Mathematics, Lower Division

A textbook for an introductory linear algebra course with an algebraic approach that serves as a transition course for math majors, emphasizing definitions, theorems, and proofs. Read more

The book that started it all, now converted to PreTeXt (its third source format).

This book is aimed at mathematics majors, seeing their first course after calculus that stresses theorems and their proofs. It contains a very thorough introduction to the use of the open source system, Sage, for linear algebra. Besides an extensive collection of traditional exercises, there are also reading questions for each of the thirty-seven (daily) sections.

Textbook for a standard one-semester multivariable calculus course, emphasizing an active learning approach. Read more

Active Calculus - Multivariable is a free, open-source calculus text that is designed to support an active learning approach in third semester of calculus, including approximately 100 activities and 300 exercises.

Each section of the text has at least 3 in-class activities to engage students in active learning. More information on our goals and the structure of the text can be found at .

Textbook for a standard two-semester calculus course, emphasizing an active learning approach. Read more

Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Print versions are in black and white to keep costs low; the electronic versions are full-color.

Through direct request to the author by email (boelkinm at gvsu dot edu), a range of ancillary materials are available to faculty, including WeBWorK .def files, activities workbooks (.pdf files that include only the activities along with room for students to write), computer laboratory exercises for chapters 1-4 that use Geogebra, and daily prep assignments to support students reading the text. Both the 2018 HTML and PDF versions include answers to activities and exercises in appendices in the back.

Each section of the text has at least 3 in-class activities to engage students in active learning. The section on the tangent line approximation is representative of the organization and style of other sections in the text: a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on our goals and the structure of the text can be found in the preface.

Active Calculus - single variable has been publicly available since August 2012. The PDF version has been downloaded over 120,000 times since August 2014 (though most users now prefer the HTML version). The author maintains an email list of interested users and communicates a few times a year with updates to the community.

Active Prelude is designed for a preparatory course for students not yet ready to take calculus; it is especially suited to students who will later study from Active Calculus. Read more

Active Prelude to Calculus is designed as a college-level preparatory text for students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. In particular, the text is intended as an appropriate prerequisite base for students who will go on to study from Active Calculus while also encouraging and promoting an active learning approach. The HTML version of the text includes about 150 anonymous, interactive exercises; static versions of those problems are included in PDF and print. In addition, the text offers about 120 activities designed for student engagement in and out of class. Learn more at

A one semester calculus course aimed at business students, using Excel, and following CRAFTY recommendations. Read more

A one semester course in calculus aimed at business students.

The book is designed to follow the recommendations of the MAA CRAFTY committee

In particular the book assumes studnets will have a laptop with Excel for the class.

Examples are heavily drawn for business context and use business notation

The order of the topics has been tweaked to match the preferences of business faculty. (Partial derivatives are before integrals.)

Numerical methods get a heavier emphasis than in a traditional book.

Homework problems are in the process of being converted to WeBWorK

A text for a standard first undergraduate differential calculus course. Read more

A text for a standard first undergraduate differential calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A text for a standard first undergraduate integral calculus course. Read more

A text for a standard first undergraduate integral calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A text for a standard first undergraduate multivariable calculus course. Read more

A text for a standard first undergraduate multivariable calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

A text for a standard first undergraduate vector calculus course. Read more

A text for a standard first undergraduate vector calculus course. Included are a substantial collection of problems with complete hints, answers and solutions. Many of those problems are taken from exams, midterms and quizzes given at UBC.

Calculus I, II, and III: A Problem-Based Approach with Early Transcendentals, W. Ted Mahavier

An inquiry-based learning approach to calculus. Read more

These notes constitute a self-contained sequence for teaching, using an inquiry-based pedagogy, most of the traditional topics of Calculus I, II, & III in classes of up to 40 students.

A lab manual with supplementary material for a first-semester calculus course. Read more

Calculus I is taught at Portland Community College using a lecture/lab format. The laboratory time is set aside for students to investigate the topics and practice the skills that are covered during their lecture periods. This lab manual serves as a guide for the laboratory component of the course.

