Math

repo: rossant/awesome-math
category: Theory related: Data Science · Algorithms

Awesome Math

A curated list of awesome mathematics resources.

All resources are freely available except those with a 💲 icon.

Contents
General Resources
Branches of Mathematics
Students Lecture Notes
[Related Awesome Lists](#related-awesome-lists)
License

General Resources

Learning Platforms

Khan Academy
Coursera
MIT OpenCourseWare
edX
Brilliant
WooTube
Mathigon
Calculus.org
Ximera : free interactive mathematics textbooks (Ohio State University)
Almost Fun
Oxford Mathematics
Math Academy
Derivative Calculus Solver — A step-by-step differentiation tool focusing on the chain rule and substitution logic.

Learn to Learn

Understanding Mathematics

Youtube Series

Tools

Symbolab
Desmos
Math Words
Wolfram Alpha
Maxima
Sympy
Sagemath
MathFlow - C# math expression library with symbolic computation (differentiation, simplification, equation solving)
Unit Converter
GeoGebra
Macaulay2
Singular
GNU Octave
Magma
Maple
Matlab
Wolfram Mathematica
Free Math
xhub
CopyPasteMathjax
Finance calculators
Mathcheap
Midpoint Calculator
Quartiles Calculator
Corca Editor
RunMat - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.
Structural Engineering Tools (SEPCO Engineering) - Free online calculators for beam diagrams, Canadian steel section properties, and pressure conversions.

Questions and Answers

Mathematics Stack Exchange
MathOverflow - for professional mathematicians

Encyclopedia

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.
💲 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.

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
Math for Frontend Web Dev
Grokking Statistics
The Math Behind Artificial Intelligence - Tiago Capelo Monteiro (freeCodeCamp)

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 simple text lightweight site for students up to highschool
MathematicsIsAScience - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)

Meetings and Conferences

MathsJam - monthly local recreational maths/puzzle meetups and an annual gathering in Staffordshire, England
Talking Maths in Public - a conference for maths communicators, running every two years, usually in the UK
Bridges - an annual conference on mathematical connections in art, music, architecture, and culture. The 2025 meeting is in Eindhoven, Netherlands.

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
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.

Branches of Mathematics

Content Format
📖 Books
🎥 Videos
📝 Lecture notes, slides, articles, papers

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
📝 Logic and Proof - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn
📝 QED - an interactive textbook - Terence Tao
📝 Open Logic Textbook - collaborative effort, main contributors listed here

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)

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

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 Introductory Number Theory Textbook - Jonathan A. Poritz

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
📝 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

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

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
📝 [MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper
📝 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)
📝 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 Done Right - Sheldon Axler

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
📝 Galois Theory — Tom Leinster (University of Edinburgh)

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
📝 [Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform](https://learngraphtheory.org/) - Hadjoudj Mohammed Islam

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
📝 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)

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
📝 Discrete Differential Geometry - Keenan Crane

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](https://stacks.math.columbia.edu/) - 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

📝 General Topology - Stephen Willard
📝 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

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
📝 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

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
📝 Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)

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

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

truncated — full list on GitHub

Math

Awesome Math

Contents

General Resources

Learning Platforms

Learn to Learn

Youtube Series

Tools

Questions and Answers

Encyclopedia

Books

Magazines

Blogs

Meetings and Conferences

Misc

Branches of Mathematics

Foundations of Mathematics

Transition To Pure Rigour Math

Set Theory

Logic

Category Theory

Type 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

Algebraic Statistics

Topology

Algebraic Topology

Analysis

Real Analysis

Harmonic Analysis

Complex Analysis

Functional Analysis