Awesome Math

A curated list of awesome mathematics resources.

Contents

• Contents
• General Resources
  • Learning Platforms
  • Learn to Learn
  • Tools
  • Questions and Answers
  • Encyclopedia
  • Books
  • Blogs
  • Misc
• Lecture Notes
  • Foundations of Mathematics
    • Set Theory
    • Logic
    • Category Theory
    • Homotopy Type Theory
    • Surreal Numbers
  • Number Theory
    • Algebraic Number Theory
    • Analytic Number Theory
  • Algebra
    • Abstract Algebra
    • Group Theory
    • Linear Algebra
    • Ring Theory
    • Galois Theory
    • Lie Algebras
  • Combinatorics
    • Graph Theory
  • Geometry and Topology
    • Differential Geometry
    • Algebraic Geometry
    • Topology
    • Algebraic Topology
  • Analysis
    • Real Analysis
    • Harmonic Analysis
    • Complex Analysis
    • Functional Analysis
    • Measure Theory
    • Ordinary Differential Equations
    • Partial Differential Equations
  • Probability and Statistics
    • Probability Theory
    • Statistics
    • Statistical Learning
    • Stochastic processes
  • Numerical Analysis
  • Signal processing
  • Mathematics for Computer Science
  • Mathematical Biology
  • Mathematical Physics
• License

General Resources

Learning Platforms

• Khan Academy
• Coursera
• MIT OpenCourseWare
• edX

Learn to Learn

• Understanding Mathematics

Tools

• Symbolab
• Desmos
• Math Words
• Wolfram Alpha

Questions and Answers

• Mathematics Stack Exchange
• MathOverflow - for professional mathematicians

Encyclopedia

• Encyclopedia of Mathematics
• Planetmath
• ProofWiki
• Wolfram Mathworld

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
• Trigonometry

Blogs

• BetterExplained - Maintained by Kalid Azad
• ILoveMaths - For grades 6 thru 12 in K-12 system
• 3blue1brown - Animated Maths

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)
• Topology Atlas

Lecture Notes

Foundations of Mathematics

• Basic Concepts of Mathematics - Elias Zakon

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)
• 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

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)

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
• 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
• An Introduction to the Theory of Numbers - Leo Moser
• Yet Another Introductary Number Theory Textbook - Jonathan A. Poritz

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)
• A Course In Algebraic Number Theory - Robert Ash

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

• A Course in Universal Algebra - S. Burris, H.P. Sankappanavar
• A Course in Commutative Algebra - Robert Ash

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

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

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
• Linear Algebra - Jim Hefferon
• Elementary Linear Algebra - Keith Matthews
• A First Courses in Linear Algebra - Rob Breezer
• 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)

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

Lie Algebras

• Lie Algebras - Shlomo Sternberg

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
• generatingfunctionology - Herbert Wilf

Graph Theory

• Graph Theory: Lecture Notes - Christopher Griffin
• Graph Theory - Reinhard Diestel

Geometry and Topology

• 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

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)
• The Geometry and Topology of Three-Manifolds - W. Thurston
• Semi-Riemann Geometry and General Relativity - Shlomo Sternberg

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)

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

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

• 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
• Analysis of Functions of a Single Variable - Lawerence Baggett
• 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

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
• Complex Analysis - G. Cain (Georgia Tech)

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

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

• 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

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)

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
• An Introduction to Probability and Random Processes - Gian-Carlo Rota, Kenneth Baclawski

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 - James E. Gentle (George Mason University)
• 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.
• Concepts and Applications of Inferential Statistics - Richard Lowry
• Rough set data analysis: A road to non-invasive knowledge discovery - Ivo Düntsch, Günther Gediga

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)
• An Introduction to Stochastic Processes in Continuous Time - Flora Spieksma (Leiden University)
• Markov Chains and Mixing Times - David A. Levin, Yuval Peres, Elizabeth L. Wilmer
• Convergence of Stochastic Processes - David Pollard

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
• Numerical Analysis for Engineers - Douglas Wilhelm Harder

Signal processing

• 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
• Linear algebra, signal processing, and wavelets. A unified approach. - Øyvind Ryan (University of Oslo)

Mathematics for Computer Science

• 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

Mathematical Biology

• Mathematical Biology - Jeffrey Chasnov

Mathematical Physics

• Introduction to Continuum Mechanics - Ray. M. Bowen
• Mathematical Tools for Physics - James Nearing
• Mechanism of the Heavens (1831) - Mary Somerville

License

To the extent possible under law, Cyrille Rossant has waived all copyright and related or neighboring rights to this work.