Textbook for a discovery-based approach to linear algebra. Read more

A discovery-based approach to linear algebra.

Extended material to cover a second course in linear algebra is being finalized and will be released Summer 2019.

Discrete Mathematics, David M. ClarkW. Ted Mahavier

An inquiry-based learning approach to Discrete Mathematics. Read more

This course constitutes a mathematically rigorous introduction to sets, functions, counting, induction, equivalence relations, recursion, elementary graph theory, finite state machines, and languages.

A textbook for a first or second year undergraduate course in discrete mathematics for math majors, especially those who will go on to teach. Read more

A free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. Also appropriate for an introduction to proofs course with discrete content.

Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions helps students gain familiarity with the language of mathematics, and two additional topics (generating functions and number theory) are also included.

While the book began as a set of lecture notes, it now contains a number of features that should support its use as a primary textbook:

  • 473 exercises, including 275 with solutions and another 109 with hints. Exercises range from easy to quite involved, with many problems suitable for homework.
  • Investigate! activities throughout the text to support active, inquiry based learning.
  • A full index and list of symbols.
  • Consistent and helpful page layout and formatting (i.e., examples are easy to identify, important definitions and theorems in boxes, etc.).

Discrete Mathematics for Computer Science, Mark Fitch

In class materials for an introduction to logic, proof, enumeration, relations, and graph theory for lower division undergraduate students of computer science and computer systems engineering. Read more

These materials were designed to introduce concepts of logic and discrete mathematics via carefully picked problems that test understanding of definitions. Another source of exercises is required at this time.

A mashup of Applied Discrete Structures by Al Doerr and Ken Levasseur and other sources and is used for University of Hawaii's CS program discrete math requirements.

An activity-based text that studies algebraic skills in the context of modeling and problem solving. Read more

Throughout the book, we incorporate applications to motivate new topics. We present ideas using verbal, numerical, and graphical tools. We use graphs extensively to illustrate algebraic techniques and to help students visualize relationships between variables. In the Homework Problems we break up skills practice into smaller sets of exercises and combine them with conceptual questions, graphing, and applications of various types.

We have included a number of features to encourage student participation.

  • The reading is broken into small segments by using boxes around Examples, definitions, and rules, and flags including Caution, Look Closer, and Look Ahead.
  • We want students to learn how to read a math book, so we have included Reading Questions that mirror the content of the lesson. For example, the first Reading Question is A numerical quantity that changes over time or in different situations is called a __________ . Ideally, students would answer these questions before class, perhaps through an on-line homework system.
  • Each section ends with a Skills Warm-Up (with answers) for students to complete on their own. The Skills Warm-Up problems review an arithmetic or algebraic technique needed for the Lesson that follows.
  • Because choosing appropriate scales for the axes is a time-consuming task for beginning students, the text includes labeled grids for most of the graphing exercises. Ready-made grids allow students to consider a wider range of examples (with harder numbers) and to focus on the properties of the graphs, such as intercepts and slope, and on interpreting the information given by the graph. If students are using technology to create graphs, the grids can help them choose an appropriate window.

Chapter Reviews include a Summary, Review Questions for writing or discussion, and a set of Review Problems. Answers to odd-numbered Homework problems are provided, as well as a Glossary of mathematical terms.

The textbook is accompanied by an Activities Workbook that provides a Lesson for each section in the book. These Lessons consist of Activities for students to complete in groups or with guidance from the instructor; or they can be used as support for a lecture format. Each Lesson ends with a Wrap-Up and a set of Homework Preview exercises.

An Instructor's Manual for the text is also available. The Manual contains objectives and teaching notes for each section of the text, as well as suggested concept questions and topics for writing or discussion. The teaching notes include suggestions for using the Activities booklet and how to structure class time.

A computer homework system for Elementary Algebra is available through xyzhomework.

An inquiry-based introduction to game theory, appropriate for a non-majors quantitative reasoning course or an extra topics course at the secondary level. Read more

An inquiry-based introduction to game theory.

