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505 lines
35 KiB
Markdown
505 lines
35 KiB
Markdown
# Awesome Math [](https://github.com/sindresorhus/awesome)
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A curated list of awesome mathematics resources.
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# Contents
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<!-- START_TOC -->
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* [Contents](#contents)
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* [General Resources](#general-resources)
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* [Learning Platforms](#learning-platforms)
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* [Learn to Learn](#learn-to-learn)
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* [Tools](#tools)
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* [Questions and Answers](#questions-and-answers)
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* [Encyclopedia](#encyclopedia)
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* [Books](#books)
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* [Blogs](#blogs)
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* [Misc](#misc)
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* [Lecture Notes](#lecture-notes)
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* [Foundations of Mathematics](#foundations-of-mathematics)
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* [Set Theory](#set-theory)
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* [Logic](#logic)
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* [Category Theory](#category-theory)
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* [Homotopy Type Theory](#homotopy-type-theory)
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* [Surreal Numbers](#surreal-numbers)
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* [Number Theory](#number-theory)
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* [Algebraic Number Theory](#algebraic-number-theory)
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* [Analytic Number Theory](#analytic-number-theory)
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* [Algebra](#algebra)
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* [Abstract Algebra](#abstract-algebra)
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* [Group Theory](#group-theory)
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* [Linear Algebra](#linear-algebra)
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* [Ring Theory](#ring-theory)
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* [Galois Theory](#galois-theory)
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* [Lie Algebras](#lie-algebras)
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* [Combinatorics](#combinatorics)
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* [Graph Theory](#graph-theory)
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* [Geometry and Topology](#geometry-and-topology)
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* [Differential Geometry](#differential-geometry)
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* [Algebraic Geometry](#algebraic-geometry)
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* [Topology](#topology)
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* [Algebraic Topology](#algebraic-topology)
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* [Analysis](#analysis)
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* [Real Analysis](#real-analysis)
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* [Harmonic Analysis](#harmonic-analysis)
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* [Complex Analysis](#complex-analysis)
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* [Functional Analysis](#functional-analysis)
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* [Measure Theory](#measure-theory)
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* [Ordinary Differential Equations](#ordinary-differential-equations)
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* [Partial Differential Equations](#partial-differential-equations)
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* [Probability and Statistics](#probability-and-statistics)
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* [Probability Theory](#probability-theory)
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* [Statistics](#statistics)
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* [Statistical Learning](#statistical-learning)
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* [Stochastic processes](#stochastic-processes)
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* [Numerical Analysis](#numerical-analysis)
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* [Signal processing](#signal-processing)
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* [Mathematics for Computer Science](#mathematics-for-computer-science)
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* [Mathematical Biology](#mathematical-biology)
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* [Mathematical Physics](#mathematical-physics)
