Awesome Math Overview
A curated list of awesome mathematics resources
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Awesome Math 
Awesome Math is a curated list of high-quality resources for learning, teaching, and doing mathematics. It covers pure mathematics, applied mathematics, computation, formal proof, and the use of AI in mathematics.
Most resources are free to access. Paid resources may be included when they are widely respected, unusually useful, and hard to replace. Access limits should be stated in the entry.
Read the contribution guidelines before suggesting a resource.
Contents
- Start Here
- General Mathematics
- Foundations and Logic
- Algebra
- Number Theory
- Combinatorics and Discrete Mathematics
- Geometry and Topology
- Analysis
- Differential Equations and Dynamical Systems
- Probability and Statistics
- Numerical and Computational Mathematics
- Optimization, Operations Research, and Control
- Mathematical Physics
- Interdisciplinary Mathematics
- Mathematical Practice
- History and Mathematics Education
- Community and Further Reading
Start Here
Learning Platforms
- Khan Academy - Free, self-paced lessons and exercises from arithmetic through calculus and beyond.
- Coursera - University and industry mathematics courses, with access and payment varying by course.
- MIT OpenCourseWare - Free MIT course materials, including notes, assignments, and exams for undergraduate and graduate mathematics.
- edX - University and professional mathematics courses, with audit and paid options varying by course.
- Brilliant - Interactive, problem-based lessons in foundational mathematics, probability, and related quantitative subjects.
- WooTube - Video lessons by Eddie Woo covering secondary-school mathematics with an emphasis on conceptual understanding.
- Mathispower4u - More than 9,000 free, closed-captioned video lessons and worked examples organized from middle-school mathematics through calculus, linear algebra, differential equations, and statistics, by James Sousa.
- Mathigon - Interactive courses, activities, and visual explanations for school and early university mathematics.
- Ximera - Free interactive mathematics textbooks from Ohio State University.
- Almost Fun - Free interactive middle- and high-school mathematics lessons, practice problems, and teacher resources from a nonprofit organization.
- Oxford Mathematics - Lectures and public talks from the University of Oxford, including accessible explanations of advanced topics.
- Math Academy - Paid adaptive platform with diagnostic assessment and mastery-based courses from fourth-grade mathematics through university topics.
- OSSU Math (⭐9k) - Free, prerequisite-ordered self-study curriculum modeled on the mathematics requirements of an undergraduate degree.
- Waterloo Open Math - Free university-level courseware with lessons, exercises, and immediate feedback from the University of Waterloo.
Proof and Problem Solving
- Basic Concepts of Mathematics - Elias Zakon.
- Book of Proof - Richard Hammack (Virginia Commonwealth University).
- How to Prove It: A Structured Approach (3rd Edition) - Paid textbook by Daniel J. Velleman.
Video Courses and Series
- Brandon Foltz - Video courses in statistics, probability, and quantitative methods with worked examples.
- StatQuest - Introductory video explanations of statistics, probability, and machine learning.
- 3Blue1Brown - Visual explanations of core mathematics, including calculus, linear algebra, and differential equations.
- NPTEL - University lecture courses from Indian institutes covering mathematics and related technical subjects.
- Numberphile - Popular mathematics videos featuring mathematicians discussing problems, ideas, and curiosities.
- PatrickJMT - Worked-example videos for algebra, calculus, and other introductory college topics.
- Professor Leonard - Full lecture series in precalculus, calculus, and differential equations for college students.
- Precalculus - College Algebra/Trigonometry - Full course playlist.
- Calculus 1 - Full course playlist.
- Calculus 2 - Full course playlist.
- Calculus 3 - Full course playlist.
- Differential Equations - Full course playlist.
- To The Point Math - Short reviews of common algebra and calculus topics.
- MIT OpenCourseWare - MIT course recordings and video lectures, including full mathematics courses.
- Mathologer - Visual videos on recreational mathematics and selected advanced topics.
- The Math District - Free guides and videos covering prealgebra, algebra, geometry, trigonometry, statistics, calculus, and technical mathematics.
Questions and Answers
- Mathematics Stack Exchange - Community questions and answers about mathematics problems and proofs.
- MathOverflow - Questions and answers for professional mathematicians.
Reference Works
Mathematics Subject Classification 2020 - The standard subject taxonomy maintained by Mathematical Reviews and zbMATH.
