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awesome-math

A curated list of awesome mathematics resources
https://github.com/rossant/awesome-math

Last synced: 3 days ago
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Encyclopedia
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Mathematics
- Planetmath
- ProofWiki
- Wolfram Mathworld
- The On-Line Encyclopedia of Integer Sequences - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- The Princeton Companion to Mathematics - Timothy Gowers (Professor, Fields medallist), June Barrow-Green (Professor), and Imre Leader (Professor).
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
- Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.
Probability and Statistics
- Probability Theory
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Introduction to Probability - Charles M. Grinstead, J. Laurie Snell
  - Introduction to Probability - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)
  - A Short Introduction to Probability - Dirk P. Kroese (University of Queensland)
  - Probability: Theory and Examples - Rick Durrett
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - The Only Probability Cheatsheet You'll Ever Need - William Chen
  - An Introduction to Probability and Random Processes - Gian-Carlo Rota, Kenneth Baclawski
  - Foundations of Constructive Probability Theory - Yuen-Kwok Chan
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
  - Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
- Statistics
  - Lecture Notes on Statistical Theory - Ryan Martin (University of Illinois)
  - Introduction to Statistics and Data Analysis for Physicists - Gerhard Bohm, Günter Zech
  - Probability and Mathematical Statistics - Prasanna Sahoo (University of Louisville)
  - Statistical Theory - Adolfo J. Rumbos
  - Theory of Statistics - James E. Gentle (George Mason University)
  - Glossary of Data Modeling - AI Access
  - Statistics 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 - Resource on practical statistics directed towards scientists and engineers.
  - Concepts and Applications of Inferential Statistics - Richard Lowry
  - Statistical Thinking for the 21st Century - Russell A. Poldrack
  - Odds and Ends: Introducing Probability & Decision with a Visual Emphasis - Jonathan Weisberg
  - Seeing Theory - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang
  - Statistics Done Wrong - Alex Reinhart
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - Rough set data analysis: A road to non-invasive knowledge discovery - Ivo Düntsch, Günther Gediga
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
  - All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman
- Statistical Learning
  - An Introduction to Statistical Learning with Applications in R - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
  - The Elements of Statistical Learning - Trevor Hastie, Robert Tibshirani, Jerome Friedman
  - Statistical Learning Theory - Percy Liang
  - Reinforcement Learning: An Introduction - Richard S. Sutton, Andrew G. Barto
- Stochastic processes
  - Lectures on Stochastic Processes - K. Ito (Tata Institute of Fundamental Research, Bombay)
  - Probability and Stochastic Processes with Applications - Oliver Knill (Harvard University)
  - Stochastic Processes - Amir Dembo (Stanford University)
  - Lecture Notes on Stochastic Processes - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin)
  - Introduction to Stochastic Processes - Lecture Notes - Gordan Žitković (University of Texas)
  - Applied Stochastic Processes in science and engineering - Matt Scott (University of Waterloo)
  - Markov Chains and Mixing Times - David A. Levin, Yuval Peres, Elizabeth L. Wilmer
  - Convergence of Stochastic Processes - David Pollard
  - Stochastic Processes - Amir Dembo (Stanford University)
Learning Platforms
- Khan Academy
- Coursera
- MIT OpenCourseWare
- edX
- Brilliant
- WooTube
- Mathigon
- Calculus.org
- Ximera
- MathRelay
- Almost Fun
- Oxford Mathematics
Youtube Series
- Brandon Foltz
- StatQuest
- 3Blue1Brown
- NPTEL
- PatrickJMT
- Professor Leonard
- Precalculus - College Algebra/Trigonometry
- Calculus 1
- Calculus 2
- Calculus 3
- Differential Equations
- To The Point Math
- Crash Course
- Harvard
- MIT OpenCourseWare
- Mathologer
- The Math District
- Mathematical Monk
Tools
- Symbolab
- Desmos
- Math Words
- Wolfram Alpha
- Maxima
- Sympy
- Sagemath
- Unit Converter
- GeoGebra
- Macaulay2
- Singular
- GNU Octave
- Magma
- Matlab
- Wolfram Mathematica
- Free Math
- xhub
- CopyPasteMathjax
- Wolfram Alpha
- Maple
- Finance calculators
Questions and Answers
- Mathematics Stack Exchange
- MathOverflow - for professional mathematicians
Books
- Calculus: Basic Concepts for High Schools - L.V. Tarasov
- Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)
- Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)
- Wikibooks
- Online Mathematics Textbooks
- Beginning and Intermediate Algebra
- Free Mathematics Books
- Trigonometry
- Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)
- Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)
- Online Mathematics Textbooks
Magazines
- Quanta Magazine - Features latest research breakthroughs in an accessible style for non-experts.