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* [License](#license)
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<!-- END_TOC -->
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# General Resources
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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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* [MIT OpenCourseWare](http://ocw.mit.edu/courses/mathematics/)
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* [edX](https://www.edx.org/course/subject/math)
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## Learn to Learn
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* [Understanding Mathematics](https://github.com/nelson-brochado/understanding-math)
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## Youtube Series
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* [Brandon Foltz](https://www.youtube.com/user/BCFoltz/playlists?view=1&sort=da&flow=grid)
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* [3blue1brown](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/playlists)
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* [NPTEL](https://www.youtube.com/watch?v=VVYLpmKRfQ8&list=PL6C92B335BD4238AB)
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* [Prof. Leonard](https://www.youtube.com/watch?v=9FtHB7V14Fo&list=PL5102DFDC6790F3D0)
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* [Crash Course](https://www.youtube.com/watch?v=zouPoc49xbk&list=PL8dPuuaLjXtNM_Y-bUAhblSAdWRnmBUcr)
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* [Harvard](https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo)
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* [MIT](https://www.youtube.com/watch?v=VPZD_aij8H0&list=PLUl4u3cNGP60uVBMaoNERc6knT_MgPKS0)
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## Tools
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* [Symbolab](https://www.symbolab.com/)
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* [Desmos](https://www.desmos.com/calculator)
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* [Math Words](http://www.mathwords.com/)
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* [Wolfram Alpha](http://www.wolframalpha.com/)
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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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* [Planetmath](http://planetmath.org/)
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* [ProofWiki](https://proofwiki.org/wiki/Main_Page)
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* [Wolfram Mathworld](http://mathworld.wolfram.com/)
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## Books
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* [Calculus: Basic Concepts for High Schools](https://archive.org/details/TarasovCalculus) - L.V. Tarasov
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* [Basics of Algebra, Topology, and Differential Calculus](http://www.cis.upenn.edu/~jean/math-basics.pdf) - Jean Gallier (University of Pennsylvania)
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* [Multivariable Calculus](http://people.math.gatech.edu/%7Ecain/notes/calculus.html) - G. Cain, J. Herod (Georgia Tech)
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* [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf)
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* [Online Mathematics Textbooks](https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html)
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* [Beginning and Intermediate Algebra](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf)
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* [Trigonometry](http://www.mecmath.net/trig/trigbook.pdf)
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## Blogs
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* [BetterExplained](https://betterexplained.com/) - Maintained by Kalid Azad
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* [ILoveMaths](http://ilovemaths.com/) - For grades 6 thru 12 in K-12 system
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* [3blue1brown](https://www.3blue1brown.com/) - Animated Maths
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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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* [Paul's Online Math Notes](http://tutorial.math.lamar.edu/) - Paul Dawkins (Lamar University)
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* [List of electronic textbooks](http://faculty.atu.edu/mfinan/nnotes.html) - Marcel B. Finan (Arkansas Tech University)
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* [Topology Atlas](http://at.yorku.ca/topology/)
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# Youtube Series
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## Statistics
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* [Brandon Foltz](https://www.youtube.com/user/BCFoltz/playlists?sort=da&view=1&flow=grid)
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# Lecture Notes
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## Foundations of Mathematics
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* [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon
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### Set Theory
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* [Sets, Relations, Functions](http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html) - Ivo Düntsch, Günther Gediga
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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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### Logic
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* [Introduction to Logic](http://logic.stanford.edu/intrologic/secondary/index.html) - Michael Genesereth, Eric Kao (Stanford University)
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* [An Introduction to Formal Logic](https://www.fecundity.com/codex/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://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/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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* [Predictive Arithmetic](https://web.math.princeton.edu/~nelson/books/pa.pdf) - Edward Nelson
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* [Proofs and Concepts: the fundamentals of abstract mathematics](http://people.uleth.ca/~dave.morris/books/proofs+concepts.html) - Joy Morris, Dave Morris
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* [Mathematical Reasoning: Writing and Proof](https://www.tedsundstrom.com/mathreasoning) - Ted Sundstrom
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### Category Theory
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* [Introduction to Category Theory and Categorical Logic](http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf) - Thomas Streicher
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* [An Introduction to Category Theory](http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf) - Harold Simmons
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* [Category Theory](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&rep=rep1&type=pdf) - Steve Awodey (Carnegie Mellon University)
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* [Category Theory](http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf) - B. Pareigis
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* [Category Theory for Computing Science](http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf) - Michael Barr, Charles Wells
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* [Toposes, Triples and Theories](http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf) - Michael Barr, Charles Wells
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* [Abelian Categories](http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html) - Peter Freyd
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* [Categories and Groupoids](http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html) - P. J. Higgins
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* [Basic Concepts of Enriched Category Theory](http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html) - G. M. Kelley
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* [Abstract and Concrete Categories: The Joy of Cats](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html) - Jiri Adamek, Horst Herrlich, George Strecker
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* [Seven Sketches in Compositionality: An Invitation to Applied Category Theory](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) - Brendan Fong and David I. Spivak (MIT)
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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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### Surreal Numbers
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* [Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness](http://www.math.harvard.edu/~knill/teaching/mathe320_2015_fall/blog15/surreal1.pdf) - D. E. Knuth
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* [An Introduction to Surreal Numbers](https://www.whitman.edu/Documents/Academics/Mathematics/Grimm.pdf) - Gretchen Grimm
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* [Surreal Numbers and Games](http://web.mit.edu/sp.268/www/2010/surreal.pdf)
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* [Conway names, the simplicity hierarchy and the surreal number tree](http://www.ohio.edu/people/ehrlich/ConwayNames.pdf) - Philip Ehrlich
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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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* [An Introduction to the Theory of Numbers](http://www.trillia.com/moser-number.html) - Leo Moser
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* [Yet Another Introductary Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz
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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
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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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* [A Course In Algebraic Number Theory](http://www.math.uiuc.edu/~r-ash/ANT.html) - Robert Ash
