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Aug 14, 2026

Start Here / Learning Platforms

• MIT OpenCourseWare - Free MIT course materials, including notes, assignments, and exams for undergraduate and graduate mathematics.

• 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.

• 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.

Start Here / Proof and Problem Solving

• Basic Concepts of Mathematics - Elias Zakon.

• How to Prove It: A Structured Approach (3rd Edition) - Paid textbook by Daniel J. Velleman.

Start Here / Video Courses and Series

• The Math District - Free guides and videos covering prealgebra, algebra, geometry, trigonometry, statistics, calculus, and technical mathematics.

Start Here / Questions and Answers

• Mathematics Stack Exchange - Community questions and answers about mathematics problems and proofs.

• MathOverflow - Questions and answers for professional mathematicians.

Start Here / 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.

• 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.

• 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.

• Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania).

• Multivariable Calculus - G. Cain, J. Herod (Georgia Tech).

• Online Mathematics Textbooks - Index of freely available mathematics textbooks maintained at Georgia Tech.

• Trigonometry - Michael Corral.

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.

Foundations and Logic / Logic

• Introduction to Logic - Michael Genesereth, Eric J. Kao (Stanford University).

• 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.

• 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.

• Open Logic Textbook - collaborative effort, main contributors listed here.

Foundations and Logic / 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.

Foundations and Logic / Type Theory

• Proofs and Types - Jean-Yves Girard.

• Programming in Martin-Lof’s Type Theory - Bengt Nordstrom, Kent Petersson, Jan M. Smith.

Foundations and Logic / 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).

Foundations and Logic / 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 / 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.

Algebra / 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).

• 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.

Algebra / Linear Algebra

• Fundamentals of Linear Algebra - James B. Carrell.

• Linear Algebra - Jim Hefferon.

• A First Course in Linear Algebra - Robert A. Beezer.

• 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.

• Immersive Linear Algebra - J. Ström, K. Åström, and T. Akenine-Möller.

Algebra / Group Theory

• Group Theory - J.S. Milne.

• Notes on Finite Group Theory - Peter J. Cameron.

• Group Theory - Predrag Cvitanović.

Algebra / 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.

• 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.

Algebra / 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.

Algebra / 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 / Representation 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 / Algebraic Number Theory

• Algebraic Number Theory - J.S. Milne.

• Algebraic Number Theory Course Notes - Matthew Baker (Georgia Tech).

Number Theory / Analytic Number Theory

• Analytic Number Theory - Otto Forster (LMU Munich).

• Analytic Number Theory - Andreas Strömbergsson (Uppsala University).

Combinatorics and Discrete Mathematics / Analytic Number Theory

• 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.

Combinatorics and Discrete Mathematics / Graph Theory

• Graph Theory: Lecture Notes - Christopher Griffin.

• Graph Theory - Reinhard Diestel.

Geometry and Topology / Graph Theory

• 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.

Geometry and Topology / Differential Geometry

• 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.

Geometry and Topology / Algebraic Geometry

• 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).

Geometry and Topology / 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 - Pierre Schapira (Sorbonne University).

• Elementary Topology Problem Textbook - Oleg Viro.

• General Topology - Jesper M. Møller.

Geometry and Topology / 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.

• 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.

• Active Calculus - Matt Boelkins.

• Calculus Made Easy - Silvanus P. Thompson (1910).

Analysis / Complex Analysis

• 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.

• Complex Analysis - G. Cain (Georgia Tech).

Analysis / Functional Analysis

• 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.

Analysis / 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.

Analysis / Harmonic Analysis

• Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana-Champaign).

Analysis / Measure Theory

• Lecture Notes in Measure Theory - Christer Borell.

• A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng.

• Lecture Notes: Measure Theory - Bruce K. Driver.

Differential Equations and Dynamical Systems / Ordinary Differential Equations

• 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.

Differential Equations and Dynamical Systems / Partial Differential Equations

• 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.

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.

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).

• The Only Probability Cheatsheet You'll Ever Need - William Chen.

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

Probability and Statistics / 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).

• 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.

Probability and Statistics / 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.