Encyclopedia of Mathematics - Reference articles on mathematical concepts, theorems, biographies, and applications.
ProofWiki - Collaborative repository of mathematical definitions, lemmas, and proofs.
nLab - Collaborative research-level notes and expositions in category theory, homotopy theory, mathematical physics, and related areas.
Wolfram Mathworld - Reference articles on mathematical definitions, formulas, identities, and related concepts.
The On-Line Encyclopedia of Integer Sequences - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.
AIM Open Textbook Initiative - Open mathematics textbooks organized by course and evaluated by the American Institute of Mathematics editorial board.
AMS Open Math Notes - Free course notes, textbooks, and research expositions hosted by the American Mathematical Society.
OpenStax Mathematics - Peer-reviewed, openly licensed textbooks for school and introductory college mathematics from Rice University.
The Princeton Companion to Mathematics - Paid reference edited by Timothy Gowers, June Barrow-Green, and Imre Leader.
Encyclopedia of Distances (4th Edition) - Paid reference by Michel Marie Deza and Elena Deza.
Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania).
Multivariable Calculus - G. Cain, J. Herod (Georgia Tech).
Wikibooks - Community-authored collection of open mathematics textbooks and instructional books.
Online Mathematics Textbooks - Index of freely available mathematics textbooks maintained at Georgia Tech.
Trigonometry - Michael Corral.
The Math Behind Artificial Intelligence - Tiago Capelo Monteiro (freeCodeCamp).
Broad Course Notes
- 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.
General Mathematics
- 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.
Foundations and Logic
Logic
- Introduction to Logic - Michael Genesereth, Eric J. Kao (Stanford University).
- An Introduction to Formal Logic - P.D. Magnus (University at Albany).
- 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).
- Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull).
- 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).
- 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.
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 - Peer-reviewed overview of set theory with historical context and references.
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 - Open textbook on homotopy type theory, univalent foundations, and higher-dimensional structures.
Category Theory
- Introduction to Category Theory and Categorical Logic - Thomas Streicher.
- Category Theory - Paid textbook by Steve Awodey.
- 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. Kelly.
- Abstract and Concrete Categories: The Joy of Cats - Jiri Adamek, Horst Herrlich, George E. Strecker.
- Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (MIT).
- Category Theory in Context - Emily Riehl (Johns Hopkins University).
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 (⭐3.9k) - 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.
- 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.
- 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.
- Archive of Formal Proofs - Refereed collection of Isabelle proof libraries, examples, and scientific developments maintained against current Isabelle releases.
- 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.
Algebra
- Elementary Algebra 2e - Free one-semester textbook from OpenStax with web and PDF editions, worked examples, practice exercises, chapter reviews, and answer keys.
Abstract Algebra
- A Course in Universal Algebra - Free online edition of Stanley Burris and H. P. Sankappanavar's graduate text on universal algebra.
- Introduction to Modern Algebra - David Joyce (Clark University).
- Algebraic Methods - F. Oggier.
- Abstract Algebra: Theory and Applications - Thomas W. Judson.
- Elements of Abstract and Linear Algebra - E.H. Connell (University of Miami).
- Abstract Algebra: Harvard Extension - Benedict Gross.
- Abstract Algebra: Harvard Extension Videos - Benedict Gross.
Linear Algebra
- Fundamentals of Linear Algebra - James B. Carrell.
- Linear Algebra - Jim Hefferon.
- MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks (⭐585) - Juan Klopper.
- A First Course in Linear Algebra - Robert A. Beezer.
- 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 Done Right - Sheldon Axler.
Group Theory
- Group Theory - J.S. Milne.
- Notes on Finite Group Theory - Peter J. Cameron.
- Group Theory - Predrag Cvitanović.
Ring and Field Theory
- Foundations of Module and Ring Theory - Robert Wisbauer (University of Düsseldorf).
- 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).
- 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.
- Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich.
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.
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.
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.
- 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).
Analytic Number Theory
- Analytic Number Theory - Otto Forster (LMU Munich).
- Analytic Number Theory - Andreas Strömbergsson (Uppsala University).
Combinatorics and Discrete Mathematics
- Basic Combinatorics - Carl G. Wagner (University of Tennessee).
- 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.
- Notes on Combinatorics - Peter J. Cameron.
- Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick.
- generatingfunctionology - Herbert Wilf.
- A=B - Marko Petkovšek, Herbert Wilf, and Doron Zeilberger on algorithms for proving hypergeometric identities.
Graph Theory
- Graph Theory: Lecture Notes - Christopher Griffin.
- Graph Theory - Reinhard Diestel.
- Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform - Hadjoudj Mohammed Islam.
Geometry and Topology
- Fundamentals of Geometry - Free geometry text by Oleg A. Belyaev.
- 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.
- 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.
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.
- Differential Geometry - Rigorous undergraduate MIT OpenCourseWare course with lecture notes and problem sets centered on curves, surfaces, and curvature.
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 (RPTU).
- The Stacks Project - Maintained by Aise Johan de Jong (Columbia).
General Topology
- General Topology - Stephen Willard.
- Elementary Applied Topology - Robert Ghrist (UPenn).
- 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 - Pierre Schapira (Sorbonne University).
- Elementary Topology Problem Textbook - Oleg Viro.
- 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 (Sorbonne University).
- Lecture Notes in Algebraic Topology - Paid textbook by James F. Davis and Paul Kirk.
Analysis
Real Analysis
- Calculus Open Textbook - Gilbert Strang (MIT OpenCourseWare).
- 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 - Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner.
- Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University).
- Advanced Real Analysis - Curtis T. McMullen.
- Real Analysis for Graduate Students - Richard F. Bass.
- Modern Real Analysis - William P. Ziemer (Indiana University).
- 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.
- 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.
Complex Analysis
- Introduction to Complex Analysis - Michael Taylor.
- 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 - 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 - Alexander C. R. Belton.
- Functional Analysis - Christian Remling.
- Theory of Functions of a Real Variable - Shlomo Sternberg.
- Functional Analysis - Lawerence Baggett.
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.
Harmonic Analysis
- Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana-Champaign).
- Lecture Notes: Fourier Transform and its Applications - Brad Osgood.
- Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University).
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).
- Measure and Integration - Dietmar A. Salamon (ETH Zürich).
- Lecture Notes: Measure Theory - Bruce K. Driver.
Differential Equations and Dynamical Systems
Ordinary Differential Equations
- Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld).
- Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu.
- Differential Equations - Gabriel Nagy.
- 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.
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.
Ergodic Theory and Chaos
- Chaos: Classical and Quantum - Maintained technical webbook on dynamical systems, periodic orbits, deterministic chaos, statistical mechanics, and quantum chaos.
Probability and Statistics
Probability
- Harvard Statistics 110: Probability - Free probability course with a textbook, lecture videos, exercises, and an optional edX version by Joe Blitzstein.
- 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 (5th edition).
- Probability and Statistics Cookbook (⭐2.3k) - 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.
Stochastic Processes
- Research and Lecture Notes - Advanced notes by Fabrice Baudoin on stochastic analysis, differential geometry, and Dirichlet spaces.
- On Stochastic Processes - K. Ito (Tata Institute of Fundamental Research).
- 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 - Paid textbook by David Pollard.
Statistics
- Lecture Notes on Statistical Theory - Undergraduate notes by Ryan Martin on estimation, likelihood, hypothesis testing, and Bayesian statistics, with some R examples.
- Introduction to Statistics and Data Analysis for Physicists - Gerhard Bohm, Günter Zech.
- Lectures on Statistics - Free text by William G. Faris covering inference, Bayesian methods, regression, principal components, and linear models.
- Theory of Statistics - Advanced, actively revised text by James E. Gentle on probability, statistical models, estimation, testing, and asymptotic theory.
- Theory of Statistics - Graduate notes by Joseph C. Watkins on measure-based probability, decision theory, estimation, testing, and hierarchical models.
- UCLA Statistical Methods and Data Analytics - Tutorials and examples for R, Stata, SAS, and SPSS.
- NIST Handbook of Statistical Methods - Resource on practical statistics directed towards scientists and engineers.
- 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.
- OpenIntro Statistics - Free introductory textbook for college courses and self-study, with datasets, labs, slides, videos, exercises, and accessible PDFs.
Statistical Learning
- An Introduction to Statistical Learning - 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 (2nd edition).
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 - Paid textbook edited by Lior Pachter and Bernd Sturmfels.
