awesome-math

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

Last synced: 15 days ago
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Algebra
- Abstract Algebra
  - A Course in Universal Algebra - Free online edition of Stanley Burris and H. P. Sankappanavar's graduate text on universal algebra.
  - Elements of Abstract and Linear Algebra - E.H. Connell (University of Miami).
  - Algebraic Methods - F. Oggier.
  - Introduction to Modern Algebra - David Joyce (Clark University).
  - Abstract Algebra: Theory and Applications - Thomas W. Judson.
  - Abstract Algebra: Harvard Extension - Benedict Gross.
- Commutative Algebra
  - The CRing Project - Open-source work-in-progress textbook introducing commutative algebra for readers with elementary abstract algebra, with an emphasis on foundations for algebraic geometry.
  - Commutative Algebra Notes - Free graduate course notes by Mel Hochster, from an introductory course through advanced topics such as Cohen-Macaulay rings, multiplicities, and étale maps.
- Formal Mathematics and Theorem Proving
  - Elementary Algebra 2e - Free one-semester textbook from OpenStax with web and PDF editions, worked examples, practice exercises, chapter reviews, and answer keys.
- Group Theory
  - Group Theory - J.S. Milne.
  - Notes on Finite Group Theory - Peter J. Cameron.
  - Group Theory - Predrag Cvitanović.
- Linear Algebra
  - Fundamentals of Linear Algebra - James B. Carrell.
  - 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).
  - Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff.
  - MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks - Juan Klopper.
  - Linear Algebra Done Right - Sheldon Axler.
  - Linear Algebra - Jim Hefferon.
  - A First Course in Linear Algebra - Robert A. Beezer.
  - Immersive Linear Algebra - J. Ström, K. Åström, and T. Akenine-Möller.
- Representation Theory
  - Lie Algebras - Shlomo Sternberg.
  - Introduction to Representation Theory - Free MIT course by Pavel Etingof with lecture notes and problem sets on representations of groups and algebras, categories, and quivers.
- Ring and Field Theory
  - Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness - D. E. Knuth.
  - Surreal Numbers and Games - Introductory notes on Conway's surreal numbers and their connection with combinatorial game theory.
  - Foundations of Module and Ring Theory - Robert Wisbauer (University of Düsseldorf).
  - Fields and Galois Theory - J.S. Milne.
  - Galois Theory - Ian Stewart.
  - Galois Theory - Tom Leinster (University of Edinburgh).
  - An Introduction to Galois Theory - Andrew Baker (University of Glasgow).
  - Galois Theory - Miles Reid.
  - Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich.
Analysis
- Complex Analysis
  - Introduction to Complex Analysis - Michael Taylor.
  - Complex Variables - R. B. Ash, W.P. Novinger.
  - Complex Analysis - Christer Bennewitz.
  - A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag.
  - Complex Analysis - G. Cain (Georgia Tech).
  - Complex Analysis - Juan Carlos Ponce Campuzano.
  - An Introduction to Complex Analysis and Geometry - Paid textbook by John P. D'Angelo.
  - A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka.
  - A Guide to Complex Variables - Paid textbook by Steven G. Krantz.
  - Complex Analysis - Charles Walkden.
  - Complex Analysis - Donald E. Marshall.
  - Complex Analysis - Christian Berg.
- Functional Analysis
  - Functional Analysis - Alexander C. R. Belton.
  - 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 - Christian Remling.
  - Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University).
- Harmonic Analysis
  - Lecture Notes: Fourier Transform and its Applications - Brad Osgood.
  - Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana-Champaign).
- Measure Theory
  - Measure Theory - John K. Hunter (University of California at Davis).
  - Measure and Integration - Dietmar A. Salamon (ETH Zürich).
  - A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng.
  - Lecture Notes: Measure Theory - Bruce K. Driver.
  - Lecture Notes in Measure Theory - Christer Borell.
- Operator Theory
  - Lecture Notes on Operator Algebras - Free graduate notes by John M. Erdman on Hilbert-space operators, Banach algebras, spectral theory, C*-algebras, compact operators, and K-theory.
