# Awesome maths

A curated list of awesome mathematics resources.

## Foundations of mathematics

### Set theory

* [An introduction to set theory](http://www.math.toronto.edu/weiss/set_theory.pdf) - William A. R. Weiss
* [Set Theory and Foundations of Mathematics](http://www.settheory.net/) - Sylvain Poirier
* [Set Theory on the Stanford Encyclopedia of Philosophy](http://plato.stanford.edu/entries/set-theory/)
* [Set Theory on Wikibooks](https://en.wikibooks.org/wiki/Set_Theory)

### Logic

* [Introduction to logic](http://logic.stanford.edu/intrologic/chapters/cover.html) - Michael Genesereth, Eric Kao (Stanford University)
* [An introduction to formal logic](https://textbookequity.org/oct/Textbooks/Magnus_forallx.pdf) - P.D. Magnus (University at Albany)
* [A problem course in mathematical logic](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf) - Stefan Bilaniuk (Trent University)
* [Language, proof, and logic](http://ssdi.di.fct.unl.pt/~pb/cadeiras/lc/0102/lpl%20textbook.pdf) - Jon Barwise, John Etchemendy
* [Mathematical logic](http://www.mathematik.uni-muenchen.de/~schwicht/lectures/logic/ws03/ml.pdf) - Helmut Schwichtenberg
* [Mathematical logic](http://www.personal.psu.edu/t20/notes/logic.pdf) - Stephen G. Simpson (Pennsylvania State University)
* [Formal logic](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf) - Miguel Palomino

### Homotopy type theory

* [Homotopy type theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf)


## Number theory

* [Elementary Number Theory: Primes, Congruences, and Secrets](http://wstein.org/ent/ent.pdf) - William Stein
* [Elementary Number Theory](http://www.iiserpune.ac.in/~ayan/MTH312/%28127%29.pdf) - W. Edwin Clark (University of South Florida)
* [A Course on Number Theory](http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf) - Peter J. Cameron
* [A Computational Introduction to Number Theory and Algebra](http://shoup.net/ntb/ntb-v2.pdf) - Victor Shoup
* [Number Theory: A Contemporary Introduction](http://math.uga.edu/~pete/4400FULL.pdf) - Pete L. Clark
* [Introduction to Algebraic Number Theory](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf)
* [Algebraic Number Theory](http://www.jmilne.org/math/CourseNotes/ANT.pdf) - J.S. Milne
* [Algebraic Number Theory Course Notes](http://people.math.gatech.edu/~mbaker/pdf/ANTBook.pdf) - Matthew Baker (Georgia Tech)

## Algebra

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## Analysis

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## Combinatorics

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## Geometry and topology

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## Probability and statistics

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## Numerical Analysis

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## Computer algebra

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## Websites

### Learning platforms

* [Khan Academy](https://www.khanacademy.org/math)
* [Coursera](https://www.coursera.org/courses?query=mathematics&languages=en)
* [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf)

### Questions and answers

* [Mathematics Stack Exchange](http://math.stackexchange.com/)
* [MathOverflow](http://mathoverflow.net/) - for professional mathematicians

### Encyclopedia

* [Encyclopedia of Mathematics](https://www.encyclopediaofmath.org)
* [Wolfram Mathworld](http://mathworld.wolfram.com/)
* [Planetmath](http://planetmath.org/)

### Misc

* [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics)