Here’s a partial checklist of free and/or open-source textbooks. In the event you discover considered one of these extra useful than one other, please let me know. Additionally, take a peek at Rob Beezer’s choice on this web page. Furthermore, the American Institute of Arithmetic maintains a listing of accredited open-source textbooks. Additionally, take a look at the free pc science books by Allen B. Downey (Olin Faculty) at Inexperienced Tea Press. Downey’s Textbook manifesto is certainly price studying.

### Calculus

- CLP Calculus Textbooks by Joel Feldman, Andrew Rechnitzer, and Elyse Yeager had been written for traditional college calculus programs on the College of British Colombia. Free PDF and web-based textbooks.
- APEX Calclus is an open-source textbook by a bunch of college from Virginia Army Institute. It has the appear and feel of a conventional calculus (e.g., Stewart’s
*Calculus*). Contains interactive 3D graphics. - MOOCulus Textbook is a free textbook from the MOOCulus of us at Ohio State College. This textual content is generally an adaptation of the Group Calculus textual content listed under.
- Group Calculus by David Guichard (Whitman Faculty). This one can also be accessible as a free PDF. You can even buy a really cheap hardcopy from Lulu.
- Lively Calculus by Matt Boelkins (Grand Valley State Faculty). This is without doubt one of the newer additions to the checklist of free calculus texts.
- Calculus by Gilbert Strang (MIT). This guide is offered as a free PDF from the MIT Open Courseware Challenge. There are additionally some corresponding movies, which will be discovered right here.
- Calculus Refresher by Paul Garrett (College of Minnesota). One other free PDF. This quick guide appears designed for college students who’ve had some expertise with calculus and wish some overview.
- Humorous Little Calculus Textual content by Robert Ghrist (College of Pennsylvania). At present solely first semester calculus, very quick, and no workout routines, however a free PDF.
- Paul’s On-line Math Notes by Paul Dawkins (Lamar College). Paul’s notes cowl Calculus 1-Three, Linear Algebra, and extra. The notes can be found as free HTML-based materials. These notes appear to be common with college students.
- Differential Calculus with Sage by David Joyner (United States Naval Academy, retired) and William Granville. This free guide is predicated on Granville’s traditional textual content guide
*Components of the Differential and Integral Calculus*, which fell into the general public area. The guide covers first semester calculus and incorporates Sage, which is an open-source arithmetic software program package deal. - Integral Calculus with Sage by Dale Hoffman (Bellevue Group Faculty), William Stein (SageMath), and David Joyner (United States Naval Academy, retired). The guide picks up the place the earlier guide left off.
- Modern Calculus by Dale Hoffman (Bellevue Group Faculty). A free on-line calculus textual content that’s being developed for the Open Course Library Challenge of the Washington State Schools. This guide is a part of the muse for the earlier guide. It covers three semesters of calculus and appears to do an intensive job of it, however the formatting is terrible.

### Differential Equations

- Elementary Differential Equations and Elementary Differential Equations with Boundary Worth Issues by William Trench (Trinity Faculty). Each books had been beforehand printed by Brooks/Cole Thomson Studying. PDF and LaTeX supply recordsdata can be found at no cost.
- Introductory Differential Equations utilizing Sage (PDF) by David Joyner (United States Naval Academy, retired).

### Discrete Arithmetic

- Discrete Arithmetic: An Open Introduction by Oscar Levin (College of Northern Colorado) is a free, open-source textbook applicable for a primary or second 12 months undergraduate course for math majors. There’s a very nice interactive book model.
- Utilized Discrete Constructions by Al Doerr (UMass Lowell) and Kenneth M. Levasseur (UMass Lowell).