- 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 - Jiří Lebl.
  - Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University).
  - Modern Real Analysis - William P. Ziemer (Indiana University).
  - 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. 2 - Wilfred Kaplan, Donald J. Lewis.
  - 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).
  - Precalculus - Carl Stitz, Jeff Zeager.
  - Calculus Open Textbook - Gilbert Strang (MIT OpenCourseWare).
  - Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler.
  - Elementary Real Analysis - Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner.
  - Advanced Real Analysis - Curtis T. McMullen.
  - Real Analysis for Graduate Students - Richard F. Bass.
  - Advanced Calculus - Lynn Loomis, Schlomo Sternberg.
  - Calculus and Linear Algebra. Vol. 1 - Wilfred Kaplan, Donald J. Lewis.
Combinatorics and Discrete Mathematics
- Analytic Number Theory
  - Basic Combinatorics - Carl G. Wagner (University of Tennessee).
  - Notes on Combinatorics - Peter J. Cameron.
  - Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick.
  - Applied Combinatorics - Mitchel T. Keller, William T. Trotter.
  - Discrete Mathematics: An Open Introduction - Free fourth-edition undergraduate textbook by Oscar Levin, with inquiry activities, more than 750 exercises, solutions and hints, and coverage of proofs, graph theory, counting, sequences, and discrete structures.
  - generatingfunctionology - Herbert Wilf.
  - A=B - Marko Petkovšek, Herbert Wilf, and Doron Zeilberger on algorithms for proving hypergeometric identities.
- Graph Theory
  - Graph Theory - Reinhard Diestel.
  - Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform - Hadjoudj Mohammed Islam.
  - Graph Theory: Lecture Notes - Christopher Griffin.
Community and Further Reading
- Blogs
  - BetterExplained - Maintained by Kalid Azad.
  - 3Blue1Brown - Animated explanations of mathematics by Grant Sanderson.
  - ILoveMaths - Mathematics lessons and activities for Indian classes 6 to 12.
  - Math Is Fun - Lightweight lessons and reference pages for school mathematics.
- Journals and Magazines
  - Quanta Magazine - Features latest research breakthroughs in an accessible style for non-experts.
  - 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 - Challenging problems for secondary and undergraduate students, including an Olympiad Corner.
  - 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.
  - Chalkdust Magazine - Independent magazine for mathematically curious readers, with free expository articles, interviews, puzzles, and downloadable issues.
  - 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.
- Meetings and Conferences
  - MathsJam - Monthly local recreational mathematics and puzzle meetups, plus an annual gathering in the United Kingdom.
  - Talking Maths in Public - Biennial conference for mathematics communicators in the United Kingdom.
  - Bridges - Annual conference on mathematical connections in art, music, architecture, and culture.
- Related Curated Lists
  - Theoretical Computer Science - Curated resources on computation, complexity, logic, algorithms, cryptography, and related mathematics.
  - Scientific Computing - Curated software for numerical analysis, scientific computing, meshing, solvers, and visualization.
  - Optimization - Courses, books, notes, and software across mathematical optimization and operations research.
  - Interactive Mathematics - Tools and libraries for building interactive mathematical explanations and explorations.
  - AI for Mathematics - Research index covering AI-assisted mathematical reasoning, discovery, formal proof, and related datasets. Individual entries require independent review.
Differential Equations and Dynamical Systems
- Ergodic Theory and Chaos
  - Chaos: Classical and Quantum - Maintained technical webbook on dynamical systems, periodic orbits, deterministic chaos, statistical mechanics, and quantum chaos.
- Ordinary Differential Equations
  - Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld).
  - Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu.
  - Ordinary Differential Equations and Dynamical Systems - Gerald Teschl.
  - 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 - Gabriel Nagy.