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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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* [A Course in Universal Algebra](http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html) - S. Burris, H.P. Sankappanavar
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* [A Course in Commutative Algebra](https://faculty.math.illinois.edu/~r-ash/ComAlg.html) - Robert Ash
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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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* [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)
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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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* [Elements of Abstract and Linear Algebra](http://www.math.miami.edu/~ec/book) - E.H. Connell (University of Miami)
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* [Abstract Algebra: The Basic Graduate Year](http://www.math.uiuc.edu/~r-ash/Algebra.html) - Robert Ash
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### Group Theory
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* [Notes on Group Theory](https://www2.bc.edu/mark-reeder/Groups.pdf) - Mark Reeder
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* [Group Theory](http://www.jmilne.org/math/CourseNotes/GT.pdf) - J.S. Milne
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* [Notes on Finite Group Theory](http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf) - Peter J. Cameron
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* [Group Theory](http://www.cns.gatech.edu/GroupTheory/index.html) - Pedrag Civitanovic
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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](https://web.archive.org/web/20140824074655/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://joshua.smcvt.edu/linearalgebra) - 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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* [MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper
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* [Linear Algebra](http://joshua.smcvt.edu/linalg.html) - Jim Hefferon
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* [Elementary Linear Algebra](http://www.numbertheory.org/book/) - Keith Matthews
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* [A First Courses in Linear Algebra](http://linear.ups.edu/) - Rob Breezer
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* [Linear Algebra](https://www.math.ucdavis.edu/~linear/) - David Cherney, Tom Denton, Andrew Waldron
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* [Introduction to vectors and tensors, Vol 1: linear and multilinear algebra](http://oaktrust.library.tamu.edu/handle/1969.1/2502) - Ray M Bowen, C. C. Wang
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* [Introduction to vectors and tensors, Vol 2: vector and tensor analysis](http://oaktrust.library.tamu.edu/handle/1969.1/3609) - Ray M Bowen, C. C. Wang
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* [Introduction to Applied Linear Algebra](https://web.stanford.edu/~boyd/vmls/vmls.pdf) - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
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### Ring Theory
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* [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)
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* [Fields and Galois Theory](http://www.jmilne.org/math/CourseNotes/FT.pdf) - J.S. Milne
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* [Galois theory](http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf) - Miles Reid
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### Lie Algebras
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* [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg
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## Combinatorics
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* [Basic Combinatorics](http://www.math.utk.edu/~wagner/papers/comb.pdf) - Carl G. Wagner (University of Tennessee)
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* [Applied Combinatorics](http://people.math.gatech.edu/~trotter/book.pdf) - Mitchel T. Keller, William T. Trotter
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* [Notes on Combinatorics](http://www.maths.qmul.ac.uk/~pjc/notes/comb.pdf) - Peter J. Cameron
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* [Analytic Combinatorics](http://algo.inria.fr/flajolet/Publications/book.pdf) - Philippe Flajolet, Robert Sedgewick
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* [generatingfunctionology](http://www.math.upenn.edu/~wilf/DownldGF.html) - Herbert Wilf
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### Graph Theory
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* [Graph Theory: Lecture Notes](http://www.personal.psu.edu/cxg286/Math485.pdf) - Christopher Griffin
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* [Graph Theory](http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf) - Reinhard Diestel
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## Geometry and Topology
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* [Fundamentals of Geometry](http://polly.phys.msu.ru/~belyaev/geometry.pdf) - Oleg A. Belyaev
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* [A=B](https://www.math.upenn.edu/~wilf/AeqB.html) - M. Petkovsek, H. Wilf, D. Zeilberger
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* [Elements](http://aleph0.clarku.edu/~djoyce/java/elements/toc.html) - Euclid
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* [Euclid's Elements Redux](http://starrhorse.com/euclid/) - Daniel Callahan
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* [Mathematical Illustrations](http://www.math.ubc.ca/~cass/graphics/manual/) - Bill Casselman
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### Differential Geometry
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* [Introduction to Differential Geometry](https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf) - Joel W. Robbin, Dietmar A. Salamon
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* [Notes on Differential Geometry and Lie Groups](http://www.seas.upenn.edu/~jean/diffgeom.pdf) - Jean Gallier (University of Pennsylvania)
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* [Topics in Differential Geometry](http://www.mat.univie.ac.at/~michor/dgbook.pdf) - Peter W. Michor
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* [Lectures on Differential Geometry](http://mysite.science.uottawa.ca/rossmann/Differential%20Geometry%20book_files/Diffgeo.pdf) - Wulf Rossmann
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* [An Introduction to Riemannian Geometry](http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf) - Sigmundur Gudmundsson (Lund University)
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* [The Geometry and Topology of Three-Manifolds](http://msri.org/publications/books/gt3m/) - W. Thurston
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* [Semi-Riemann Geometry and General Relativity](http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf) - Shlomo Sternberg
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### Algebraic Geometry
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* [A Brief Introduction to Algebraic Geometry](http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/rickksda1107.pdf) - R.C. Churchill
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* [Introduction to Algebraic Geometry](http://www.math.lsa.umich.edu/~idolga/631.pdf) - Igor V. Dolgachev
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* [Foundations of Algebraic Geometry](http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf) - Ravi Vakil
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* [Algebraic Geometry](http://www.cis.upenn.edu/~jean/algeoms.pdf) - Jean Gallier, Stephen S. Shatz (University of Pennsylvania)
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* [Algebraic Geometry](http://www.jmilne.org/math/CourseNotes/AG.pdf) - J.S. Milne
|
||
* [Algebraic Geometry](http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf) - Andreas Gathmann (University of Kaiserslautern)
|
||
* [The Stacks Project](https://stacks.math.columbia.edu/) - Maintained by Aise Johan de Jong (Columbia)
|
||
|
||
### Topology
|
||
|
||
* [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) - Robert Ghrist (UPenn)
|
||
* [Introduction to Topology](http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf)
|
||
* [Introduction to Topology](http://www.math.bme.hu/~kalex/Teaching/Spring10/Topology/TopNotes_Spring10.pdf) - Alex Küronya
|
||
* [Introductory Topology](http://www.math.clemson.edu/~jimlb/Teaching/2009-10/Math986/Topology.pdf) - Jim L. Brown
|
||
* [General Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/Topo.pdf) - Pierre Schapira (Paris VI University)
|
||
* [Elementary Topology Problem Textbook](http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf)
|
||
* [General Topology](http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf) - Jesper M. Møller
|
||
|
||
### Algebraic Topology
|
||
|
||
* [Algebraic Topology](http://www.math.cornell.edu/~hatcher/AT/AT.pdf) - Allen Hatcher
|
||
* [A Concise Course in Algebraic Topology](http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf) - J. P. May
|
||
* [Introduction to Algebraic Topology](http://www.math.muni.cz/~cadek/at/at.pdf) - Martin Cadek
|
||
* [Algebra and Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/AlTo.pdf) - Pierre Schapira (Paris VI University)
|
||
* [Lecture Notes in Algebraic Topology](http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf) - James F. Davis, Paul Kirk (Indiana University)
|
||
* [Algebraic Topology](https://www.ma.utexas.edu/ibl1/courses/resources/12_15_07_grad_alg_top_mooremethod.pdf) - Michael Starbird
|
||
* [Lecture Notes on Algebraic Topology](http://www.math.nus.edu.sg/~matwujie/ma5209.pdf) - Jie Wu
|
||
|
||
|
||
## Analysis
|
||
|
||
### Real Analysis
|
||
|
||
* [MIT OpenCourseWare Lectures on Calculus](https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/) - G. Strang
|
||
* [Elementary Calculus: An Approach Using Infinitesimals](http://www.math.wisc.edu/~keisler/calc.html) - Professor H. Jerome Keisler
|
||
* [An Introduction to Real Analysis](https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf) - John K. Hunter (University of California at Davis)
|
||
* [Introduction to Real Analysis](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF) - William F. Trench (Trinity University, Texas)
|
||
* [Basic Analysis: Introduction to Real Analysis](http://www.jirka.org/ra/realanal.pdf) - Jiří Lebl
|
||
* [Elementary Real Analysis](http://prac.im.pwr.wroc.pl/~kwasnicki/pl/stuff/tbb-hyper.pdf) - Thomson, Bruckner
|
||
* [Lecture Notes in Real Analysis](http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf) - Eric T. Sawyer (McMaster University)
|
||
* [Real Analysis](http://math.harvard.edu/~ctm/papers/home/text/class/harvard/212a/course/course.pdf) - C. McMullen
|
||
* [Real Analysis for Graduate Students](http://bass.math.uconn.edu/3rd.pdf) - Richard F. Bass
|
||
* [Modern Real Analysis](http://www.math.purdue.edu/~torres/pubs/Modern-real-analysis.pdf) - William P. Ziemer (Indiana University)
|
||
* [Mathematical Analysis Vol I](http://www.trillia.com/zakon-analysisI.html) - Elias Zakon
|
||
* [Mathematical Analysis Vol II](http://www.trillia.com/zakon-analysisII.html) - Elias Zakon
|
||
* [Advanced Calculus](http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf) - Lynn Loomis, Schlomo Sternberg
|
||
* [ Analysis of Functions of a Single Variable](http://spot.colorado.edu/~baggett/analysis.html) - Lawerence Baggett
|
||
* [The Calculus of Functions of Several Variables](http://www.synechism.org/wp/the-calculus-of-functions-of-several-variables/) - Dan Sloughter
|
||
* [A ProblemText in Advanced Calculus](http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf) - John M. Erdman
|
||
* [Calculus and Linear Algebra. Vol. 1](http://hdl.handle.net/2027/spo.5597602.0001.001) - Wilfred Kaplan, Donald J. Lewis
|
||
* [Calculus and Linear Algebra. Vol. 2](https://quod.lib.umich.edu/s/spobooks/5597602.0002.001) - Wilfred Kaplan, Donald J. Lewis
|
||
* [Introduction to Calculus I and II](http://www.math.odu.edu/~jhh/counter10.html) - J.H. Heinbockel
|
||
* [Active Calculus](http://faculty.gvsu.edu/boelkinm/Home/Active_Calculus.html) - Matt Boelkins
|
||
|
||
### Harmonic Analysis
|
||
|
||
* [Harmonic Analysis Lecture Notes](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf) - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
|
||
* [Harmonic Analysis](http://www.math.uchicago.edu/~schlag/harmonicnotes.pdf) - W. Schlag
|
||
* [Lecture Notes: Fourier Transform and its Applications](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf) - Brad Osgood
|
||
* [Fourier Analysis](http://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf) - Lucas Illing
|
||
|
||
### Complex Analysis
|
||
|
||
* [Introduction to Complex Analysis](http://www.unc.edu/math/Faculty/met/complex.pdf) - Michael Taylor
|
||
* [An Introduction to Complex Analysis and Geometry](http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book-5-refs-bip.pdf) - John P. D'Angelo (University of Illinois)
|
||
* [A First Course in Complex Analysis](http://math.sfsu.edu/beck/papers/complex.pdf) - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
|
||
* [A Guide to Complex Variables](http://www.math.wustl.edu/~sk/books/guide.pdf) - Steven G. Krantz
|
||
* [Complex Analysis](http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex_analysis.pdf) - Charles Walkden
|
||
* [Complex Analysis](http://www.math.ku.dk/noter/filer/koman-12.pdf) - Christian Berg
|
||
* [Complex Variables](http://people.math.sc.edu/girardi/m7034/book/AshComplexVariablesWithHyperlinks.pdf) - R. B. Ash, W.P. Novinger
|
||
* [Complex Analysis](http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf) - Christer Bennewitz
|
||
* [Complex Analysis](https://web.archive.org/web/20150620124453/https://www.math.washington.edu/~marshall/math_536/Notes.pdf) - Donald E. Marshall
|
||
* [A Concise Course in Complex Analysis and Riemann Surfaces](http://www.math.uchicago.edu/~schlag/bookweb.pdf) - Wilhelm Schlag
|
||
* [Complex Analysis](http://people.math.gatech.edu/%7Ecain/winter99/complex.html) - G. Cain (Georgia Tech)
|
||
|
||
### Functional Analysis
|
||
|
||
* [An Introduction to Functional Analysis](http://www.math.uwaterloo.ca/~lwmarcou/Preprints/LinearAnalysis.pdf) - Laurent W. Marcoux (University of Waterloo)
|
||
* [Functional Analysis: Lecture Notes](http://users.math.msu.edu/users/jeffrey/920/920notes.pdf) - Jeff Schenker (Michigan State University)
|
||
* [Functional Analysis Lecture Notes](http://www.math.hkbu.edu.hk/~zeng/Teaching/math3680/FAnotes.pdf) - T.B. Ward (University of East Anglia)
|
||
* [Functional Analysis](http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf) - Alexander C. R. Belton
|
||
* [Topics in Real and Functional Analysis](https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf) - Gerald Teschl
|
||
* [Functional Analysis](http://www2.math.ou.edu/~cremling/teaching/lecturenotes/fa-new/LN-I.pdf) - Christian Remling
|
||
* [Theory of Functions of a Real Variable](http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf) -
|
||
Shlomo Sternberg
|
||
* [Functional Analysis](http://spot.colorado.edu/~baggett/functional.html) - Lawerence Baggett
|
||
|
||
### Measure Theory
|
||
|
||
