• 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 - 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.

• 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.

• 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.

• Mathematics Stack Exchange - Community questions and answers about mathematics problems and proofs.
• MathOverflow - Questions and answers for professional mathematicians.

• 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).

• 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.

• 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.

• 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.

• 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.

• 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.

• 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).

• 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.
• 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.

• Elementary Algebra 2e - Free one-semester textbook from OpenStax with web and PDF editions, worked examples, practice exercises, chapter reviews, and answer keys.

• 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.

• Fundamentals of Linear Algebra - James B. Carrell.
• Linear Algebra - Jim Hefferon.
• MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks - 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 - J.S. Milne.
• Notes on Finite Group Theory - Peter J. Cameron.
• Group Theory - Predrag Cvitanović.

• 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.

• 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.

• 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.

• 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.

• 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 - Otto Forster (LMU Munich).
• Analytic Number Theory - Andreas Strömbergsson (Uppsala University).

• 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: Lecture Notes - Christopher Griffin.
• Graph Theory - Reinhard Diestel.
• Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform - Hadjoudj Mohammed Islam.

• 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.

• 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.

• 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 - 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 - 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.

• 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.

• 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.

• 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.

• 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 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).

• 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.

• 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.

• 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.

• Chaos: Classical and Quantum - Maintained technical webbook on dynamical systems, periodic orbits, deterministic chaos, statistical mechanics, and quantum chaos.

• 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 - 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.

• 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.

• 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.

• 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).

• 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.

• 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.

• 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.

• 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.

• 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.

• 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 - 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 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.

• 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 - Jeffrey Chasnov.

• 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.

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 - Cross-system benchmark of formalized olympiad, high-school, and undergraduate problems for evaluating automated theorem provers.
• AlphaGeometry - 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 - Open thirteen-week course with notes, notebooks, exercises, and case studies on coding agents, machine learning, language models, reinforcement learning, and experimental mathematical research.

• 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 - 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 - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.

• 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.

• 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.

• 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.

• 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.

• 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.