- Bulletin of the American Mathematical Society - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.
- Notices of the American Mathematical Society - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.
- European Mathematical Society Magazine - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.
- Mathematics Today by Institute of Mathematics and its Applications - News, opinions, and articles related to mathematics, so the reader stays updated.
- Crux Mathematicorum by Canadian Mathematical Society - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions.
Blogs
- BetterExplained - Maintained by Kalid Azad
- ILoveMaths - For grades 6 thru 12 in K-12 system
- 3blue1brown - Animated Maths
- Mathsisfun
- MathematicsIsAScience - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)
Misc
- Areas of mathematics on Wikipedia
- List of electronic textbooks - Marcel B. Finan (Arkansas Tech University)
- Topology Atlas
- Recreations in Math - H. E. Licks (1917)
- Magic Squares and Cubes - W. S. Andrews (1917)
- Convex Optimization - Stephen Boyd and Lieven Vandenberghe
- Fabrice Baudoin's Notes - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more.
- List of electronic textbooks - Marcel B. Finan (Arkansas Tech University)
Foundations of Mathematics
- Transition To Pure Rigour Math
  - Basic Concepts of Mathematics - Elias Zakon
  - Book of Proof - Richard Hammak (Virginia Commonwealth University)
  - How to Prove It: A Structured Approach (3rd Edition) - Daniel J. Velleman (Professor).
- Set Theory
  - Sets, Relations, Functions - Ivo Düntsch, Günther Gediga
  - An Introduction to Set Theory - William A. R. Weiss
  - Set Theory and Foundations of Mathematics - Sylvain Poirier
  - Set Theory on the Stanford Encyclopedia of Philosophy
- Logic
  - Introduction to Logic - Michael Genesereth, Eric Kao (Stanford University)
  - An Introduction to Formal Logic - P.D. Magnus (University at Albany)
  - A Problem Course in Mathematical Logic - Stefan Bilaniuk (Trent University)
  - Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull)
  - Language, Proof, and Logic - Jon Barwise, John Etchemendy
  - Mathematical Logic - Helmut Schwichtenberg
  - Mathematical Logic - Stephen G. Simpson (Pennsylvania State University)
  - Formal Logic - Miguel Palomino
  - Predictive Arithmetic - Edward Nelson
  - Proofs and Concepts: the fundamentals of abstract mathematics - Joy Morris, Dave Morris
  - Mathematical Reasoning: Writing and Proof - Ted Sundstrom
  - Open Logic Textbook - collaborative effort, main contributors listed [here](https://openlogicproject.org/people/)
- Category Theory
  - Introduction to Category Theory and Categorical Logic - Thomas Streicher
  - An Introduction to Category Theory - Harold Simmons
  - Category Theory - Steve Awodey (Carnegie Mellon University)
  - Category Theory - B. Pareigis
  - Category Theory for Computing Science - Michael Barr, Charles Wells
  - Toposes, Triples and Theories - Michael Barr, Charles Wells
  - Abelian Categories - Peter Freyd
  - Categories and Groupoids - P. J. Higgins
  - Basic Concepts of Enriched Category Theory - G. M. Kelley
  - Abstract and Concrete Categories: The Joy of Cats - Jiri Adamek, Horst Herrlich, George Strecker
  - Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (MIT)
  - Category Theory in Context - Emily Riehl (John Hopkins University)
  - Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (MIT)
- Type Theory
  - Proofs and Types - Jean-Yves Girard
  - Intuitionistic Type Theory - Per Martin-Lof
