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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.


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).


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.

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.

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  • $\begingroup$ Modifying for personal use without redistribution does not require open source license. $\endgroup$ – Martín-Blas Pérez Pinilla Nov 18 '14 at 18:41
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    $\begingroup$ @Martín-BlasPérezPinilla but without the source-code you have to write and typeset everything on your own. Having some other good work as a basis makes everything easier. $\endgroup$ – Dal Nov 18 '14 at 18:43
  • $\begingroup$ OK, I understandt your requirement. $\endgroup$ – Martín-Blas Pérez Pinilla Nov 18 '14 at 18:47
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    $\begingroup$ @dustin So far, I've checked some of the links provided by Martin and Mark, and they have indeed the source-codes. $\endgroup$ – Dal Nov 20 '14 at 22:16
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    $\begingroup$ I feel the .tex wont be easy to come by for a notes or book level document. If you get one or two, that would be good. $\endgroup$ – dustin Nov 20 '14 at 22:18
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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.

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

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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.

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

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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

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  • $\begingroup$ At least this covers not only the technical aspect of being copyable but also the license. That being said, while one can find a couple of interesting and famous original texts, other stuff is not really up to date (regarding content, methods, or even notation) $\endgroup$ – Hagen von Eitzen Nov 26 '14 at 9:11
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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.)

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protected by Community Aug 2 '17 at 11:18

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