Appropriate for a non-majors quantitative reasoning course or an extra topics course at the secondary level.

Includes discussion questions on game theory in popular culture.

Complete instructor's guide available by request.

A textbook for a one-semester introductory linear algebra course, using real vector spaces and linear maps to introduce abstract mathematical thinking. Read more

A one-semester `modern' approach to Linear Algebra, at a 2nd year level.

Uses real vector spaces and linear maps to introduce abstract mathematical thinking (definitions, thereoms and proofs).

The style is conversational, the material is elementary, but the approach offers a glimpse of higher mathematics.

Notable features include: multivariable calculus (multivariable polynomials, polynomial vector fields, gradient, divergence, double integrals, etc.) as examples of vector spaces and linear maps, as well as studying differential equations from a linear algebra point of view.

A follow-up second semester course also incorporates the differential geometry of surfaces (tangent spaces, the shape operator) into linear algebra.

Includes numerous videos, images, Geogebra apps, JSXGraph apps, SageMath worksheets, as well as Tutorials.

Set of class notes for a first course in discrete math. Read more

This is a set of class notes I developed for the first discrete course at Wichita State University.

What makes this unique is that it includes complete worked examples as videos, complete solutions to exercises, and an embedded discussion forum powered by Discourse.

In the past, I've used this as my platform for my online course. For the COVID-19 Fall Hybrid-Online-Experience, I will be using this to flip my class, having this be the first point of contact for the material and running lectures.

We cover:

  • Math objects
  • Propositional Logic
  • Basic concepts of proof
  • Basic number theory, specifically applying proof techniques and building to RSA encryption
  • Sequences, recursion, and induction
  • Basic counting

Algorithms from the mathematician's viewpoint: an introductory course with Python code and Sage interacts. Read more

Mathématiques et algorithmes is an open-access textbook written in French and designed for use in a one-semester introduction to algorithms from the mathematician's viewpoint. It only assumes basic knowledge in calculus as a prerequesite: good highschool students should understand this material. Also, this digital textbook is fueled with Python code and Sage interacts to help students experiment with algorithms. Topics covered include root finding, polynomial interpolation, numerical integration and number theory.

A textbook that covers the content of a typical college algebra course with an emphasis on functions and modeling; when combined with a trigonometry text or supplement, this text can be used in a precalculus course. Read more

The text employs a variety of applications to motivate mathematical thinking. Each chapter opens with a problem of historical or contemporary significance highlighting the material in the chapter. We have also provided a set of more challenging Projects at the end of each chapter.

Function notation is introduced in Chapter 1 and is used consistently in subsequent chapters treating the various families of functions. We study functions using algebraic, numerical, graphical, and verbal methods, and work to establish the connections between these approaches. We want students to learn to write an algebraic expression from a verbal description, recognize trends in a table of data, and extract and interpret information from the graph of a function. Many students have trouble progressing from a point-wise understanding of graphs to a more global view. By taking advantage of graphing utilities, we can examine a large number of examples and study them in detail, and we can consider more realistic models.

An in-text Exercise or Checkpoint, with answers, follows each Example, allowing students to try out new concepts and skills as they are presented. Each Section Summary includes a list of new Vocabulary words that can be found in the Glossary, a brief review of new Concepts introduced in the section, a short set of Study Questions for students to test their understanding of the material, and a list of mastery Skills and the appropriate Homework Problems for practicing each skill.

The text frequently refers students to the appropriate section of Appendix A, Algebra Skills Refresher. We hope that this Appendix will be useful both to individual students and to instructors who want to provide just-in-time parallel support for their classes.

An Activities Workbook is available from xyztextbooks. The Workbook provides a Lesson for each section in the book, consisting of Activities for students to complete in groups or with guidance from the instructor; or they can be used as support for a lecture format. Each Lesson ends with a Wrap-Up and a set of questions for discussion.