  - Type Theory and Functional Programming - Simon Thompson
  - Programming in Martin-Lof’s Type Theory - Bengt Nordstrom, Kent Petersson, Jan M. Smith
- Homotopy Type Theory
  - Homotopy Type Theory
- Surreal Numbers
  - Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness - D. E. Knuth
  - Surreal Numbers and Games
  - Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich
Algebra
- Linear Algebra
  - A First Courses in Linear Algebra - Rob Breezer
  - Fundamentals of Linear Algebra - James B. Carrell
  - Linear Algebra and Matrices - Martin Fluch
  - Vector Space Theory - Robert Howlett
  - Linear Algebra - Jim Hefferon
  - Elementary Linear Algebra - Keith Matthews
  - Linear Algebra - David Cherney, Tom Denton, Andrew Waldron
  - Introduction to vectors and tensors, Vol 1: linear and multilinear algebra - Ray M Bowen, C. C. Wang
  - Introduction to vectors and tensors, Vol 2: vector and tensor analysis - Ray M Bowen, C. C. Wang
  - Introduction to Applied Linear Algebra - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
  - Linear Algebra Done Wrong - Sergei Treil
  - Immersive Linear Algebra - J. Ström, K. Åström, and T. Akenine-Möller
  - Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff
  - Linear Algebra, Infinite Dimensions, and Maple - James Herod
  - Linear Algebra, Infinite Dimensions, and Maple - James Herod
- Abstract Algebra
  - Introduction to Abstract Algebra - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)
  - Introduction to Modern Algebra - David Joyce (Clark University)
  - Algebraic Methods - F. Oggier
  - Abstract Algebra : Theory and Applications - Thomas W. Judson, Robert A. Beezer (Austin State University)
  - An Undergraduate Course in Abstract Algebra - Robert Howlett
  - Elements of Abstract and Linear Algebra - E.H. Connell (University of Miami)
  - Abstract Algebra: The Basic Graduate Year - Robert Ash
  - Abstract Algebra: Harvard Extension (Archived) - Benedict Gross
  - Abstract Algebra: Harvard Extension Videos - Benedict Gross
- Analytic Number Theory
  - A Course in Universal Algebra - S. Burris, H.P. Sankappanavar
  - A Course in Commutative Algebra - Robert Ash
  - First Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910)
  - Second Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911)
  - Algebra: An Elementary Text-Book, Part I - G. Chrystal (1904)
  - Algebra: An Elementary Text-Book, Part II - G. Chrystal (1900)
  - Understanding Algebra - James W. Brennan
  - Algebra: An Elementary Text-Book, Part II - G. Chrystal (1900)
  - First Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910)
  - Algebra: An Elementary Text-Book, Part I - G. Chrystal (1904)
- Group Theory
  - Notes on Group Theory - Mark Reeder
  - Group Theory - J.S. Milne
  - Notes on Finite Group Theory - Peter J. Cameron
  - Group Theory - Pedrag Civitanovic
- Ring Theory
  - Foundations of Module and Ring Theory - Robert Wisbauer (University of Düsseldorf)
- Galois Theory
  - An Introduction to Galois Theory - Andrew Baker (University of Glasgow)
  - Fields and Galois Theory - J.S. Milne
  - Galois theory - Miles Reid
  - Galois Theory - Ian Stewart
  - An Introduction to Galois Theory - Andrew Baker (University of Glasgow)
- Lie Algebras
  - Lie Algebras - Shlomo Sternberg
Number Theory
- Surreal Numbers
  - Elementary Number Theory: Primes, Congruences, and Secrets - William Stein
  - Elementary Number Theory - W. Edwin Clark (University of South Florida)
  - A Course on Number Theory - Peter J. Cameron
  - A Computational Introduction to Number Theory and Algebra - Victor Shoup
