galvão-Sousa and Jason Siefken (University of Toronto)
2020
Licence: CC BY-SA 4.0
This book is designed for a one-semester introductory modelling course focusing on differential and difference equations (MAT231 at the University of Toronto). Each module contains exposition about a subject, practice problems (for students to work on by themselves), and core exercises (for students to work on with your guidance). Modules group related concepts, but the modules have been designed to facilitate learning modelling rather than to serve as a reference.
Format: PDF
Suggested for:
MAT 3395 Introduction to Mathematical Models
MAT 1332 Calculus for the Life Sciences II
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
Number Theory: In Context and Interactive
Karl-Dieter Crisman (Gordon College)
2021
Licence: CC BY-NC 4.0
The book tackles all standard topics of modular arithmetic, congruences, and prime numbers, including quadratic reciprocity. In addition, there is significant coverage of various cryptographic issues, geometric connections, arithmetic functions, and basic analytic number theory, ending with a beginner’s introduction to the Riemann Hypothesis. Ordinarily this should be enough material for a semester course with no prerequisites other than a proof-transition experience and vaguely remembering some calculus.
Format: Online
Suggested for:
MAT 3166 Introduction to Number Theory
Numerical Analysis
Benoit Dionne (University of Ottawa)
2023
Licence: CC BY-NC-SA 4.0
This book covers the material normally presented in a two-term course on numerical analysis, starting with the basic concept and ending with topics that are more appropriate for a course in numerical analysis for differential equations: numerical solution of systems of linear and nonlinear equations, polynomial interpolation, numerical approximation of functions, numerical computation of eigenvalues, numerical derivation and integration, numerical solution of ordinary and partial differential equations.
With a focus on algorithms, it can be used as an introduction to numerical analysis for engineering and applied science students. With a focus on theory, it can be used as an introduction to numerical analysis for students in mathematics or physics. Most of the numerical methods presented in this book are accompanied by a MATLAB code.
Formats: PDF and LaTeX (on Github)
Suggested for:
MAT 3380 Introduction to Numerical Methods
MAT 5180 Numerical Analysis for Differential Equations
Open-Access Clicker Question Bank for Numerical Analysis
John Stockie and Petra Menz (Simon Fraser University)
2019
Licence: CC BY-NC-SA 4.0
This open educational resource is a bank of over 250 multiple-choice and true-false questions that explores the material taught in a typical introductory undergraduate course in numerical analysis. The questions are typeset in LaTeX and are intended for classroom use with clickers (also known as student response systems) where students use a hand-held clicker remote or smartphone to submit their responses to questions.
Format: LaTeX and PDF
Suggested for:
MAT 1320 Calculus I
MAT 1325 Calculus II and an Introduction to Analysis
OpenIntro Statistics – Fourth Edition
David M. Diez (Harvard School of Public Health), Christopher D. Barr (Harvard School of Public Health), and Mine Cetinkaya-Rundel (Duke University)
2015, updated 2019
Licence: CC BY-SA 4.0
OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to applied statistics that is clear, concise, and accessible. This book was written with the undergraduate level in mind, but it’s also popular in high schools and graduate courses.
Format: PDF
Reviews: Open Textbook Library
Suggested for:
MAT 2375 Introduction to Statistics
Optimal, Integral, Likely: Optimization, Integral Calculus, and Probability
Bruno Belevan, Parham Hamidi, Nisha Malhotra, and Elisse Yeager (University of British Columbia)
2020
Licence: CC BY-NC-SA 4.0
Optimal, Integral, Likely is a free, open-source textbook intended for UBC’s course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences.