An Instructor's Manual for the text is also available. The Manual contains objectives and teaching notes for each section of the text, as well as suggested concept questions and topics for writing or discussion. The teaching notes include suggestions for using the Activities booklet and how to structure class time.

A computer homework system for the text is also available through xyzhomework.

ORCCA: Open Resources for Community College Algebra, Portland Community College Faculty

A textbook package for basic and intermediate algebra, suitable for a three-term course at a community college. Read more

Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.

ORCCA is available as an interactive eBook, as a downloadable PDF (in B/W or color), and as a printed/bound copy.

Math Resources review introductory algebra, intermediate algebra, college algebra, and trigonometry. Read more

The materials begin with linear equations in two variables and extends through trigonometry. The materials can be used in various ways, particularly in online courses.

The material was written with review in mind, but there is enough detail that it would be useful for new students as well. All exercises in the content areas are fully keyed, with no steps excluded. The supplemental problem sets only include answers; they are not fully keyed. While video instruction is useful for many, there are also learners who prefer written exposition, hence the redundancy in presentation of material.

This text aims to address all learning outcomes from the first course in Mt. Hood Community College's preacalculus sequence. Read more

Precalculus is taught at Mt. Hood Community College over two 10-week courses. This text aims to address all learning outcomes from the first course, suitable for use in a single 10-week term.

Trigonometry, Katherine Yoshiwara, Bruce Yoshiwara

An introductory trigonometry text that can be used in a variety of programs, starting with intuitive notions before developing a more abstract and general framework for the ideas. Read more

For flexibility, students who have encountered elements of triangle trig in previous courses may be able to skip all or part of Chapters 1 through 3. Students preparing for technical courses may not need much of the material after Chapter 6 or 7. Chapters 9 and 10 cover vectors and polar coordinates, optional topics that occur in some trigonometry courses but are often reserved for precalculus.

Chapter 1 reviews only the most basic facts about triangles and circles that students will need to begin their study of trigonometry, and may be omitted or assigned as homework. Other facts about functions and angles are introduced when they are needed.

Chapter 2 introduces the three (not six) basic trig ratios, and considers angles in the first quadrant only. This initial simplicity allows students to focus on the fundamental concepts without simultaneously trying to master a welter of peripheral detail.

Chapter 3 introduces reference angles for the second quadrant in order to study obtuse triangles and the Laws of Sines and Cosines. Reference angles are covered again in more generality in Chapter 4.

Chapter 4 considers angles as rotations in preparation for the graphs of sine and cosine. Applications of periodic functions in this chapter are functions of degrees only. Radians come later, after students have some experience with sinusoidal graphs.

Chapter 5 begins with a section on algebraic manipulations with trig ratios, a skill that is often neglected but can engender endless confusion for students. We solve equations both graphically and analytically, and we use graphs as well as algebra to verify trigonometric identities.

Chapter 6 introduces radians and the circular functions of real numbers. Most of this chapter and Chapter 7 revisit basic skills such as analyzing graphs and solving equations, but working now in radians rather than degrees.

Chapter 8 studies identities and their use in more detail, including the sum and difference formulas and the double angle identities. Inverse trig functions are included here, and the three reciprocal trig functions.

Chapters 9 and 10 cover ancillary topics; typical trigonometry courses may include one or more of these topics: vectors, polar coordinates, and complex numbers.

Each Example in the book is followed by a similar Exercise for students to test their understanding. Each Section concludes with a Summary, a set of Study Questions, and a list of Skills to be addressed in the Homework. A Summary and a set of Review Problems follows each chapter. Chapters 1 through 8 include Activities for students to work through some of the main ideas. We have described the use of a graphing calculator, but other graphing utilities can easily be substituted.

A textbook for a one-semester introduction to linear algebra that does not assume calculus as a prerequisite, emphasizing conceptual thinking, motivating applications, and computation. Read more

Understanding Linear Algebra is an open-source, open-access textbook designed for use in a one-semester introduction to linear algebra that does not assume calculus as a prerequisite. There is an emphasis on conceptual thinking, motivating applications, and computation using the open-source software Sage. The text supports active learning by including preview activities and several in-class activities for each of its 22 sections.

Material for a second semester follow-up course is in development and will be published in May 2020.

Mathematics, Upper Division

A standard two-semester introductory course in abstract algebra covering groups, rings, and fields, plus other topics including Galois theory, featuring computations and nontrivial applications. Read more

This is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. Rob Beezer has contributed complementary material using the open source system, Sage.

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.

An IBL Introduction to Geometries, Mark Fitch

This is an IBL problem set designed to introduce a student to euclidean, hyperbolic, and projective geometry from axiomatic and transformational approaches. Read more

An IBL approach to a introduction to geometries course for future secondary teachers.

Analysis, W. Ted Mahavier

An inquiry-based learning approach to Analysis. Read more

An undergraduate, introductory, inquiry-based learning course in undergraduate real analysis on the real line.

Textbook for a one-semester introduction to combinatorics, primarily aimed at computer science majors. Read more

This is a text with more than enough material for a one-semester introduction to combinatorics. The original target audience was primarily computer science majors, but the topics included make it suitable for a variety of different students. Topics include:

  • Basic enumeration: strings, sets, binomial coefficients
  • Recursion and mathematical induction
  • Graph theory
  • Partially ordered sets
  • Additional enumeration techniques: inclusion-exclusion, generating functions, recurrence relations, and Polya theory
  • Graph algorithms: minimum weight spanning trees, Dijkstra's algorithm, network flows

For some sections, embedded SageMath Cells are used to provide assistance with computations.

A discrete mathematics text for a two-semester sequence that includes applied abstract algebra.

An introduction to combinatorics, consisting almost entirely of problems arranged in an order that encourages students to discover the underlying principles. Read more

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially, but not exclusively, on the part of combinatorics that mathematicians refer to as "counting." The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on.

There are six chapters as well as an appendix with three additional topics:

  1. What is Combinatorics?
  2. Applications of Induction and Recursion in Combinatorics and Graph Theory.
  3. Distribution Problems.
  4. Generating Functions.
  5. The Principle of Inclusion and Exclusion.
  6. Groups Acting on Sets.
The three supplemental sections deal with relations, mathematical induction, and exponential generating functions.

Many of problems have hints, which can be found in the back of the book (for the pdf and print versions) or linked directly from the problem (in the online version).

A textbook suitable for an upper level undergraduate or Master's level discrete math or combinatorics course, especially if the intended audience is pre-service or in-service secondary teachers. Read more

Exploring Combinatorial Mathematics is a free and open source textbook suitable for an upper level undergraduate or Master's level discrete math or combinatorics course, especially if the intended audience is pre-service or in-service secondary teachers. The text borrows material from Bogart's Combinatorics through Guided Discovery and Levin's Discrete Mathematics: an Open Introduction, falling somewhere between these in terms of difficulty.

This book was written specifically to be used as the textbook for the Master's level Discrete Mathematics course at the University of Northern Colorado. This course is part of a MA in Mathematics with a Teaching Emphasis. Most of the students in the course are current secondary math teachers. This intended audience has influenced the style and content of the book in a few important ways.

First, we acknowledge that not everyone reading this book will be immediately familiar with the content of a standard undergraduate discrete mathematics course. Little is assumed about the reader's previous work in the subject, beyond a general understanding of how abstract mathematics proceeds, as well as some basic ability with mathematical proof. For the reader completely unfamiliar with these and the basic objects of mathematical study (sets and functions), background material is included in an Appendix.

Topics have been selected to illustrate larger concepts of interest to secondary teachers. We have put an emphasis on understanding simple concepts deeply and in more than one way. Although some topics intersect secondary curriculum, most of the questions here are at a higher level. Still, the problem solving strategies and big ideas illustrated by our questions have applications to secondary mathematics. This emphasis is quite different than other mid level discrete and combinatorics textbooks, since we are not preparing our readers to begin a career in research mathematics.

