General

A Gentle Introduction to the Art of Mathematics

Joe Fields (Southern Connecticut State University)

2023

GNU Free Documentation Licence

This text covers several topics in the foundations of mathematics (logic, sets, relations, functions and cardinality) and introduces the reader to many techniques of mathematical proof (direct, indirect, contradiction, contrapositive, mathematical induction, combinatorial proofs and magic). There are amusing quotations at the start of each chapter.

Format: PDF

Mathematical Reasoning: Writing and Proof

Ted Sundstrom (Grand Valley State University)

2014

Licence: CC BY-NC-SA

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

Proofs and Concepts: The Fundamentals of Abstract Mathematics

Dave Witte Morris and Joy Morris (University of Lethbridge)

2013

Licence: CC BY-NC-SA

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.

Format: LaTeX and PDF

Technical Mathematics 2e

Morgan Chase

2024

Licence: CC BY-NC-SA

This developmental-level mathematics textbook is intended for career-technical students. It is FREE online and costs $17.35 in print plus shipping; don’t get tricked into paying for access! The approach is conversational—inviting rather than intimidating—and many of the examples are drawn from everyday life rather than from the technical trades. Practice assignments are available on the MyOpenMath platform.

Format: Online, PDF, EPUB

Algebra

Abstract Algebra

Tom Judson

2022

GNU Free Documentation Licence

This text is designed to teach the principles and theory of abstract algebra. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.

Format: Online, PDF, EPUB

Algebra and Trigonometry 2e

Jay Abramson (Arizona State University)

2021

Licence: CC BY

Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Format: PDF

College Algebra 2e (OpenStax)

Jay Abramson (Arizona State University)

2021

Licence: CC BY

College Algebra 2e provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book addresses the needs of a variety of courses. College Algebra 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Format: Online and PDF

College Algebra & Trigonometry

Richard W. Beveridge

2018

Licence: CC BY-NC-SA

This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.

Format: PDF

A First Course in Linear Algebra

Robert A. Beezer (University of Puget Sound)

2021

GNU Free Documentation Licence

An introductory textbook designed for university sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.

Format: Online, PDF

Suggested for: MATH 270, MATH 271

Fundamentals of Matrix Algebra

Gregory Hartman (Virginia Military Institute)

2011

Licence: CC BY-NC

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.

Format: PDF

Suggested for: MATH 270, MATH 271

Introduction to Complex Numbers

Licence: CC BY

This is an introduction to the mathematics of complex numbers, starting from the very basics of their definitions, up to proving theorems for polynomials. The text covers everything required of most first-year mathematics courses on complex numbers with proofs, where appropriate.

Format: PDF

Suggested for: MATH 366

Linear Algebra

Jim Hefferon (St. Michael’s College)

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

Suggested for: MATH 270, MATH 271

Linear Algebra I: Skills, Concepts and Applications

Gregg Waterman (Oregon Institute of Technology)

2016

Licence: CC BY

Systems of linear equations, Euclidean spaces and victors, matrices and vectors, vector spaces and subspaces, linear transformations.

Format: PDF

Suggested for: MATH 270, MATH 271

Linear Algebra with Applications

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

2021

Licence: CC BY-NC-SA

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

Suggested for: MATH 270, MATH 271

Matrix Algebra with Computational Applications

Dirk Colbry (Michigan State University)

2021

Licence: CC BY-NC

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: Online

Modelling, Functions, and Graphs: Algebra for College Students

Katherine Yoshiwara

2018

GNU Free Documentation Licence

All students, not just those headed for science and engineering, should develop a mathematical viewpoint, including critical thinking, problem-solving strategies, and estimation, in addition to computational skills. Modeling, Functions and Graphs employs a variety of applications to motivate mathematical thinking.

Format: Online

Suggested for: MATH 270, MATH 271

Tea Time Linear Algebra Explorations in Mathematics – 2nd Edition

Leon Q. Brin

2022

Licence: CC BY-SA

This creation is an all-purpose open source textbook for linear algebra classes of all ilks. Inside you will find a complete and engaging introduction to linear algebra, making it a perfect primary resource for classroom study. Take a ride through the landscape of linear algebra from basic mechanics through inner product spaces.

