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A curated list of awesome mathematics resources
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Awesome Math 
A curated list of awesome mathematics resources.
Contents
- General Resources
- Lecture Notes
General Resources
Learning Platforms
Learn to Learn
Questions and Answers
- Mathematics Stack Exchange
- MathOverflow - for professional mathematicians
Encyclopedia
Books
- Calculus: Basic Concepts for High Schools - L.V. Tarasov
- Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)
- Wikibooks
- Online Mathematics Textbooks
- Beginning and Intermediate Algebra
- Trignometry
Blogs
- BetterExplained - Maintained by Kalid Azad
- ILoveMaths - For grades 6 thru 12 in K-12 system
Misc
- Areas of mathematics on Wikipedia
- Paul's Online Math Notes - Paul Dawkins (Lamar University)
- List of electronic textbooks - Marcel B. Finan (Arkansas Tech University)
Lecture Notes
Foundations of Mathematics
Set Theory
- 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)
- Language, Proof, and Logic - Jon Barwise, John Etchemendy
- Mathematical Logic - Helmut Schwichtenberg
- Mathematical Logic - Stephen G. Simpson (Pennsylvania State University)
- Formal Logic - Miguel Palomino
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
Homotopy Type Theory
Surreal Numbers
- Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness - D. E. Knuth
- An Introduction to Surreal Numbers - Gretchen Grimm
- Surreal Numbers and Games
- Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich
Number Theory
- 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
Algebraic Number Theory
- Introduction to Algebraic Number Theory
- Introduction to Algebraic Number Theory - F. Oggier
- Algebraic Number Theory - J.S. Milne
- Algebraic Number Theory Course Notes - Matthew Baker (Georgia Tech)
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
Algebra
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
Group Theory
- Notes on Group Theory - Mark Reeder
- Group Theory - J.S. Milne
- Notes on Finite Group Theory - Peter J. Cameron
Linear Algebra
- Fundamentals of Linear Algebra - James B. Carrell
- Linear Algebra and Matrices - Martin Fluch
- Vector Space Theory - Robert Howlett
- Linear Algebra - Jim Hefferon
- Linear Algebra - Peter Petersen
- MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks - Juan Klopper
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
Combinatorics
- 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
Graph Theory
- Graph Theory: Lecture Notes - Christopher Griffin
- Graph Theory - Reinhard Diestel
Geometry and Topology
- Fundamentals of Geometry - Oleg A. Belyaev
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)
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)
Topology
- 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
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
Analysis
Real Analysis
- 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 - Jirí 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)
Harmonic Analysis
- Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
- Harmonic Analysis - W. Schlag
- Lecture Notes: Fourier Transform and its Applications - Brad Osgood
- Fourier Analysis - Lucas Illing
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
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
Measure Theory
- An Introduction to Measure Theory - Terence Tao (UCLA)
- Lecture Notes on Measure Theory and Functional Analysis - P. Cannarsa, T. D’Aprile
- 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)
- Measure and Integration - Dietmar A. Salamon (ETH Zürich)
- Lecture notes: Measure Theory - Bruce K. Driver
Ordinary Differential Equations
- 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
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)
Probability and Statistics
Probability Theory
- 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
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)
- Lectures on Statistics - William G. Faris
- Statistical Theory - Adolfo J. Rumbos
- Theory of Statistics - http://mason.gmu.edu/~jgentle/books/MathStat.pdf
- Theory of Statistics - Joseph C. Watkins (University of Arizona)
- 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.
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
Numerical Analysis
- 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
Mathematics for Computer Science
- Mathematics for Computer Science - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
License
To the extent possible under law, Cyrille Rossant has waived all copyright and related or neighboring rights to this work.