• OpenIntro Statistics - Free introductory textbook for college courses and self-study, with datasets, labs, slides, videos, exercises, and accessible PDFs.

Probability and Statistics / 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.

• Reinforcement Learning: An Introduction - Richard S. Sutton, Andrew G. Barto (2nd edition).

Probability and Statistics / Algebraic Statistics

• 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.

• 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 / Numerical Analysis

• 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.

Optimization, Operations Research, and Control / 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 / Control Theory

• 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.

Interdisciplinary Mathematics / 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.

Interdisciplinary Mathematics / 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.

Interdisciplinary Mathematics / 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.

Interdisciplinary Mathematics / Mathematical Biology

• Mathematical Biology - Jeffrey Chasnov.

Interdisciplinary Mathematics / Signal Processing

• Introduction to Signal Processing - Sophocles J. Orfanidis (Rutgers University).

• Foundations of Signal Processing - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal.

Mathematical Practice / AI for Mathematics

• 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 Practice / Mathematical Software and Tools

• Wolfram Alpha - Computational knowledge engine for evaluating expressions, plotting functions, and answering structured queries. Some advanced features require a paid plan.

• 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.

• Macaulay2 - Research system for algebraic geometry and commutative algebra with specialized computational packages.

• 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.

• MATLAB - Paid numerical computing environment by MathWorks.

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.

• 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

• 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.

• Chalkdust Magazine - Independent magazine for mathematically curious readers, with free expository articles, interviews, puzzles, and downloadable issues.

Community and Further Reading / Blogs

• 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.

Community and Further Reading / Related Curated Lists

• 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.

May 19, 2026

Foundations and Logic / Logic

• 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).

Apr 07, 2026

Geometry and Topology / General Topology

• General Topology - Stephen Willard.

Mar 02, 2026

Start Here / Video Courses and Series

• Numberphile - Popular mathematics videos featuring mathematicians discussing problems, ideas, and curiosities.

Feb 08, 2026

Start Here / Reference Works

• The Math Behind Artificial Intelligence - Tiago Capelo Monteiro (freeCodeCamp).

Nov 27, 2025

Mathematical Practice / Mathematical Software and Tools

• RunMat (⭐247) - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.

Nov 24, 2025

Combinatorics and Discrete Mathematics / Graph Theory

• Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform - Hadjoudj Mohammed Islam.

Mathematical Practice / Mathematical Software and Tools

• MathFlow (⭐56) - C# math expression library with symbolic computation (differentiation, simplification, equation solving).

Jul 18, 2025

Algebra / Abstract Algebra

• Algebraic Methods - F. Oggier.

Number Theory / Algebraic Number Theory

• Introduction to Algebraic Number Theory - F. Oggier.

Jan 22, 2025

Algebra / Linear Algebra

• Linear Algebra Done Right - Sheldon Axler.

Nov 12, 2024

Start Here / Proof and Problem Solving

• Book of Proof - Richard Hammack (Virginia Commonwealth University).

Geometry and Topology / Differential Geometry

• Notes on Differential Geometry and Lie Groups - Jean Gallier (University of Pennsylvania).

Sep 19, 2024

Start Here / Learning Platforms

• Math Academy - Paid adaptive platform with diagnostic assessment and mastery-based courses from fourth-grade mathematics through university topics.

Sep 15, 2024

Community and Further Reading / 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.

Aug 16, 2024

Algebra / Ring and Field Theory

• Galois Theory - Ian Stewart.

• Galois Theory - Tom Leinster (University of Edinburgh).

Mar 29, 2024

Numerical and Computational Mathematics / Numerical Analysis

• Advanced Linear Algebra: Foundations to Frontiers - Online text by Robert van de Geijn and Margaret Myers on algorithms for advanced numerical linear algebra.

Mar 12, 2024

Start Here / Reference Works

• 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.

Mar 02, 2024

Analysis / Functional Analysis

• An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo).

Feb 28, 2024

Numerical and Computational Mathematics / Numerical Analysis

• 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.

Aug 10, 2023

Number Theory / Representation Theory

• Yet Another Introductory Number Theory Textbook - Jonathan A. Poritz.