Numerical and Computational Mathematics
Numerical Analysis
- Introduction to Numerical Analysis - Undergraduate notes by Doron Levy on root finding, interpolation, approximation, numerical differentiation, and quadrature.
- Numerical Analysis (Second Edition) - Free second-edition textbook by L. Ridgway Scott on the theory and practice of numerical methods.
- Lectures in Basic Computational Numerical Analysis - Archived University of Kentucky textbook by J. M. McDonough, focused on computational methods for differential equations.
- Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods - Specialized notes by Alfred Schmidt and Arsen Narimanyan on adaptive finite element methods.
- Numerical Analysis for Engineers - University of Waterloo course with lectures, assignments, projects, and MATLAB material on numerical methods for engineers.
- Advanced Linear Algebra: Foundations to Frontiers - Online text by Robert van de Geijn and Margaret Myers on algorithms for advanced numerical linear algebra.
- Fundamentals of Numerical Computation - Online textbook by Tobin Driscoll and Richard Braun with Julia, MATLAB, and Python editions covering core numerical methods for linear systems, approximation, root finding, ODEs, and PDEs.
Optimization, Operations Research, and Control
- Convex Optimization - A free textbook with slides, exercises, code, and course material by Stephen Boyd and Lieven Vandenberghe.
- Nonlinear Optimization - Free graduate MIT course covering analytical and computational methods for unconstrained and constrained optimization.
- CVXPY - Open-source Python modeling language for convex, geometric, quasiconvex, and related optimization problems.
Control Theory
- Feedback Systems: An Introduction for Scientists and Engineers - Free textbook by Karl J. Åström and Richard M. Murray on modeling, feedback, stability, performance, state feedback, and control design.
Mathematical Physics
- Introduction to Continuum Mechanics - Ray M. Bowen.
- Mechanism of the Heavens (1831) - Mary Somerville.
- Quantum Field Theory - David Tong's Cambridge master's-level lecture notes, problem sheets, HTML text, and recorded lectures on classical fields, quantization, Dirac fields, and quantum electrodynamics.
Interdisciplinary Mathematics
Mathematics for Computer Science
- Mathematics for Computer Science - Free MIT OpenCourseWare course with an open textbook, videos, notes, problem sets, and exams on proofs, discrete structures, counting, graphs, modular arithmetic, and discrete probability.
- 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.
Mathematics for Machine Learning
- Mathematics for Machine Learning - Free textbook on the linear algebra, geometry, calculus, probability, and optimization needed to study machine learning.
- Deep Learning: Foundations and Concepts - Free-to-read online textbook by Christopher M. Bishop and Hugh Bishop, with a probability-based treatment of modern deep-learning models and methods.
- Mathematics of Machine Learning - Free graduate MIT course on the mathematical and statistical foundations of machine learning, with lecture notes, assignments, and problem-set solutions.
- Probabilistic Machine Learning - Introductory and advanced books by Kevin Murphy, with free draft PDFs, code, figures, exercises, and teaching resources.
Information and Coding Theory
- Information Theory - Free graduate MIT course on entropy, source and channel coding, rate distortion, Gaussian channels, feedback, and multi-user information theory.
- Essential Coding Theory - Free graduate MIT course on error-correcting codes, Hamming spaces, and the algebraic and complexity aspects of coding theory.
- Error Correction Zoo - Maintained reference database of classical, quantum, and hybrid error-correcting codes, with definitions, relationships, and references.
Mathematical Finance
- Topics in Mathematics with Applications in Finance - Free undergraduate MIT course covering bond mathematics, probability, portfolio methods, time series, stochastic processes, and quantitative finance.
Mathematical Biology
- Mathematical Biology - Jeffrey Chasnov.
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.
- Think DSP - Allen B. Downey.
Mathematical Practice
AI for Mathematics
This section covers AI-assisted theorem proving, formalization, and mathematical discovery. Resources that teach the mathematics used in machine learning appear under Mathematics for Machine Learning.
- LeanDojo v2 - Open-source framework and benchmark data for training, evaluating, and deploying AI-assisted theorem provers for Lean 4.
- miniF2F (⭐104) - Cross-system benchmark of formalized olympiad, high-school, and undergraduate problems for evaluating automated theorem provers.
- AlphaGeometry (⭐4.9k) - Open research implementation combining learned guidance with symbolic deduction for olympiad geometry problems.