### Introduction to Proof

- An Introduction to Proof by way of Inquiry-Based mostly Studying by Dana C. Ernst (Northern Arizona College). IBL course supplies for an introduction to proof course. The primary half of the notes are an adaptation of notes written by Stan Yoshinobu (Cal Poly) and Matthew Jones (California State College Dominguez Hills).
- Introduction to Proof by Ron Taylor (Berry Faculty). These IBL notes can be found from the Journal of Inquiry-Based mostly Studying in Arithmetic.
- Notes for a Course on Proofs by Jacqueline A. Jensen-Vallin (Slippery Rock College). One other set of IBL notes accessible from the Journal of Inquiry-Based mostly Studying in Arithmetic.
- Mathematical Reasoning: Writing and Proof by Ted Sundstrom (Grand Valley State College). This textbook is designed for the primary course within the faculty arithmetic curriculum that introduces college students to the method of developing and writing proofs. This guide is included within the accredited checklist of textbooks for the Open Textbook Initiative by the American Institute of Arithmetic. There are additionally over 100 screencasts that accompany the guide.

### Linear Algebra

- A First Course in Linear Algebra by Rob Beezer (Puget Sound College). FCLA is a free and open-source introductory textbook designed for college sophomores and juniors. The guide begins with programs of linear equations, then covers matrix algebra, earlier than taking over finite-dimensional vector areas in full generality. The guide is offered at no cost in PDF and HTML type.
- Linear Algebra by Jim Hefferon (St. Michael’s Faculty). That is one other free and open-source textbook.
- Linear Algebra by David Clark (SUNY New Paltz). These notes can be found at no cost from the Journal of Inquiry-Based mostly Studying in Arithmetic. The notes are designed for an inquiry-based studying (IBL) strategy to the topic.
- Linear Algebra by Gilbert Strang (MIT). This isn’t actually a textbook, however moderately free course supplies, together with movies, accessible from the MIT Open Courseware Challenge.
- Paul’s On-line Math Notes by Paul Dawkins (Lamar College).

### Combinatorics

- Combinatorics Via Guided Discovery by Kenneth Bogart. These notes are maintained by the chair of the Arithmetic Division at Dartmouth Faculty.

### Summary Algebra

- An Inquiry-Based mostly Method to Summary Algebra by Dana C. Ernst (Northern Arizona College). Free and open-source course supplies for an summary algebra course.
- Summary Algebra: Principle and Functions by Tom Judson (Stephen F. Austin College).
- Elementary Summary Algebra: Examples and Functions by Justin Hill (Temple Faculty) and Chris Thron (Texas A&M College-Central Texas) with contributions from others. The textual content is designed for college students who’re planning to turn out to be secondary-school academics. The authors notably emphasize materials that has relevance to highschool math, in addition to sensible purposes. A lot of the content material is derived from the Judson guide talked about above.
- Important Group Principle by Michael Batty (College of Durham).
- Group Principle: Birdtracks, Lie’s, and Distinctive Teams by Predrag Cvitanović (Georgia Tech).

### Actual Evaluation

- Evaluation by W. Ted Mahavier (Lamar College). These notes are for an IBL actual evaluation course and can be found from the Journal of Inquiry-Based mostly Studying in Arithmetic.
- Evaluation WebNotes by John Lindsay Orr (College of Nebraska at Lincoln).
- Classical Actual Evaluation incorporates hyperlinks to some actual evaluation texts. The phrase on the road is that
*Elementary Actual Evaluation*by Bruckner and Bruckner is superb. - Measure, Integration & Actual Evaluation by Sheldon Axler (San Francisco State College). This guide is in Springer’s Open Entry program. Thus the digital model of the guide is offered with out price. The content material and degree of this guide match properly with the first-year graduate course on these subjects at most American universities. This textbook includes a reader-friendly model and format that can enchantment to right this moment’s college students.

### Computing & Programming

- An Introduction to Useful Programming Via Lambda Calculus by Greg Michaelson (Heriot-Watt College). PDF accessible at no cost.
- Sage for Undergraduates by Gregory V. Bard (College of Wisconsin Stout). PDF accessible at no cost.
- Computational Arithmetic with SageMath by Paul Zimmermann et al. PDF accessible at no cost.
- Peering into Arithmetic by Sage-colored Glasses by John Harris (College of Southern Mississippi), Karen Kohl (College of Southern Mississippi), and John Perry (College of Southern Mississippi). This free guide serves as an introduction to mathematical computation and incorporates Sage.