Jul 21, 2023

Probability and Statistics / 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.

Jul 06, 2023

Start Here / Reference Works

• The On-Line Encyclopedia of Integer Sequences - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.

May 26, 2023

Start Here / Video Courses and Series

• StatQuest - Introductory video explanations of statistics, probability, and machine learning.

Jan 26, 2023

Start Here / Video Courses and Series

• Brandon Foltz - Video courses in statistics, probability, and quantitative methods with worked examples.

• 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.

• 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.

Nov 16, 2022

Analysis / Measure Theory

• An Introduction to Measure Theory - Terence Tao (UCLA).

May 18, 2022

Numerical and Computational Mathematics / Numerical Analysis

• Numerical Analysis for Engineers - University of Waterloo course with lectures, assignments, projects, and MATLAB material on numerical methods for engineers.

Apr 19, 2022

Start Here / Learning Platforms

• Oxford Mathematics - Lectures and public talks from the University of Oxford, including accessible explanations of advanced topics.

Mar 16, 2022

Community and Further Reading / Related Curated Lists

• Theoretical Computer Science (⭐1.2k) - Curated resources on computation, complexity, logic, algorithms, cryptography, and related mathematics.

Feb 18, 2022

Community and Further Reading / 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.

Jan 27, 2022

Start Here / Learning Platforms

• Almost Fun - Free interactive middle- and high-school mathematics lessons, practice problems, and teacher resources from a nonprofit organization.

Aug 19, 2021

Geometry and Topology / Algebraic Geometry

• A Brief Introduction to Algebraic Geometry - R.C. Churchill.

Aug 04, 2021

Start Here / Learning Platforms

• Ximera - Free interactive mathematics textbooks from Ohio State University.

Jun 04, 2021

Analysis / Complex Analysis

• A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag.

Apr 09, 2021

Mathematical Practice / Mathematical Software and Tools

• Maxima - Free computer algebra system for symbolic and numerical calculations, plotting, and scripting.

Apr 08, 2021

Mathematical Practice / Mathematical Software and Tools

• Free Math - Free, open-source software for recording, organizing, and reviewing digital mathematics homework without solving the problems automatically.

Mar 05, 2021

Analysis / Complex Analysis

• Introduction to Complex Analysis - Michael Taylor.

Jan 08, 2021

Start Here / 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.

Oct 03, 2020

Analysis / Real Analysis

• Precalculus - Carl Stitz, Jeff Zeager.

Analysis / Harmonic Analysis

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

Oct 01, 2020

Mathematical Practice / Mathematical Software and Tools

• GeoGebra - Interactive mathematics suite for geometry, graphing, algebra, spreadsheets, statistics, and calculus.

• Singular - Computer algebra system for polynomial computations in commutative algebra, algebraic geometry, and singularity theory.

• Maple - Paid computer algebra and numerical mathematics system for symbolic computation, visualization, and programming.

• Wolfram Mathematica - Paid technical-computing system for symbolic and numerical mathematics, visualization, programming, and data analysis.

Aug 06, 2020

Foundations and Logic / Logic

• QED - an interactive textbook - Terence Tao.

Aug 03, 2020

Start Here / Learning Platforms

• Mathigon - Interactive courses, activities, and visual explanations for school and early university mathematics.

Algebra / Linear Algebra

• Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff.

Geometry and Topology / Graph Theory

• Byrne's Euclid - Interactive web edition of Oliver Byrne's color-coded presentation of Euclid's first six books.

Analysis / Complex Analysis

• Complex Analysis - Juan Carlos Ponce Campuzano.

Probability and Statistics / Probability

• Foundations of Constructive Probability Theory - Yuen-Kwok Chan.

Probability and Statistics / Statistics

• 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.

Optimization, Operations Research, and Control / Numerical Analysis

• Convex Optimization - A free textbook with slides, exercises, code, and course material by Stephen Boyd and Lieven Vandenberghe.

Interdisciplinary Mathematics / Mathematics for Computer Science

• The Chaos Textbook: Mathematics in the age of the computer - Glenn Elert.