Formats: PDF

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

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)

Suggested for: MATH 270, MATH 271

Analysis

Basic Analysis: Introduction to Real Analysis

Jiri Lebl

2023

Licence: CC BY-SA

This free online textbook (OER more formally) is a course in undergraduate real analysis (somewhere it is called “advanced calculus”). The book is meant both for a basic course for students who do not necessarily wish to go to graduate school, but also as a more advanced course that also covers topics such as metric spaces and should prepare students for graduate study.

Formats: Online and PDF

Introduction to Mathematical Analysis I – Third Edition

Beatriz Lafferriere, Gerardo Lafferriere, and Nguyen Mau Nam (Portland State University)

2022

Licence: CC BY-NC

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels of difficulty. Hints and solutions to selected exercises are available in the back of the book. For each section, there is at least one exercise with hints or fully solved. For those exercises, besides the solutions, there are explanations about the process itself and examples of more general problems where the same technique may be used.

The last chapter contains additional topics. These include topological properties of the real line, generalizations of the extreme value theorem and more contemporary topics that expand on the notions of continuity or optimization. Lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects.

Format: PDF

Suggested for: MATH 370

Introduction to the Modeling and Analysis of Complex Systems

Hiroki Sayama

2015

Licence: CC BY-NC-SA

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.

Format: PDF

Suggested for: MATH 480, MATH 481

Introduction to Real Analysis

William Trench

2013

Licence: CC BY-NC-SA

Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

Format: PDF

Suggested for: MATH 380

Mathematical Analysis I

Elias Zakon (University of Windsor)

2017

Licence: CC BY

This text leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor’s theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.

Format: PDF

Suggested for: MATH 370

Measure, Integration & Real Analysis

Sheldon Axler (San Francisco State University)

2021

Licence: CC BY-NC

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

Suggested for: MATH 370

Tea Time Numerical Analysis

Leon Q. Brin

2021

Licence: CC BY-SA

This textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics. The ultimate goal of Tea Time Numerical Analysis is to be a complete, one-semester, single-pdf, downloadable textbook designed for mathematics classes.

Format: PDF

Calculus

3D Interactive Plots for Multivariate Calculus

Na Yu (Toronto Metropolitan University) 

2022

Licence: CC BY-NC-SA

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: Online

Suggested for: MATH 365

Active Calculus Multivariable

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

2017

Licence: CC BY-NC-SA

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

Suggested for: MATH 365

Active Calculus 2.0

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

2017

Licence: CC BY-NC-SA

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

Suggested for: MATH 256, MATH 266

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

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

Suggested for: MATH 265, MATH 266

Applied Calculus

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

2014

Licence: CC BY

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

Format: PDF

Suggested for: MATH 260

Business Calculus with Excel

Mike May (Saint Louis University)

2024

Licence: CC BY-NC-SA

This text is intended for a one semester calculus course for business students with the equivalent of a college algebra prerequisite. Rather than being a three-semester engineering calculus course that has been watered down to fit into one semester it is designed for the business students.

Format: Online, PDF

Calculus

Gilbert Strang (MIT)

1991

Licence: CC BY-NC-SA

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.

Format: PDF

Suggested for: MATH 265, MATH 266

Calculus Early Transcendentals: Integral & Multi-Variable Calculus for Social Sciences

Petra Menz and Nicola Mulberry (Simon Fraser University)

2018

Licence: CC BY-NC-SA

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: MATH 260

Calculus Volume 1

Gilbert Strang (Massachusetts Institute of Technology) and Edwin Herman (University of Wisconsin-Stevens Point) (OpenStax)

2016

Licence: CC BY-NC-SA

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

Suggested for: MATH 265, MATH 266

Calculus Volume 2

Gilbert Strang (Massachusetts Institute of Technology) (Open Stax)

2016

Licence: CC BY-NC-SA

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

Suggested for: MATH 265, MATH 266

Calculus Volume 3

Gilbert Strang (Massachusetts Institute of Technology) (Open Stax)

2016

Licence: CC BY-NC-SA

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

Suggested for: MATH 265, MATH 266

CLP-1 Differential Calculus

Joel Feldman, Andrew Rechnitzer, and Elyse Yeager

2023

Licence: CC BY-NC-SA

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.

Format: PDF

Suggested for: MATH 265, MATH 266

CLP-2 Integral Calculus

Joel Feldman, Andrew Rechnitzer, and Elyse Yeager

2023

Licence: CC BY-NC-SA

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.

Format: PDF

Suggested for: MATH 265, MATH 266

CLP-3 Multivariable Calculus

Joel Feldman, Andrew Rechnitzer, and Elyse Yeager

2023

Licence: CC BY-NC-SA

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.