  - Number Theory: A Contemporary Introduction - Pete L. Clark
  - An Introduction to the Theory of Numbers - Leo Moser
  - Yet Another Introductory Number Theory Textbook - Jonathan A. Poritz
- Algebraic Number Theory
  - Algebraic Number Theory - J.S. Milne
  - Algebraic Number Theory Course Notes - Matthew Baker (Georgia Tech)
  - A Course In Algebraic Number Theory - Robert Ash
  - Introduction to Algebraic Number Theory - F. Oggier
- Analytic Number Theory
  - Introduction to Analytic Number Theory - A.J. Hildebrand (University of Illinois)
  - Elements of Analytic Number Theory - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
  - Analytic Number Theory - Otto Forster (LMU Munich)
  - Analytic Number Theory - Lecture Notes based on Davenport’s book - Andreas Strömbergsson
Combinatorics
- Lie Algebras
  - Basic Combinatorics - Carl G. Wagner (University of Tennessee)
  - Applied Combinatorics - Mitchel T. Keller, William T. Trotter
  - Notes on Combinatorics - Peter J. Cameron
  - Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick
  - generatingfunctionology - Herbert Wilf
  - Basic Combinatorics - Carl G. Wagner (University of Tennessee)
- Graph Theory
  - Graph Theory: Lecture Notes - Christopher Griffin
  - Graph Theory - Reinhard Diestel
Geometry and Topology
- Graph Theory
  - Fundamentals of Geometry - Oleg A. Belyaev
  - A=B - M. Petkovsek, H. Wilf, D. Zeilberger
  - Elements - Euclid
  - Euclid's Elements Redux - Daniel Callahan
  - Mathematical Illustrations - Bill Casselman
  - Byrne's Euclid - Oliver Byrne
  - Plane Geometry - George Wentworth and David Eugene Smith (1913)
  - Planes and Spherical Trigonometry - George Wentworth and David Eugene Smith (1915)
  - Coordinate Geometry - Henry Buchard Fine and Henry Dallas Thompson (1911)
  - Analytic Geometry - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922)
  - Euclid's Elements Redux - Daniel Callahan
  - Coordinate Geometry - Henry Buchard Fine and Henry Dallas Thompson (1911)
  - Plane Geometry - George Wentworth and David Eugene Smith (1913)
  - Planes and Spherical Trigonometry - George Wentworth and David Eugene Smith (1915)
- Differential Geometry
  - Introduction to Differential Geometry - Joel W. Robbin, Dietmar A. Salamon
  - Notes on Differential Geometry and Lie Groups - Jean Gallier (University of Pennsylvania)
  - Topics in Differential Geometry - Peter W. Michor
  - Lectures on Differential Geometry - Wulf Rossmann
  - An Introduction to Riemannian Geometry - Sigmundur Gudmundsson (Lund University)
  - Semi-Riemann Geometry and General Relativity - Shlomo Sternberg
  - Discrete Differential Geometry - Keenan Crane
  - The Geometry and Topology of Three-Manifolds - W. Thurston
- Algebraic Geometry
  - A Brief Introduction to Algebraic Geometry - R.C. Churchill
  - Introduction to Algebraic Geometry - Igor V. Dolgachev
  - Foundations of Algebraic Geometry - Ravi Vakil
  - Algebraic Geometry - Jean Gallier, Stephen S. Shatz (University of Pennsylvania)
  - Algebraic Geometry - J.S. Milne
  - Algebraic Geometry - Andreas Gathmann (University of Kaiserslautern)
  - The Stacks Project - Maintained by Aise Johan de Jong (Columbia)
- Algebraic Statistics
  - Lectures on Algebraic Statistics - Mathias Drton, Bernd Sturmfels, Seth Sullivant
  - An Introduction to Algebraic Statistics - Cristiano Bocci, Luca Chiantini and Anthony V. Geramita
  - Algebraic Statistics - Karl-Heinz Zimmermann
  - Algebraic Statistics for Computational Biology - Pachter, and Sturmfels.