Jul 02, 2020

Interdisciplinary Mathematics / Signal Processing

• Think DSP - Allen B. Downey.

Oct 15, 2019

Foundations and Logic / Type Theory

• Type Theory and Functional Programming - Simon Thompson.

Oct 14, 2019

Foundations and Logic / Type Theory

• Intuitionistic Type Theory - Per Martin-Lof.

Apr 09, 2019

Algebra / Abstract Algebra

• Abstract Algebra: Harvard Extension Videos - Benedict Gross.

Algebra / Linear Algebra

• Linear Algebra Done Wrong - Sergei Treil.

Analysis / Real Analysis

• Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis" - George M. Bergman.

Apr 02, 2019

Start Here / Learning Platforms

• 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.

Nov 30, 2018

Geometry and Topology / General Topology

• Elementary Applied Topology - Robert Ghrist (UPenn).

Nov 19, 2018

Geometry and Topology / Algebraic Geometry

• The Stacks Project - Maintained by Aise Johan de Jong (Columbia).

Jul 08, 2018

Mathematical Practice / 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.

Jun 07, 2018

Algebra / Linear Algebra

• Introduction to Applied Linear Algebra - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA).

Mar 04, 2018

Foundations and Logic / Logic

• Predictive Arithmetic - Edward Nelson.

Algebra / Linear Algebra

• Linear Algebra - David Cherney, Tom Denton, Andrew Waldron.

Analysis / Real Analysis

• Calculus and Linear Algebra. Vol. 2 - Wilfred Kaplan, Donald J. Lewis.

Feb 11, 2018

Combinatorics and Discrete Mathematics / Analytic Number Theory

• A=B - Marko Petkovšek, Herbert Wilf, and Doron Zeilberger on algorithms for proving hypergeometric identities.

Nov 17, 2017

Probability and Statistics / Stochastic Processes

• Introduction to Stochastic Processes - Lecture Notes - Gordan Žitković (University of Texas).

• Applied Stochastic Processes in science and engineering - Matt Scott (University of Waterloo).

Interdisciplinary Mathematics / Signal Processing

• An Introduction to Statistical Signal Processing - Robert M. Gray, Lee D. Davisson.

Jun 30, 2017

Community and Further Reading / Blogs

• BetterExplained - Maintained by Kalid Azad.

May 23, 2017

Foundations and Logic / Logic

• An Introduction to Formal Logic - P.D. Magnus (University at Albany).

Apr 18, 2017

Probability and Statistics / Probability

• Probability and Statistics Cookbook (⭐2.3k) - Matthias Vallentin (UC Berkeley).

Feb 11, 2017

Start Here / Reference Works

• ProofWiki - Collaborative repository of mathematical definitions, lemmas, and proofs.

Sep 15, 2016

Algebra / Linear Algebra

• MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks (⭐585) - Juan Klopper.

Sep 02, 2015

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.

• edX - University and professional mathematics courses, with audit and paid options varying by course.

Start Here / Reference Works

• Wikibooks - Community-authored collection of open mathematics textbooks and instructional books.

Foundations and Logic / Type Theory

• Homotopy Type Theory - Open textbook on homotopy type theory, univalent foundations, and higher-dimensional structures.

Geometry and Topology / Differential Geometry

• Introduction to Differential Geometry - Joel W. Robbin, Dietmar A. Salamon.

Aug 31, 2015

Analysis / Real Analysis

• An Introduction to Real Analysis - John K. Hunter (University of California at Davis).

Analysis / Harmonic Analysis

• Lecture Notes: Fourier Transform and its Applications - Brad Osgood.

Analysis / Measure Theory

• Measure Theory - John K. Hunter (University of California at Davis).

• Measure and Integration - Dietmar A. Salamon (ETH Zürich).

Differential Equations and Dynamical Systems / Ordinary Differential Equations

• Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld).

Differential Equations and Dynamical Systems / Partial Differential Equations

• Notes on Partial Differential Equations - John K. Hunter (University of California at Davis).

Probability and Statistics / Statistical Learning

• Statistical Learning Theory - Percy Liang.