Format: PDF

Suggested for: MATH 265, MATH 266

CLP-4 Vector Calculus

Joel Feldman, Andrew Rechnitzer, and Elyse Yeager

2023

Licence: CC BY-NC-SA

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.

Format: PDF

Suggested for: MATH 265, MATH 266

Community Calculus (Single, Multivariable)

David Guichard (Whitman College)

2023

Licence: CC BY-NC-SA

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.

Format: PDF

Suggested for: MATH 365

Contemporary Calculus

Dale Hoffman (Bellevue College) and Jeff Eldridge (Edmonds Community College) 

2018

Licence: CC BY-SA

Chapters 0-3 cover differential calculus while chapters 4-8 cover integral calculus.

Formats: PDF and LaTeX

Suggested for: MATH 265, 266

Differential Calculus for the Life Sciences

Leah Edelstein-Keshet (University of British Columbia)

2017

Licence: CC BY-NC-SA

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

Suggested for: MATH 376

Elementary Calculus

Michael Corral, Schoolcraft College

2020

Licence: Free Documentation License (GNU)

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences). There are 943 exercises in the book, with answers and hints to selected exercises.

Formats: PDF, LaTex

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

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: MATH 260

Precalculus

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

2014

Licence: CC BY

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

Precalculus – College Algebra – Trigonometry

Carl Stitz (Lakeland Community College) and Jeff Zeager (Lorain County Community College)

2013

Licence: CC BY-NC-SA

This text covers the following topics: Relations and Functions, Linear and Quadratic Functions, Polynomial Functions, Rational Functions, Further Topics in Functions, Exponential and Logarithmic Functions, Hooked on Conics, Systems of Equations and Matrices, Sequences and the Binomial Theorem, Foundations of Trigonometry, and Applications of Trigonometry.

Format: PDF

Vector Calculus

Michael Corral (Schoolcraft College)

2022

GNU Free Documentation Licence

This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

Format: PDF

Differential Math

Elementary Differential Equations with Boundary Value Problems

William F. Trench (Trinity University)

2013

Licence: CC BY-NC-SA

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

Formats: PDF and LaTex

Suggested for: MATH 376

Modelling with Differential and Difference Equations

Bernardo Galvão-Sousa and Jason Siefken (University of Toronto) 

2020

Licence: CC BY-SA

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: MATH 376, MATH 476, MATH 480, MATH 481

Notes on Diffy Qs: Differential Equations for Engineers

Jirí Lebl (Oklahoma State University)

2020

Licence: CC BY-NC-SA

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

Formats: Online, PDF, and LaTex

Suggested for: MATH 376, MATH 476

Ordinary Differential Equations for Engineers and Scientists

Gregg Waterman (Oregon Institute of Technology)

2017

Licence: CC BY

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: MATH 376

Discrete Mathematics

A Cool Brisk Walk Through Discrete Mathematics

Stephen Davies (University of Mary Washington)

2023

Licence: CC BY-SA

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

Format: PDF

Suggested for: MATH 265, MATH 266

Discrete Mathematics: An Open Introduction

Oscar Levin (University of Northern Colorado)

2016

Licence: CC BY-SA

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

Suggested for: MATH 309

A Spiral Workbook for Discrete Mathematics

Harris Kwong

2015

Licence: CC BY-NC-SA

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.

Format: PDF

Number Theory

An Introduction to the Theory of Numbers

Leo Moser

2004

Licence: CC BY

This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.

Format: PDF

Number Theory: In Context and Interactive

Karl-Dieter Crisman (Gordon College) 

2021

Licence: CC BY-NC

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: MATH 409

Statistics

Basic Probability

Mike Weimerskirch (University of Minnesota) 

2022

Licence: CC BY-NC

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: Online, EPUB, PDF, and MOBI

Beginning Statistics

2012

Licence: CC BY-NC-SA

This book is meant to be a textbook for a standard one-semester introductory statistics course for general education students.

Format: Online

Suggested for: MATH 215

Collaborative Statistics

Barbara Illowsky and Susan Dean (De Anza College) 

2012

Licence: CC BY

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

Suggested for: MATH 215

Intermediate Statistics with R

Mark C. Greenwood

2014

Licence: CC BY-NC

This textbook builds on the basic statistical thinking from an introductory course to explore a large number of statistical methods.