- Topology
  - Elementary Applied Topology - Robert Ghrist (UPenn)
  - Introduction to Topology
  - Introduction to Topology - Alex Küronya
  - Introductory Topology - Jim L. Brown
  - General Topology - Pierre Schapira (Paris VI University)
  - Elementary Topology Problem Textbook
  - General Topology - Jesper M. Møller
  - Topology Topics
  - General Topology - Jesper M. Møller
- Algebraic Topology
  - Algebraic Topology - Allen Hatcher
  - A Concise Course in Algebraic Topology - J. P. May
  - Introduction to Algebraic Topology - Martin Cadek
  - Algebra and Topology - Pierre Schapira (Paris VI University)
  - Lecture Notes in Algebraic Topology - James F. Davis, Paul Kirk (Indiana University)
  - Algebraic Topology - Michael Starbird
  - Lecture Notes on Algebraic Topology - Jie Wu
  - Algebraic Topology - Allen Hatcher
Analysis
- Real Analysis
  - MIT OpenCourseWare Lectures on Calculus - G. Strang
  - Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler
  - An Introduction to Real Analysis - John K. Hunter (University of California at Davis)
  - Introduction to Real Analysis - William F. Trench (Trinity University, Texas)
  - Basic Analysis: Introduction to Real Analysis - Jiří Lebl
  - Elementary Real Analysis - Thomson, Bruckner
  - Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University)
  - Real Analysis - C. McMullen
  - Real Analysis for Graduate Students - Richard F. Bass
  - Modern Real Analysis - William P. Ziemer (Indiana University)
  - Mathematical Analysis Vol I - Elias Zakon
  - Mathematical Analysis Vol II - Elias Zakon
  - Advanced Calculus - Lynn Loomis, Schlomo Sternberg
  - The Calculus of Functions of Several Variables - Dan Sloughter
  - A ProblemText in Advanced Calculus - John M. Erdman
  - Calculus and Linear Algebra. Vol. 1 - Wilfred Kaplan, Donald J. Lewis
  - Calculus and Linear Algebra. Vol. 2 - Wilfred Kaplan, Donald J. Lewis
  - Introduction to Calculus I and II - J.H. Heinbockel
  - Active Calculus - Matt Boelkins
  - Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis" - George M. Bergman
  - Calculus Made Easy - Silvanus P. Thompson (1910)
  - Elements of Differential and Integral Calculus - William Anthony Granville (1911)
  - Precalculus - Carl Stitz, Jeff Zeager
  - Analysis of Functions of a Single Variable - Lawerence Baggett
  - Elements of Differential and Integral Calculus - William Anthony Granville (1911)
- Harmonic Analysis
  - Harmonic Analysis - W. Schlag
  - Lecture Notes: Fourier Transform and its Applications - Brad Osgood
  - Fourier Analysis - Lucas Illing
  - Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)
  - Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
- Complex Analysis
  - Introduction to Complex Analysis - Michael Taylor
  - An Introduction to Complex Analysis and Geometry - John P. D'Angelo (University of Illinois)
  - A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
  - A Guide to Complex Variables - Steven G. Krantz
  - Complex Analysis - Charles Walkden
  - Complex Analysis - Christian Berg
  - Complex Variables - R. B. Ash, W.P. Novinger
  - Complex Analysis - Christer Bennewitz
  - Complex Analysis - Donald E. Marshall
  - A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag
  - Complex Analysis - G. Cain (Georgia Tech)
  - Complex Analysis - Juan Carlos Ponce Campuzano
  - Complex Analysis - G. Cain (Georgia Tech)
  - Complex Analysis - Christian Berg
- Functional Analysis
  - An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo)
  - Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University)
  - Functional Analysis Lecture Notes - T.B. Ward (University of East Anglia)
  - Functional Analysis - Alexander C. R. Belton
  - Topics in Real and Functional Analysis - Gerald Teschl
  - Functional Analysis - Christian Remling
  - Theory of Functions of a Real Variable - Shlomo Sternberg
  - Functional Analysis - Lawerence Baggett
  - An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo)