- Partial Differential Equations
  - Notes on Partial Differential Equations - John K. Hunter (University of California at Davis).
  - Linear Methods of Applied Mathematics - Evans M. Harrell II, James V. Herod (Georgia Tech).
  - Partial Differential Equations - Lawrence C. Evans's concise survey of modern PDE theory from analytical, qualitative, and computational viewpoints.
Foundations and Logic
- Category Theory
  - Introduction to Category Theory and Categorical Logic - Thomas Streicher.
  - Category Theory - B. Pareigis.
  - 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. Kelly.
  - Abstract and Concrete Categories: The Joy of Cats - Jiri Adamek, Horst Herrlich, George E. Strecker.
  - Category Theory in Context - Emily Riehl (Johns Hopkins University).
  - Category Theory - Paid textbook by Steve Awodey.
  - Category Theory for Computing Science - Michael Barr, Charles Wells.
  - Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (MIT).
- Formal Mathematics and Theorem Proving
  - Lean - Open-source interactive theorem prover and programming language based on dependent type theory, used for formal mathematics and software verification.
  - mathlib - Community-maintained mathematical library for Lean 4, with formalized theories, proof tactics, programming infrastructure, and generated documentation.
  - Mathematics in Lean - Free textbook with examples and exercises for mathematicians learning Lean 4 and mathlib.
  - Natural Number Game - Interactive Lean 4 game that introduces theorem proving through guided exercises about natural numbers.
  - Isabelle - General-purpose interactive theorem prover with higher-order logic and set-theory environments for formalizing mathematics and computer science.
  - Rocq Prover - Open-source interactive theorem prover and dependently typed programming language for mechanized mathematics and verified software.
  - Mathematical Components - Rocq libraries and tools for large-scale formalized mathematics, including substantial developments in algebra and analysis.
  - Metamath - Minimal formal language and proof verifier with explicit, inspectable proofs built from simple foundations.
  - Courses Using Lean - Maintained, filterable index of university courses that teach Lean or use it for mathematics, logic, programming, and formal verification.
  - Lean-related Conferences and Events - Maintained calendar and archive of conferences, workshops, and tutorials about Lean, mathlib, and formalized mathematics.
  - Theorem Proving in Lean 4 - Free official textbook on dependent type theory, propositions, tactics, inductive types, type classes, and constructing verified proofs in Lean 4.
  - Archive of Formal Proofs - Refereed collection of Isabelle proof libraries, examples, and scientific developments maintained against current Isabelle releases.
- Logic
  - An Introduction to Formal Logic - P.D. Magnus (University at Albany).
  - Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull).
  - Formal Logic - Miguel Palomino.
  - Predictive Arithmetic - Edward Nelson.
  - Proofs and Concepts: the fundamentals of abstract mathematics - Joy Morris, Dave Morris.
  - Open Logic Textbook - collaborative effort, main contributors listed [here](https://openlogicproject.org/people/).
  - forall x: Calgary (An Introduction to Formal Logic) - P.D. Magnus and Tim Button, remixed by Aaron Thomas-Bolduc and Richard Zach (Open Logic Project).
  - Introduction to Logic - Michael Genesereth, Eric J. Kao (Stanford University).
  - Language, Proof, and Logic, Second Edition - Paid textbook by Dave Barker-Plummer, Jon Barwise, and John Etchemendy.
  - Mathematical Logic - Helmut Schwichtenberg.
  - Mathematical Logic - Stephen G. Simpson (Pennsylvania State University).
  - Mathematical Reasoning: Writing and Proof - Ted Sundstrom.
  - Logic and Proof - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn.
- Set Theory
  - Sets, Relations, Functions - Ivo Düntsch, Günther Gediga.
  - Set Theory and Foundations of Mathematics - Sylvain Poirier.
  - Set Theory on the Stanford Encyclopedia of Philosophy - Peer-reviewed overview of set theory with historical context and references.
  - An Introduction to Set Theory - William A. R. Weiss.
