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# Awesome maths
A curated list of awesome mathematics resources.
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## Foundations of mathematics
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### Set theory
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* [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
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* [Set Theory on the Stanford Encyclopedia of Philosophy ](http://plato.stanford.edu/entries/set-theory/ )
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* [Set Theory on Wikibooks ](https://en.wikibooks.org/wiki/Set_Theory )
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### 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)
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* [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
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* [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)
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* [Formal logic ](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf ) - Miguel Palomino
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### Category theory
* [Introduction to category theory and categorical logic ](http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf ) - Thomas Streicher
* [An introduction to Category Theory ](http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf ) - Harold Simmons
* [Category Theory ](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&rep=rep1&type=pdf ) - Steve Awodey (Carnegie Mellon University)
* [Category Theory ](http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf ) - B. Pareigis
* [Category Theory for Computing Science ](http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf ) - Michael Barr, Charles Wells
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### Homotopy type theory
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* [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
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### Algebraic number theory
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* [Introduction to Algebraic Number Theory ](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf )
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* [Introduction to Algebraic Number Theory ](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf ) - F. Oggier
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* [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)
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### Analytic number theory
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* [Introduction to Analytic Number Theory ](http://www.math.uiuc.edu/~hildebr/ant/main.pdf ) - A.J. Hildebrand (University of Illinois)
* [Elements of analytic number theory ](http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf ) - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
* [Analytic Number Theory ](http://www.mathematik.uni-muenchen.de/~forster/v/ann/annth_all.pdf ) - Otto Forster (LMU Munich)
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* [Analytic number theory - Lecture notes based on Davenport’ ](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf ) - Andreas Strömbergsson
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## Algebra
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### Abstract algebra
* [Introduction to Abstract Algebra ](https://people.creighton.edu/~dsm33733/MTH581/Introduction%20to%20Abstract%20Algebra.pdf ) - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)
* [Introduction to Modern Algebra ](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf ) - David Joyce (Clark University)
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* [Algebraic methods ](http://www1.spms.ntu.edu.sg/~frederique/AA11.pdf ) - F. Oggier
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* [Abstract Algebra : Theory and Applications ](http://abstract.ups.edu/download/aata-20150812.pdf ) - Thomas W. Judson, Robert A. Beezer (Austin State University)
* [An undergraduate course in Abstract Algebra ](http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf ) - Robert Howlett
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### Group theory
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* [Notes on Group Theory ](https://www2.bc.edu/~reederma/Groups.pdf ) - Mark Reeder
* [Group theory ](http://www.jmilne.org/math/CourseNotes/GT.pdf ) - J.S. Milne
* [Notes on finite group theory ](http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf ) - Peter J. Cameron
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### Linear algebra
* [Fundamentals of linear algebra ](http://www.math.ubc.ca/~carrell/NB.pdf ) - James B. Carrell
* [Linear algebra and matrices ](http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf ) - Martin Fluch
* [Vector space theory ](http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf ) - Robert Howlett
* [Linear Algebra ](http://www.mathematik.uni-muenchen.de/~renesse/AP09/hefferon.pdf ) - Jim Hefferon
* [Linear algebra ](http://www.calpoly.edu/~jborzell/Courses/Year%2010-11/Fall%202010/Petersen-Linear_Algebra-Math_306.pdf ) - Peter Petersen
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### Ring theory
* [Foundations of Module and Ring Theory ](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf ) - Robert Wisbauer (University of Düsseldorf)
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### Galois theory
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* [An Introduction to Galois Theory ](http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf ) - Andrew Baker (University of Glasgow)
* [Fields and Galois Theory ](http://www.jmilne.org/math/CourseNotes/FT.pdf ) - J.S. Milne
* [ Galois theory ](http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf ) - Miles Reid
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## Analysis
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## Combinatorics
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### Graph theory
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## Geometry and topology
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Algebraic geometry
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## Probability and statistics
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* [Statistical Learning Theory ](https://web.stanford.edu/class/cs229t/notes.pdf ) - Percy Liang
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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 )