  - Functional Analysis Lecture Notes - T.B. Ward (University of East Anglia)
- Measure Theory
  - An Introduction to Measure Theory - Terence Tao (UCLA)
  - Lecture Notes in Measure Theory - Christer Borell
  - A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng
  - Measure Theory - John K. Hunter (University of California at Davis)
  - Lecture notes: Measure Theory - Bruce K. Driver
  - Lecture notes: Measure Theory - Bruce K. Driver
  - Lecture Notes on Measure Theory and Functional Analysis - P. Cannarsa, T. D’Aprile
  - Measure and Integration - Dietmar A. Salamon (ETH Zürich)
- Ordinary Differential Equations
  - Difference Equations To Differential Equations - Dan Sloughter
  - Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld)
  - Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu
  - Ordinary Differential Equations - Peter Philip
  - Ordinary Differential Equations - Gabriel Nagy
  - Ordinary Differential Equations and Dynamical Systems - Gerald Teschl
  - Notes on Differential Equations - Bob Terrell
  - Elementary Differential Equations - William F. Trench
  - Elementary Differential Equations With Boundary Value Problems - William F. Trench
  - Notes on Diffy Qs: Differential Equations for Engineers - Jiří Lebl
  - Differential Equations - H. B. Phillips (1922)
  - Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu
- Partial Differential Equations
  - Notes on Partial Differential Equations - John K. Hunter (University of California at Davis)
  - Partial Differential Equations: Lecture Notes - Erich Miersemann (Leipzig University)
  - Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)
Numerical Analysis
- Stochastic processes
  - Introduction to Numerical Analysis - Doron Levy (University of Maryland)
  - A Concise Introduction to Numerical Analysis - Douglas N. Arnold (University of Minnesota)
  - Numerical Analysis - L. Ridgway Scott
  - Lectures In Basic Computational Numerical Analysis - J. M. McDonough (University of Kentucky)
  - Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods - Alfred Schmidt, Arsen Narimanyan
  - Numerical Analysis for Engineers - Douglas Wilhelm Harder
  - Advanced Linear Algebra: Foundations to Frontiers - Robert van de Geijn, Margaret Myers (University of Texas at Austin)
  - A Concise Introduction to Numerical Analysis - Douglas N. Arnold (University of Minnesota)
  - Lectures In Basic Computational Numerical Analysis - J. M. McDonough (University of Kentucky)
  - Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods - Alfred Schmidt, Arsen Narimanyan
Signal processing
- Stochastic processes
  - Introduction to Signal Processing - Sophocles J. Orfanidis (Rutgers University)
  - Foundations of Signal Processing - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal
  - An Introduction to Statistical Signal Processing - Robert M. Gray, Lee D. Davisson
  - Think DSP - Allen B. Downey
  - Linear algebra, signal processing, and wavelets. A unified approach. - Øyvind Ryan (University of Oslo)
Mathematics for Computer Science
- Stochastic processes
  - Mathematics for Computer Science - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
  - Algorithms and Complexity - H. Wilf
  - Lecture Notes on Optimization - Pravin Varaiya
  - Information Theory, Inference, and Learning Algorithms - David J. C. MacKay
  - The Chaos Textbook: Mathematics in the age of the computer - Glenn Elert
Mathematical Biology
- Stochastic processes
  - Mathematical Biology - Jeffrey Chasnov
Mathematical Physics
- Stochastic processes
  - Introduction to Continuum Mechanics - Ray. M. Bowen
  - Mathematical Tools for Physics - James Nearing
  - Mechanism of the Heavens (1831) - Mary Somerville
  - Evan Chen - MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more.
  - Dexter Chua - Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more.
  - Theoretical Computer Science
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  - Cyrille Rossant
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