While this course is not a course on teaching mathematics, we have tried to model good pedagogical practice. As you will see, almost all of the textbook consists of Activities and Exercises that guide students to discover mathematics for themselves. This will require quite a bit more work both from students and instructors, but we strongly believe that the best way to learn mathematics is by doing mathematics. Most of all, discovering mathematics is fun.

One-semester undergraduate textbook emphasizing structure, homomorphisms, and isomorphisms. Read more

Our focus in this book is the study of algebraic structures called groups. Along the way, we will explore rigorous mathematical notions of similarity and difference: When can we consider two objects to be more or less the same? When are they fundamentally different? For instance, consider two houses that have exactly the same construction, but are painted different colors. Are they the same house? No. But viewed structurally (as opposed to aesthetically) they are the same. This means that if we know certain information about one of the houses (say, how far the bathroom is from the kitchen) we know the same information about the other house. However, knowing that the first house is painted yellow does not tell us anything about the second house's color. We explore an analogous idea in mathematics, namely, the concept of isomorphism.

Throughout, we provide readers with many mathematical proofs, as well as specific examples demonstrating more general ideas.

An introduction to hyperbolic, elliptic, and Euclidean geometry, motivated by questions in cosmology. Read more

Motivated by questions in cosmology, the text investigates hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.

It is written for students who have taken vector calculus, and intended to be suitable as a one-semester course or as a guide to independent study in non-Euclidean geometry and the geometry of surfaces.

An historically accurate introduction to real analysis for undergraduates. Read more

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.

This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.

A one-semester course combining introductory group theory with Möbius, hyperbolic, elliptic, and projective geometries in the Kleinian framework. Read more

This free, online text is designed for a one-semester undergraduate mathematics course that combines an introduction to group theory with an introduction to modern geometries using the Kleinian paradigm.

The chapter on groups develops the basic theory of groups and homomorphisms, culminating with group actions. The chapter on geometry makes use of group symmetries in the basic theory of Möbius, hyperbolic, elliptic, and projective geometries.

The text is designed for active engagement, with carefully structured exercises throughout.

The text assumes prerequisite courses in calculus, linear algebra, and experience with proof writing.

Logic and Proof for Teachers, Lesa L. Beverly, Kimberly M. Childs, Thomas W. Judson, Deborah A. Pace

Logic and Proof for Teachers (LPT) is an open source textbook designed to teach logic and proof to middle and high school teachers.

An undergraduate course on differential equations aimed at students in engineering and the applied sciences. Read more

An undergraduate course on differential equations aimed at engineers and applied sciences. Covers undergraduate ODEs including linear and nonlinear systems and very basic PDE theory. Also includes an appendix on basic linear algebra. Usable for one or two semester sequences.

The PreTeXt code for this project is automatically generated from the LaTeX source code, and uses some custom tags, therefore it requires a custom xsl (see the github repository) to build the HTML version.

An undergraduate number theory text covering all the traditional topics from the point of view of the whole curriculum, with online interactivity embedded throughout.

In this book, we take an inquiry-oriented approach to modern algebra, with a focus on properties of rings, especially the structure required for unique factorization. Read more

In this book, we take an inquiry-oriented approach to ring theory, in the style of Marshall, Odell, and Starbird's Number Theory Through Inquiry, which serves as inspiration for the first chapter. No proofs or solutions are given; instead, the theorems and exercises are carefully chosen and sequenced to provide sufficient scaffolding for students to supply the proofs.

In chapters 2 and 3, students are introduced to fields, rings, and ideals, with aim of understanding the structural properties required for preserving unique factorization. In chapter 4, ideals and homomorphisms are explored.

An open source textbook designed to teach ordinary differential equations to upper level undergraduates. Read more

The textbook focuses on modeling, an early introduction to systems, and systems of linear equations. More specifically, the order of topics covered is first-order differential equations, systems of differential equations, linear systems, second-order linear equations, nonlinear systems, and the Laplace transform. There is more than enough material for a one-semester course. There are many interactive Sage cells in the HTML version of the book.