- 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.
General Mathematics
- Broad Course Notes
  - Paul's Online Math Notes - Free notes, examples, and practice problems for algebra, calculus, and differential equations, by Paul Dawkins at Lamar University.
  - UBC CLP Calculus Textbooks - Free textbooks, problem books, and source files for a four-course university sequence in differential, integral, multivariable, and vector calculus.
Geometry and Topology
- Algebraic Geometry
  - A Brief Introduction to Algebraic Geometry - R.C. Churchill.
  - Foundations of Algebraic Geometry - Ravi Vakil.
  - Algebraic Geometry - Jean Gallier, Stephen S. Shatz (University of Pennsylvania).
  - Algebraic Geometry - J.S. Milne.
  - The Stacks Project - Maintained by Aise Johan de Jong (Columbia).
  - Introduction to Algebraic Geometry - Igor V. Dolgachev.
  - Algebraic Geometry - Andreas Gathmann (RPTU).
- 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 (Sorbonne University).
  - Lecture Notes in Algebraic Topology - Paid textbook by James F. Davis and Paul Kirk.
- Differential Geometry
  - Introduction to Differential Geometry - Joel W. Robbin, Dietmar A. Salamon.
  - Topics in Differential Geometry - Peter W. Michor.
  - Lectures on Differential Geometry - Wulf Rossmann.
  - Semi-Riemann Geometry and General Relativity - Shlomo Sternberg.
  - Discrete Differential Geometry - Keenan Crane.
  - Notes on Differential Geometry and Lie Groups - Jean Gallier (University of Pennsylvania).
  - An Introduction to Riemannian Geometry - Sigmundur Gudmundsson (Lund University).
  - Differential Geometry - Rigorous undergraduate MIT OpenCourseWare course with lecture notes and problem sets centered on curves, surfaces, and curvature.
  - The Geometry and Topology of Three-Manifolds - W. Thurston.
- General Topology
  - Introduction to Topology - Free introductory notes associated with Renzo Cavalieri's Colorado State University topology course and compiled by students. Covers point-set topology, compactness, connectedness, surfaces, Euler characteristic, and the fundamental group.
  - Introduction to Topology - Alex Küronya.
  - General Topology - Jesper M. Møller.
  - Elementary Applied Topology - Robert Ghrist (UPenn).
  - General Topology - Stephen Willard.
  - General Topology - Pierre Schapira (Sorbonne University).
  - Elementary Topology Problem Textbook - Oleg Viro.
- Graph Theory
  - Fundamentals of Geometry - Free geometry text by Oleg A. Belyaev.
  - Mathematical Illustrations - Bill Casselman's guide to creating clear mathematical diagrams and illustrations.
  - Byrne's Euclid - Interactive web edition of Oliver Byrne's color-coded presentation of Euclid's first six books.
  - Euclid's Elements (David Joyce edition) - Complete web edition with diagrams, commentary, and references by David Joyce.
  - Euclid's Elements Redux - Open textbook by Daniel Callahan that presents Euclid with modern commentary and exercises.
History and Mathematics Education
- Mathematical Software and Tools
  - MacTutor History of Mathematics Archive - University of St Andrews archive of mathematician biographies, histories of mathematical topics, timelines, institutions, and related reference material.

Programming Languages

Jupyter Notebook 3 Python 3 HTML 1 Lean 1 TeX 1 Rust 1 Objective-C++ 1

awesome-math

Algebra

Abstract Algebra

Commutative Algebra

Formal Mathematics and Theorem Proving

Group Theory

Linear Algebra

Representation Theory

Ring and Field Theory

Analysis

Complex Analysis

Functional Analysis

Harmonic Analysis

Measure Theory

Operator Theory

Real Analysis

Combinatorics and Discrete Mathematics

Analytic Number Theory

Graph Theory

Community and Further Reading

Blogs

Journals and Magazines

Meetings and Conferences

Related Curated Lists

Differential Equations and Dynamical Systems

Ergodic Theory and Chaos

Ordinary Differential Equations

Partial Differential Equations

Foundations and Logic

Category Theory

Formal Mathematics and Theorem Proving

Logic

Set Theory

Type Theory

General Mathematics

Broad Course Notes

Geometry and Topology

Algebraic Geometry

Algebraic Topology

Differential Geometry

General Topology

Graph Theory

History and Mathematics Education

Mathematical Software and Tools