Here is a partial list of free and/or open-source textbooks. If you find one of these more helpful than another, please let me know. Also, take a peek at Rob Beezer’s selection on this page. Moreover, the American Institute of Mathematics maintains a list of approved open-source textbooks. Also, check out the free computer science books by Allen B. Downey (Olin College) at Green Tea Press. Downey’s Textbook manifesto is definitely worth reading.

- CLP Calculus Textbooks by Joel Feldman, Andrew Rechnitzer, and Elyse Yeager were written for standard university calculus courses at the University of British Colombia. Free PDF and web-based textbooks.
- APEX Calculus is an open-source textbook by a group of faculty from Virginia Military Institute. It has the look and feel of a traditional calculus (e.g., Stewart’s
*Calculus*). Includes interactive 3D graphics. - MOOCulus Textbook is a free textbook from the MOOCulus folks at Ohio State University. This text is mostly an adaptation of the Community Calculus text listed below.
- Community Calculus by David Guichard (Whitman College). This one is also available as a free PDF. You can also purchase a very inexpensive hardcopy from Lulu.
- Active Calculus by Matt Boelkins (Grand Valley State College). This is one of the newer additions to the list of free calculus texts.
- Coordinated Calculus by Nathan Wakefield (University of Nebraska) et al. This is the calculus textbook used at the Univerisity of Nebraska. Based upon Active Calculus by Matthew Boelkins (see above).
- Calculus by Gilbert Strang (MIT). This book is available as a free PDF from the MIT Open Courseware Project. There are also some corresponding videos, which can be found here.
- Calculus Refresher by Paul Garrett (University of Minnesota). Another free PDF. This short book seems designed for students who have had some experience with calculus and need some review.
- Funny Little Calculus Text by Robert Ghrist (University of Pennsylvania). Currently only first semester calculus, very short, and no exercises, but a free PDF.
- Paul’s Online Math Notes by Paul Dawkins (Lamar University). Paul’s notes cover Calculus 1-3, Linear Algebra, and more. The notes are available as free HTML-based material. These notes seem to be popular with students.
- Differential Calculus with Sage by David Joyner (United States Naval Academy, retired) and William Granville. This free book is based on Granville’s classic text book
*Elements of the Differential and Integral Calculus*, which fell into the public domain. The book covers first semester calculus and incorporates Sage, which is an open-source mathematics software package. - Integral Calculus with Sage by Dale Hoffman (Bellevue Community College), William Stein (SageMath), and David Joyner (United States Naval Academy, retired). The book picks up where the previous book left off.
- Contemporary Calculus by Dale Hoffman (Bellevue Community College). A free online calculus text that is being developed for the Open Course Library Project of the Washington State Colleges. This book is part of the foundation for the previous book. It covers three semesters of calculus and seems to do a thorough job of it, but the formatting is awful.

- Elementary Differential Equations and Elementary Differential Equations with Boundary Value Problems by William Trench (Trinity College). Both books were previously published by Brooks/Cole Thomson Learning. PDF and LaTeX source files are available for free.
- Introductory Differential Equations using Sage (PDF) by David Joyner (United States Naval Academy, retired).

- Discrete Mathematics: An Open Introduction by Oscar Levin (University of Northern Colorado) is a free, open-source textbook appropriate for a first or second year undergraduate course for math majors. There is a really nice interactive ebook version.
- Applied Discrete Structures by Al Doerr (UMass Lowell) and Kenneth M. Levasseur (UMass Lowell).

- An Introduction to Proof via Inquiry-Based Learning by Dana C. Ernst (Northern Arizona University). IBL course materials for an introduction to proof course. The first half of the notes are an adaptation of notes written by Stan Yoshinobu (Cal Poly) and Matthew Jones (California State University Dominguez Hills).
- Introduction to Proof by Ron Taylor (Berry College). These IBL notes are available from the Journal of Inquiry-Based Learning in Mathematics.
- Notes for a Course on Proofs by Jacqueline A. Jensen-Vallin (Slippery Rock University). Another set of IBL notes available from the Journal of Inquiry-Based Learning in Mathematics.
- Mathematical Reasoning: Writing and Proof by Ted Sundstrom (Grand Valley State University). This textbook is designed for the first course in the college mathematics curriculum that introduces students to the process of constructing and writing proofs. This book is included in the approved list of textbooks for the Open Textbook Initiative by the American Institute of Mathematics. There are also over 100 screencasts that accompany the book.

- A First Course in Linear Algebra by Rob Beezer (Puget Sound University). FCLA is a free and open-source introductory textbook designed for university sophomores and juniors. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The book is available for free in PDF and HTML form.
- Linear Algebra by Jim Hefferon (St. Michael’s College). This is another free and open-source textbook.
- Linear Algebra by David Clark (SUNY New Paltz). These notes are available for free from the Journal of Inquiry-Based Learning in Mathematics. The notes are designed for an inquiry-based learning (IBL) approach to the subject.
- Linear Algebra by Gilbert Strang (MIT). This isn’t really a textbook, but rather free course materials, including videos, available from the MIT Open Courseware Project.
- Paul’s Online Math Notes by Paul Dawkins (Lamar University).

- Combinatorics Through Guided Discovery by Kenneth Bogart. These notes are maintained by the chair of the Mathematics Department at Dartmouth College.

- An Inquiry-Based Approach to Abstract Algebra by Dana C. Ernst (Northern Arizona University). Free and open-source course materials for an abstract algebra course.
- Abstract Algebra: Theory and Applications by Tom Judson (Stephen F. Austin University).
- Elementary Abstract Algebra: Examples and Applications by Justin Hill (Temple College) and Chris Thron (Texas A\&M University-Central Texas) with contributions from others. The text is designed for students who are planning to become secondary-school teachers. The authors particularly emphasize material that has relevance to high school math, as well as practical applications. Much of the content is derived from the Judson book mentioned above.
- Essential Group Theory by Michael Batty (University of Durham).
- Group Theory: Birdtracks, Lie’s, and Exceptional Groups by Predrag Cvitanović (Georgia Tech).

- Analysis by W. Ted Mahavier (Lamar University). These notes are for an IBL real analysis course and are available from the Journal of Inquiry-Based Learning in Mathematics.
- Analysis WebNotes by John Lindsay Orr (University of Nebraska at Lincoln).
- Classical Real Analysis contains links to a few real analysis texts. The word on the street is that
*Elementary Real Analysis*by Bruckner and Bruckner is excellent. - Measure, Integration & Real Analysis by Sheldon Axler (San Francisco State University). This book is in Springer’s Open Access program. Thus the electronic version of the book is available without cost. 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.

- An Introduction to Functional Programming Through Lambda Calculus by Greg Michaelson (Heriot-Watt University). PDF available for free.
- Sage for Undergraduates by Gregory V. Bard (University of Wisconsin Stout). PDF available for free.
- Computational Mathematics with SageMath by Paul Zimmermann et al. PDF available for free.
- Peering into Mathematics through Sage-colored Glasses by John Harris (University of Southern Mississippi), Karen Kohl (University of Southern Mississippi), and John Perry (University of Southern Mississippi). This free book serves as an introduction to mathematical computation and incorporates Sage.

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MAT 320: Foundations of Math

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Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.