Format: PDF

Suggested for: MATH 216

Introduction to Modern Statistics

Mine Çetinkaya-Rundel and Johanna Hardin

Licence: CC BY-SA

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: MATH 215

Introduction to Probability

Charles M. Grinstead (Swarthmore College), J. Laurie Snell (Dartmouth College)

2006

GNU Free Documentation Licence

This introductory probability book, published by the American Mathematical Society, emphasizes the use of computing to simulate experiments and make computations. The authors have prepared a set of programs to go with the book, along with solutions available to instructors. They also provide links to other probability resources.

Format: PDF

Introduction to Statistics

David Lane (Rice University)

2003

Licence: CC0 (Public Domain)

Introduction to Statistics is a resource for learning and teaching introductory statistics.

Format: Online, PDF, EPUB

Suggested for: MATH 215

Introductory Statistics 2e (OpenStax)

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

2024

Licence: CC BY

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

Suggested for: MATH 215

Introductory Statistics

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

2012

Licence: CC BY-NC-SA

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

Suggested for: MATH 215

Introductory Statistics for Life and Biomedical Sciences

Open Intro 

Licence: CC BY-SA

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: MATH 215

Learning Statistics with R: A tutorial for psychology students and other beginners

Danielle Navarro (University of New South Wales)

2018

Licence: CC BY-SA

This book covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book.

Format: PDF and LaTeX

Suggested for: MATH 216

Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics

Jonathan A. Poritz (Colorado State University)

2017

Licence: CC BY-SA

This textbook is intended for a one-semester, undergraduate statistics course. There are many concrete, specific questions that humans have about the world which are best answered by carefully collecting some data and using a modest amount of mathematics and a fair bit of logic to analyze them.  It is, therefore, the goal of this book to help you learn How to Tell the Truth with Statistics and, therefore, how to tell when others are telling the truth … or are faking their “news.”

Format: PDF

Suggested for: MATH 215

Mathematical Statistics

Gregg Waterman (Oregon Institute of Technology) 

2015

Licence: CC BY-NC-SA

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: MATH 215

Mostly Harmless Elementary Statistics – 1st Edition

Rachel L. Webb (Portland State University)

2023

Licence: CC BY-SA

This text is for an introductory level probability and statistics course with an intermediate algebra prerequisite. The focus of the text follows the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education (GAISE). Software examples provided for Microsoft Excel, TI-84 & TI-89 calculators. Students new to statistics are sure to benefit from this ADA accessible and relevant textbook. The examples are current and resonate with everyday life. The casual narrative style, has a conversational tone to provide an inclusive and easy to read format for students.

Format: PDF

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)

2019

Licence: CC BY-SA

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

Suggested for: MATH 215

Statistical Methods in Quality Control

Hamid Bazargan

2020

Licence: CC BY-SA

This book is the outcome of more than 30 years teaching a course titled “Statistical Quality Control” to B.S. students. The book is divided into fourteen chapters that cover the topics on statistical quality control needed for a one-semester course. Due to the importance of control charts and Acceptance Sampling Standards, most chapters of the book deal with the control charts and Standard Sampling Tables.

Format: PDF

Statistics Through an Equity Lens

Yvonne E. Anthony (Framingham State University)

2024

Licence: CC BY-NC-SA

This Open Educational Resource (OER) carries a significant responsibility by presenting statistics through an equity lens. The metaphor of a lens is used intentionally–as the glasses one wears can have a profound effect on what one sees. The book encourages further inspection of the ways in which data is collected, interpreted, and analyzed on a variety of social justice issues, such as health disparities, hunger and food insecurity, homelessness, behavioral health (mental health and substance use), and incarceration of males of color. It also attempts to reveal how the misuse of data can reinforce inequities, for example, by stigmatizing people and labeling neighborhoods as high poverty, violent, and having poor educational opportunities. Whether an intended or unintended consequence, irresponsible data use can contribute to racist impressions of people and communities.

Format: Online, PDF, eBook

Statistics Using Technology – Third Edition

Kathryn Kozak (Coconino Community College) 

2021

Licence: CC BY-SA

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

Suggested for: MATH 216

Think Bayes: Bayesian Statistics Made Simple

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

2012

Licence: CC BY-NC-SA

This statistics text covers introductory concepts in Bayesian statistics, from computational statistics to dimensions. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops.

Formats: Online, PDF, and LaTex

Suggested for: MATH 215