Open source lecture notes and textbooks

Question

This question is inspired by the popular "Best Sets of Lecture Notes and Articles".

Indeed, I would like to collect a "big-list" of open source (that is, with $\LaTeX$ code available) high-quality (according to strictly mathematical and pedagogical standard) lecture notes or textbooks on as many mathematical topics as possible.

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Note that here the focus is only on open source lecture notes or books (which could help students to create their own notes for self-study more easily by modifying existing works).

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Among the many other topics that I would like the material to cover, in particular I am currently interested in:

• calculus;
• real analysis;
• complex and functional analysis;
• abstract algebra;
• linear algebra;
• number theory;
• general physics;
• mathematical physics (mainly classical mechanics);
• probability;
• geometry;
• etc.

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Update: I am thankful for the answers provided so far, and I encourage to share here more examples of good opensource material in the areas which have not been covered.

Answer 1

The course Measure Theory by D.H.Fremlin includes TeX source.

Topology Course by Aisling McCluskey and Brian McMaster in HTML.

Diverse lecture notes by Conor Houghton.

Cryptography homework by Boaz Barak.

Digital Image Processing.

Abstract Algebra handouts and Number Theory lecture notes.

Answer 2

Many of the courses in MIT's OCW have such notes: http://ocw.mit.edu/courses/find-by-department/

Answer 3

Here are a few I've found over the years. I've included some brief comments on the first four, which I've personally used in my classes.

• Stitz and Zeager Precalculus materials
  Outstanding. Includes a lot of ancillaries like answers and youtube videos. CCL
• Mooculus
  Very, very good calculus MOOC offered at Ohio State University. Text is freely available by itself. One limitation - it covers only single variable. CCL
• Whitman Calclus by David Guichard
  Very good and complete Calculus text. CCL
• APEX Calculus
  The most recent open text that I've used for Calculus. Almost as good as Mooculus and almost as complete as Guichard.
  CCL
• A First Course in Complex Analysis Beck, Marchesi, and Pixton
  Very good - Freely available but not open.
• Linear Algebra by Jim Hefferon
  This book won the 2020 Daniel Solow Author's Award from the Mathematical Association of America.
  GFDL or CC BY-SA
• A First Course in Linear Algebra GFDL
• Abstract Algebra by Tom Judson GFDL
• Basic Analysis - An Introduction to Real Analysis by Jiri Lebl CCL

Answer 4

The Stacks Project and the CRing project are good for learning algebraic geometry and commutative algebra, respectively:

• Stacks Project: http://stacks.math.columbia.edu/
• CRing Project: http://people.fas.harvard.edu/~amathew/cr.html

Answer 5

Rob Beezer's "A First Course in Linear Algebra" represents the future of OER textbooks for math, imho. His MathBook XML production flow allows a single source input (written in xml) to output in multiple formats (right now pdf-via-LaTeX and html, but the future could include more). To compete with commercial textbooks, both a quality book and a quality web-accessible e-book are necessary. (As well as a third leg: a quality online homework platform like WeBWorK.)

Answer 6

You may want to check this site for over 46.000 free ebooks. Copyrights of the books contained in this site are expired so you can freely download books. You can download the books in PDF, EPUB or LATEX.

main site : https://www.gutenberg.org/wiki/Main_Page

math bookshelf : https://www.gutenberg.org/wiki/Mathematics_%28Bookshelf%29

Answer 7

Here are some lecture notes for Operations Research that I have found on professor’s sites (that are now defunct due to the passage of time and losing domain names) that I’ve been using as a supplement to my own self-studying and coursework:

Operations Research - Deterministic Models lecture notes by Juraj Stacho of Columbia University New York

Operations Research lecture notes by Dr. Y Īlker Topcu