* [An Introduction to Measure Theory](https://terrytao.files.wordpress.com/2011/01/measure-book1.pdf) - Terence Tao (UCLA)
|
||
* [Lecture Notes on Measure Theory and Functional Analysis](http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf) - P. Cannarsa, T. D’Aprile
|
||
* [Lecture Notes in Measure Theory](http://www.math.chalmers.se/~borell/MeasureTheory.pdf) - Christer Borell
|
||
* [A Crash Course on the Lebesgue Integral and Measure Theory](http://www.gold-saucer.org/math/lebesgue/lebesgue.pdf) - Steve Cheng
|
||
* [Measure Theory](https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf) - John K. Hunter (University of California at Davis)
|
||
* [Measure and Integration](https://people.math.ethz.ch/~salamon/PREPRINTS/measure.pdf) - Dietmar A. Salamon (ETH Zürich)
|
||
* [Lecture notes: Measure Theory](http://www.math.ucsd.edu/~bdriver/240-00-01/Lecture_Notes/measurep.pdf) - Bruce K. Driver
|
||
|
||
### Ordinary Differential Equations
|
||
|
||
* [Difference Equations To Differential Equations](http://www.synechism.org/wp/difference-equations-to-differential-equations/) - Dan Sloughter
|
||
* [Ordinary Differential Equation](https://www.math.uni-bielefeld.de/~grigor/odelec2008.pdf) - Alexander Grigorian (University of Bielefeld)
|
||
* [Ordinary Differential Equations: Lecture Notes](http://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf) - Eugen J. Ionascu
|
||
* [Ordinary Differential Equations](http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf) - Peter Philip
|
||
* [Ordinary Differential Equations](http://users.math.msu.edu/users/gnagy/teaching/ode.pdf) - Gabriel Nagy
|
||
* [Ordinary Differential Equations and Dynamical Systems](http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf) - Gerald Teschl
|
||
* [Notes on Differential Equations](http://leipper.org/manuals/zip-fill/dn-difeq-notes.pdf) - Bob Terrell
|
||
* [Elementary Differential Equations](http://digitalcommons.trinity.edu/mono/8/) - William F. Trench
|
||
* [Elementary Differential Equations With Boundary Value Problems](http://digitalcommons.trinity.edu/mono/9/) - William F. Trench
|
||
* [Notes on Diffy Qs: Differential Equations for Engineers](http://www.jirka.org/diffyqs/) - Jiří Lebl
|
||
|
||
### Partial Differential Equations
|
||
|
||
* [Notes on Partial Differential Equations](https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf) - John K. Hunter (University of California at Davis)
|
||
* [Partial Differential Equations: Lecture Notes](http://www.math.uni-leipzig.de/~miersemann/pdebook.pdf) - Erich Miersemann (Leipzig University)
|
||
* [Linear Methods of Applied Mathematics](http://www.mathphysics.com/pde/) - E. Harrell, J. Herod (Georgia Tech)
|
||
|
||
|
||
## Probability and Statistics
|
||
|
||
### Probability Theory
|
||
|
||
* [Introduction to Probability](https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf) - Charles M. Grinstead, J. Laurie Snell
|
||
* [Introduction to Probability](http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf) - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)
|
||
* [A Short Introduction to Probability](http://www.maths.uq.edu.au/~kroese/asitp.pdf) - Dirk P. Kroese (University of Queensland)
|
||
* [Probability: Theory and Examples](https://www.math.duke.edu/~rtd/PTE/PTE4_1.pdf) - Rick Durrett
|
||
* [Probability and Statistics Cookbook](https://github.com/mavam/stat-cookbook/releases/download/0.2.3/stat-cookbook.pdf) - Matthias Vallentin (UC Berkeley)
|
||
* [The Only Probability Cheatsheet You'll Ever Need](http://www.wzchen.com/probability-cheatsheet/) - William Chen
|
||
* [An Introduction to Probability and Random Processes](http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf) - Gian-Carlo Rota, Kenneth Baclawski
|
||
|
||
### Statistics
|
||
|
||
* [Lecture Notes on Statistical Theory](http://homepages.math.uic.edu/~rgmartin/Teaching/Stat411/Notes/411notes.pdf) - Ryan Martin (University of Illinois)
|
||
* [Introduction to Statistics and Data Analysis for Physicists](http://www-library.desy.de/preparch/books/vstatmp_engl.pdf) - Gerhard Bohm, Günter Zech
|
||
* [Probability and Mathematical Statistics](http://www.iiserpune.ac.in/~ayan/MTH201/Sahoo_textbook.pdf) - Prasanna Sahoo (University of Louisville)
|
||
* [Lectures on Statistics](http://math.arizona.edu/~faris/stat.pdf) - William G. Faris
|
||
* [Statistical Theory](http://pages.pomona.edu/~ajr04747/Fall2009/Math152/Notes/Math152NotesFall09.pdf) - Adolfo J. Rumbos
|
||
* [Theory of Statistics](http://mason.gmu.edu/~jgentle/books/MathStat.pdf) - James E. Gentle (George Mason University)
|
||
* [Theory of Statistics](http://math.arizona.edu/~jwatkins/notests.pdf) - Joseph C. Watkins (University of Arizona)
|
||
* [Glossary of Data Modeling](https://web.archive.org/web/20130523134625/http://www.aiaccess.net/e_gm.htm) - AI Access
|
||
* [Statistics Papers](http://www.ats.ucla.edu/stat/papers/) - List of statistics papers curated by the Institute for Digital Research and Education (IDRE) at UCLA on methods such as bootstrap and factor invariance.
|
||
* [NIST Handbook of Statistical Methods](http://itl.nist.gov/div898/handbook/index.htm) - Resource on practical statistics directed towards scientists and engineers.
|