Format: PDF
Suggested for:
MAT 1300 Mathematical Methods I
MAT 1308 Introduction to Calculus
Ordinary Differential Equations for Engineers and Scientists
Gregg Waterman (Oregon Institute of Technology)
2017
Licence: CC BY 4.0
This book is a fairly straightforward introduction to differential equations, with an applied emphasis. The student should be aware that this is a huge subject, with lifetimes of study possible. Our hope is that this collection of explanations, examples and exercises will create a solid foundation for understanding differential equations when they are encountered in subject-specific courses, and for further study of differential equations themselves. In the past an introduction to differential equations has usually consisted of learning specific techniques for solving a variety differential equations. It should be no surprise that those techniques are easily forgotten in short order! We will look at techniques for obtaining solutions – that is an essential part of the subject. However, we will also attend to the “bigger picture,” in the hopes of giving the student an overall understanding of the subject that will be more lasting than just a bunch of ‘recipes” for obtaining solutions. Our study of the subject of differential equations will be guided by some overarching goals, and essential questions related to those goals.
Format: PDF
Suggested for:
MAT 3320 Mathematics for Engineers
Partial Differential Equations
Benoit Dionne (University of Ottawa)
2024
Licence: CC BY NC SA 4.0
With an emphasis on teaching and learning, this book is for an advanced undergraduate course on partial differential equations or a beginning graduate course on partial differential equations. Divided into 13 chapters, this textbook covers most of the important topics found in books on partial differential equations, using most of the time the same approach. This book contains material on partial differential equations usually taught at the undergraduate level for science and engineering students. The reason for including this material is that many mathematics students do not have the chance to study partial differential equations at the undergraduate level. The sections covering the undergraduate material are accessible to readers with only a calculus background. The presentation in these sections is usually more formal and therefore appropriate for introducing partial differential equations for science and engineering students. This book is accessible to students with a minimal introduction to measure and integration, and functional analysis.
Format: PDF
Suggested for:
MAT 3320 Mathematics for Engineers
MAT 3335 Numerical Methods for Differential Equations
MAT 4130 Introduction to Partial Differential Equations
MAT 5133 Partial Differential Equations I
MAT 5180 Numerical Analysis for Differential Equations
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
Statistics 250 – Introduction to Statistics and Data Analysis
Brenda Gunderson (University of Michigan)
Revised September 2015
Licence: CC BY-NC-SA 3.0
Statistics is the science that turns data into information and information into knowledge. This class covers applied statistical methodology from an analysis-of-data viewpoint. Topics covered include frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentation; elementary probability; populations and samples; sampling distributions; one sample univariate inference problems, and two sample problems; categorical data; regression and correlation; and analysis of variance. Use of computers in data analysis is also explored.
Formats: PDF and Word
Includes: Workbooks and interactive lecture notes
Suggested for:
MAT 1371 Descriptive Statistics
MAT 1372 Elements of Probability and Statistical Inference
MAT 2375 Introduction to Statistics
Statistics Using Technology – Third Edition
Kathryn Kozak (Coconino Community College)
2021
Licence: CC BY-SA 4.0
This is an introductory Statistics textbook for first-year college courses. This book places data at the center of the course. It also uses the statistical package R, though you can use another statistical computer package if you wish.
Formats: PDF, Word, and R Markdown
Reviews: BCcampus
Suggested for:
MAT 1373 Data Analysis By Computer
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
Vector Spaces First: An Introduction to Linear Algebra (Fourth Edition)
Thierry Giordano, Barry Jessup, and Monica Nevins (University of Ottawa)
2021
Licence: CC BY-NC-SA 4.0
Created for a first-year university course, this linear algebra textbook takes an unusual approach: it introduces vector spaces at the outset and deals with linear systems only after a thorough introduction to vector spaces. This approach is based on the authors’ experience over the past 25 years that students often need more time to master vector spaces while traditional textbooks relegate the topic to the end of the course. In this way, these new notions at the heart of linear algebra that are often considered abstract and difficult in an introductory course can then be used in the rest of the course as well as in different contexts.
Formats: PDF and LaTeX (on Github)
Used in:
MAT 1341 Introduction to Linear Algebra