- First Proof Project - Independent project that publishes research-level problems, evaluation methods, solutions, and expert commentary for assessing AI systems in mathematics.
- Math AI Seminar - University of Washington research seminar on formalization, theorem proving, mathematical AI, and machine-learning applications in mathematics, with a multi-year event archive.
- b=M²L - Barcelona Mathematics and Machine Learning colloquia on the interaction between mathematics and machine learning, with multi-year editions and recorded talks.
- AI for Mathematics and Theoretical Computer Science - Simons Institute and SLMath workshop archive with recorded talks on proof assistants, automated reasoning, machine learning, and mathematical discovery.
- Mathematics and AI - University of Washington Fall 2025 graduate course with public slides, Lean examples, projects, and readings on machine learning, formalization, autoformalization, mathematical discovery, and ethics.
- AI-Assisted Mathematical Discovery (⭐116) - Open thirteen-week course with notes, notebooks, exercises, and case studies on coding agents, machine learning, language models, reinforcement learning, and experimental mathematical research.
Mathematical Software and Tools
- Symbolab - Online solver with step-by-step solutions, graphing, calculators, and practice tools. Some solution steps and study features require a paid plan.
- Desmos - Browser-based graphing calculator with geometry, tables, statistics, and classroom activities.
- Wolfram Alpha - Computational knowledge engine for evaluating expressions, plotting functions, and answering structured queries. Some advanced features require a paid plan.
- Maxima - Free computer algebra system for symbolic and numerical calculations, plotting, and scripting.
- SymPy - Python library for symbolic algebra, calculus, equation solving, matrices, and code generation.
- SageMath - Free mathematics software combining computer algebra, numerical computation, geometry, statistics, and visualization through Python.
- MathFlow (⭐56) - C# math expression library with symbolic computation (differentiation, simplification, equation solving).
- GeoGebra - Interactive mathematics suite for geometry, graphing, algebra, spreadsheets, statistics, and calculus.
- Macaulay2 - Research system for algebraic geometry and commutative algebra with specialized computational packages.
- Singular - Computer algebra system for polynomial computations in commutative algebra, algebraic geometry, and singularity theory.
- GNU Octave - Free environment for numerical computing, linear algebra, plotting, and MATLAB-compatible scripts.
- Magma - Subscription-based computer algebra system for research in algebra, number theory, algebraic geometry, and combinatorics.
- Maple - Paid computer algebra and numerical mathematics system for symbolic computation, visualization, and programming.
- MATLAB - Paid numerical computing environment by MathWorks.
- Wolfram Mathematica - Paid technical-computing system for symbolic and numerical mathematics, visualization, programming, and data analysis.
- Free Math - Free, open-source software for recording, organizing, and reviewing digital mathematics homework without solving the problems automatically.
- RunMat (⭐247) - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.
History and Mathematics Education
- MacTutor History of Mathematics Archive - University of St Andrews archive of mathematician biographies, histories of mathematical topics, timelines, institutions, and related reference material.
- NRICH - Free curriculum-linked problems, investigations, articles, and teacher guidance from the University of Cambridge for learners aged 3 to 18.
Community and Further Reading
Journals and 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 - Challenging problems for secondary and undergraduate students, including an Olympiad Corner.
- Chalkdust Magazine - Independent magazine for mathematically curious readers, with free expository articles, interviews, puzzles, and downloadable issues.
Blogs
- BetterExplained - Maintained by Kalid Azad.
- ILoveMaths - Mathematics lessons and activities for Indian classes 6 to 12.
- 3Blue1Brown - Animated explanations of mathematics by Grant Sanderson.
- Math Is Fun - Lightweight lessons and reference pages for school mathematics.
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 (⭐1.2k) - Curated resources on computation, complexity, logic, algorithms, cryptography, and related mathematics.
- Scientific Computing (⭐1.6k) - Curated software for numerical analysis, scientific computing, meshing, solvers, and visualization.
- Optimization (⭐723) - Courses, books, notes, and software across mathematical optimization and operations research.
- Interactive Mathematics (⭐301) - Tools and libraries for building interactive mathematical explanations and explorations.
- AI for Mathematics (⭐78) - Research index covering AI-assisted mathematical reasoning, discovery, formal proof, and related datasets. Individual entries require independent review.