||
* [Concepts and Applications of Inferential Statistics](http://vassarstats.net/textbook/) - Richard Lowry
|
||
* [Rough set data analysis: A road to non-invasive knowledge discovery](http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html) - Ivo Düntsch, Günther Gediga
|
||
|
||
### Statistical Learning
|
||
|
||
* [An Introduction to Statistical Learning with Applications in R](http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf) - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
|
||
* [The Elements of Statistical Learning](http://web.stanford.edu/~hastie/Papers/ESLII.pdf) - Trevor Hastie, Robert Tibshirani, Jerome Friedman
|
||
* [Statistical Learning Theory](https://web.stanford.edu/class/cs229t/notes.pdf) - Percy Liang
|
||
* [Reinforcement Learning: An Introduction](https://webdocs.cs.ualberta.ca/~sutton/book/bookdraft2016sep.pdf) - Richard S. Sutton, Andrew G. Barto
|
||
|
||
### Stochastic processes
|
||
|
||
* [Lectures on Stochastic Processes](http://www.math.tifr.res.in/~publ/ln/tifr24.pdf) - K. Ito (Tata Institute of Fundamental Research, Bombay)
|
||
* [Probability and Stochastic Processes with Applications](http://www.math.harvard.edu/~knill/teaching/math144_1994/probability.pdf) - Oliver Knill (Harvard University)
|
||
* [Stochastic Processes](http://statweb.stanford.edu/~adembo/math-136/nnotes.pdf) - Amir Dembo (Stanford University)
|
||
* [Lecture Notes on Stochastic Processes](http://www.mi.fu-berlin.de/wiki/pub/CompMolBio/MarkovKetten15/stochastic_processes_2011.pdf) - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin)
|
||
* [Introduction to Stochastic Processes - Lecture Notes](https://www.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf) - Gordan Žitković (University of Texas)
|
||
* [Applied Stochastic Processes in science and engineering](https://www.math.uwaterloo.ca/~mscott/Little_Notes.pdf) - Matt Scott (University of Waterloo)
|
||
* [An Introduction to Stochastic Processes in Continuous Time](http://www.math.leidenuniv.nl/~spieksma/colleges/sp-master/sp-hvz1.pdf) - Flora Spieksma (Leiden University)
|
||
* [Markov Chains and Mixing Times](http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf) - David A. Levin, Yuval Peres, Elizabeth L. Wilmer
|
||
* [Convergence of Stochastic Processes](http://www.stat.yale.edu/~pollard/Books/1984book/pollard1984.pdf) - David Pollard
|
||
|
||
|
||
## Numerical Analysis
|
||
|
||
* [Introduction to Numerical Analysis](http://www.math.umd.edu/~dlevy/books/na.pdf) - Doron Levy (University of Maryland)
|
||
* [A Concise Introduction to Numerical Analysis](http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf) - Douglas N. Arnold (University of Minnesota)
|
||
* [Numerical Analysis](http://people.cs.uchicago.edu/~ridg/newna/nalrs.pdf) - L. Ridgway Scott
|
||
* [Lectures In Basic Computational Numerical Analysis](http://www.engr.uky.edu/~acfd/egr537-lctrs.pdf) - J. M. McDonough (University of Kentucky)
|
||
* [Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods](http://www.math.uni-bremen.de/~schmidt/SS04/YSU_Notes.pdf) - Alfred Schmidt, Arsen Narimanyan
|
||
* [Numerical Analysis for Engineers](https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/) - Douglas Wilhelm Harder
|
||
|
||
|
||
## Signal processing
|
||
|
||
* [Introduction to Signal Processing](http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf) - Sophocles J. Orfanidis (Rutgers University)
|
||
* [Foundations of Signal Processing](http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf) - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal
|
||
* [An Introduction to Statistical Signal Processing](https://ee.stanford.edu/~gray/sp.pdf) - Robert M. Gray, Lee D. Davisson
|
||
* [Linear algebra, signal processing, and wavelets. A unified approach.](https://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v15/kompendium/applinalgpython.pdf) - Øyvind Ryan (University of Oslo)
|
||
|
||
|
||
## Mathematics for Computer Science
|
||
|
||
* [Mathematics for Computer Science](https://people.csail.mit.edu/meyer/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
|
||
* [Algorithms and Complexity](http://www.math.upenn.edu/%7Ewilf/AlgComp3.html) - H. Wilf
|
||
* [Lecture Notes on Optimization](http://people.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf) - Pravin Varaiya
|
||
* [Information Theory, Inference, and Learning Algorithms](http://www.inference.org.uk/mackay/itila/book.html) - David J. C. MacKay
|
||
|
||
## Mathematical Biology
|
||
|
||
* [Mathematical Biology](http://www.math.ust.hk/~machas/mathematical-biology.pdf) - Jeffrey Chasnov
|
||
|
||
## Mathematical Physics
|
||
|
||
* [Introduction to Continuum Mechanics](http://oaktrust.library.tamu.edu/handle/1969.1/2501) - Ray. M. Bowen
|
||
* [Mathematical Tools for Physics](http://www.physics.miami.edu/nearing/mathmethods/) - James Nearing
|
||
* [Mechanism of the Heavens (1831)](http://www.malaspina.com/etext/heavens.htm) - Mary Somerville
|
||
|
||
# License
|
||
|
||
[](http://creativecommons.org/publicdomain/zero/1.0/)
|
||
|
||
To the extent possible under law, [Cyrille Rossant](http://cyrille.rossant.net) has waived all copyright and related or neighboring rights to this work.
|