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203 lines
5.6 KiB
Markdown
203 lines
5.6 KiB
Markdown
# Awesome maths
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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
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* [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
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* [Introduction to logic](http://logic.stanford.edu/intrologic/chapters/cover.html) - Michael Genesereth, Eric Kao (Stanford University)
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* [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)
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* [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
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* [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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### Homotopy type theory
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* [Homotopy type theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf)
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## Number theory
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* [Elementary Number Theory: Primes, Congruences, and Secrets](http://wstein.org/ent/ent.pdf) - William Stein
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* [Elementary Number Theory](http://www.iiserpune.ac.in/~ayan/MTH312/%28127%29.pdf) - W. Edwin Clark (University of South Florida)
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* [A Course on Number Theory](http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf) - Peter J. Cameron
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* [A Computational Introduction to Number Theory and Algebra](http://shoup.net/ntb/ntb-v2.pdf) - Victor Shoup
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* [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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* [Algebraic Number Theory](http://www.jmilne.org/math/CourseNotes/ANT.pdf) - J.S. Milne
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* [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)
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* [Elements of analytic number theory](http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf) - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
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* [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’s book](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf) - Andreas Strömbergsson
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## Algebra
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### Abstract algebra
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* [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)
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* [Introduction to Modern Algebra](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf) - David Joyce (Clark University)
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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)
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* [An undergraduate course in Abstract Algebra](http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf) - Robert Howlett
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### Linear algebra
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* [Fundamentals of linear algebra](http://www.math.ubc.ca/~carrell/NB.pdf) - James B. Carrell
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* [Linear algebra and matrices](http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf) - Martin Fluch
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* [Vector space theory](http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf) - Robert Howlett
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* [Linear Algebra](http://www.mathematik.uni-muenchen.de/~renesse/AP09/hefferon.pdf) - Jim Hefferon
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* [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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### Galois theory
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### Universal algebra
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### Category theory
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### Group theory
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### Ring theory
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### Field theory
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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
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### Learning platforms
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* [Khan Academy](https://www.khanacademy.org/math)
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* [Coursera](https://www.coursera.org/courses?query=mathematics&languages=en)
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* [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf)
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### Questions and answers
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* [Mathematics Stack Exchange](http://math.stackexchange.com/)
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* [MathOverflow](http://mathoverflow.net/) - for professional mathematicians
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### Encyclopedia
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* [Encyclopedia of Mathematics](https://www.encyclopediaofmath.org)
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* [Wolfram Mathworld](http://mathworld.wolfram.com/)
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* [Planetmath](http://planetmath.org/)
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### Misc
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* [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics)
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