Mathematics, Graduate

A monograph on algebraic graph theory illustrated with many embedded Sage cells.

Computer Science

An introduction to how computer hardware works from a programmer's point of view, using assembly language programming on the Raspberry Pi. Read more

This is the first computer science textbook authored with PreTeXt. It has been used in the classroom two semesters (2016/17 AY) at Sonoma State University and Santa Rosa Jr. College. I and the PreTeXt developers would very much appreciate hearing your feedback about the formats used to display the various elements in the book. And of course, I welcome any comments you have about the content, especially any errors that your find. I maintain a log of corrections in Errata so you can see if any sections you have already read may have been changed.


The first real PreTeXt project - an expository article on linear algebra published in the American Mathematical Monthly. Read more

This short expository note was authored in PreTeXt early in the development of PreTeXt itself (Summer 2013). The LaTeX output required very few adjustments to be acceptable to the journal's editorial processes.

The XML source has been updated to reflect early changes in PreTeXt, and the HTML output was last built in March 2015. As of early 2020 the online version seems to still be rendering just fine, a testimony to certain fundamental technical decisions.

A humorous work of mathematical historical fiction aimed at celebrating the greatness of the number 8, while showcasing a variety of features in PreTeXt publishing.

CalcPlot3D Help, Paul Seeburger

This is a help manual for using CalcPlot3D, an interactive JavaScript app for visualizing multivariable calculus, differential equations, physics, and more!

A tutorial or primer on git, using the management of a manuscript for examples.

The definitive guide to writing and publishing documents in PreTeXt.


Bylaws for the Eastern Pennsylvania and Delaware Section of the Mathematical Association of America (from Bud Boman).

Meeting Program of Northeastern Section of the Mathematical Association of America, Fall 2018 at Southern New Hampshire University (from Joe Fields)


A guide to good academic writing at the college level, by students, for students. Read more

The purpose of Sound Writing is to help you develop a range of techniques that you can use to succeed as an academic writer. As you'll soon discover (if you have not discovered already), academic writing is a practice with its own conventions and expectations. Academic inquiry is about using the best possible evidence to grapple with contested issues. Academic writing places special emphasis on rigorous use of evidence to substantiate claims, on clear and specific theses, and on the framing of arguments within scholarly contexts. These traits distinguish academic writing from most popular writing (the type of writing that one finds on blogs, in newspapers and magazines, and on Facebook). Though it is possible to discuss academic writing as a coherent entity, academic writing is also diverse and reflects writers' own personal, disciplinary, and sub-disciplinary biases. (Take a look at the example student essays included in the Resources section of this book.) In Sound Writing, we hope to provide you with the essentials of university writing so that you can write with as little stress and as much success as possible. Inside this book, you'll find a breakdown of research, composition, and revision processes; strategies for overcoming common writing challenges; advice from faculty members; a guide to APA-, Chicago-, and MLA-style citations; and much more.

Mature, Converting to PreTeXt

An inexpensive, open-source alternative to the traditional Calculus textbook.

Advanced High School Statistics provides a thorough intro to statistics and supports students preparing for the AP Statistics exam.

Textbook for a typical one semester course in Differential Calculus, seen through the lens of history. Read more

This text will cover all of the usual topics in the typical first semester course in Calculus, as taught in American colleges. However the topics are arranged to reflect the history of the topic, rather than its logical structure in order to use history to illuminate the progression of ideas and concepts. The current version is being written in LaTeX. However the authors will be starting a conversion to PreTeXt in the near future. The text will be published under a Creative Commons license by the Open SUNY Textbook (OST) program and projected to be completed no later than December 2020.

Warning: The version at the URL above is the authors' working draft, not a final version. It is thus subject to change without notice.

Textbook for a typical selection of topics in discrete mathematics, with a focus on developing mathematical logic skills. Read more

Introductory material in each of logic, set theory, graph theory, and combinatorics.

Includes worksheets for in-class activities suitable for a partially-flipped classroom.

In Development

Advanced topics in linear algebra such as canonical forms, with an emphasis on topics inmportant for applications, such as the singular value decomposition and least squares fit. Read more

The text begins with fundamentals such as invariant subspaces, refelctors, projectors, and positive semi-definite matrics. A chapter on matrix decompositions includes LU, QR, SVD, and Cholesky, with Schur planned. Canonical forms is mostly about Jordan canonical form, with plans for rational form. The final two chapters are applications and further topics.

Notation agrees with, and cross-references point to, the author's A First Course in Linear Algebra.

Abstract Algebra For Teachers, Thomas W. Judson, Oscar Levin

A one-semester introductory course in abstract algebra for teachers covering groups, rings, and fields with sections relating abstract algebra to the secondary classroom. Read more

AAFT is organized into three parts: (1) An Introduction to Groups and Rings, (2) Topics in Group Theory, and (3) Topics in Ring and Field Theory. The first part introduces the key concepts of both groups and rings. Instructors may then taylor the course by selecting topics from parts (2) and (3). AFTA was developed from the open source textbook Abstract Algebra: Theory and Applications. AAFT is still in development.

Notes de cours pour un premier cours d'algèbre linéaire, avec une forte emphase sur la géométrie vectorielle. Read more

Une approche géométrique à l'algèbre linéaire avec de nombreux exemples dynamiques et interactifs.

La théorie est présentée à la fois d'une manière intuitive (se basant sur la géométrie) et rigoureuse.

A hands-on, original source, look at the evolution of cryptology.

Engineering Statics, Dan Baker, William Haynes

A collaboratively authored textbook for a traditional, one-semester, engineering mechanics course. Read more

Topics include forces, moments, equilibrium of particles, rigid bodies and structures.

Currently in progress and soliciting additional contributors.

These notes introduce the basics of general topology, including metrizability, compactness, connectedness, product spaces, and quotient spaces. Read more

A theorem sequence for an inquiry-based introductory topology course.

Introduction to Digital Logic Design, Eric W. Hansen

Introductory course in digital logic design, focusing on system design with the hardware description language VHDL and prototyping with field programmable gate arrays (FPGAs). Read more

The initial version of this book, available March 2020, contains supplemental material for the Dartmouth course Engs31/CoSc56. Topics include: Boolean logic; electronics and logic gates; computer-assisted tools for design capture, simulation, and synthesis; prototyping with discrete components and with programmable logic (FPGAs); top-down modular and register transfer level (RTL) design with bottom-up construction and physical testing; interfacing with peripheral devices (SPI, UART). Other topics will be filled in over time to cover an entire course.

The only prerequisite is an introduction to programming. Basic electronics are taught as they are needed. To serve both engineering and computer science students, I emphasize the differences between VHDL, a hardware description language, and software languages like C or Python. Practical examples and lab assignments use the Xilinx Vivado tool set, Xilinx Artix7 FPGA, and Digilent Basys3 development board.

An introduction to high-performance computing, using matrix-matrix multiplication as an illustrative example. Read more

These are the notes for the edX course Programming for High Performance to be launched in late May 2019. This course uses matrix-matrix multiplication to illustrate how algorithms and architectures need to interact if high performance is to be attained.

Second course in linear algebra including vector spaces, linear transformations, orthogonality, Jordan canonical form, with Python(SymPy)-based computational examples. Read more

Lecture notes for a third-year course in linear algebra.

Contains a mixture of theoretical and computational content.

Computations are done in Sage cells using the SymPy Python library.

Based on Linear Algebra with Applications, by Keith Nicholson.

Textbook for a four-semester college course in music theory. Read more

Music Theory for the 21st-Century Classroom is an openly-licensed online four-semester college music theory textbook. This text differs from other music theory textbooks by focusing less on four-part (SATB) voiceleading and more on relating harmony to the phrase.

A highly tailored linear algebra book to be used at the University of Manitoba for students with mathematical inclinations.

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