Track Awesome Math Updates Daily

A curated list of awesome mathematics resources

🏠 Home · 🔍 Search · 🔥 Feed · 📮 Subscribe · ❤️ Sponsor · 😺 rossant/awesome-math · ⭐ 16K · 🏷️ Theory

[ Daily / Weekly / Overview ]

Aug 14, 2026

Foundations and Logic / Formal Mathematics and Theorem Proving

• 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.

• 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.

Combinatorics and Discrete Mathematics / Analytic Number Theory

• 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.

Geometry and Topology / Differential Geometry

• Differential Geometry - Rigorous undergraduate MIT OpenCourseWare course with lecture notes and problem sets centered on curves, surfaces, and curvature.

Differential Equations and Dynamical Systems / Partial Differential Equations

• 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 / Statistics

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

Numerical and Computational Mathematics / Numerical Analysis

• 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.

Mathematical Physics / Control Theory

• 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.

Interdisciplinary Mathematics / Mathematics for Machine Learning

• 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.

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.

• 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.

Aug 13, 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 (⭐3.8k) - Community-maintained mathematical library for Lean 4, with formalized theories, proof tactics, programming infrastructure, and generated documentation.

• Mathematics in Lean - Free textbook with examples and exercises for mathematicians learning Lean 4 and mathlib.

• Natural Number Game - Interactive Lean 4 game that introduces theorem proving through guided exercises about natural numbers.

• Isabelle - General-purpose interactive theorem prover with higher-order logic and set-theory environments for formalizing mathematics and computer science.

• 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.

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.

• 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.

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).

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.

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.

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.

Interdisciplinary Mathematics / Mathematics for Computer Science

• 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.

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

• 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.

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 06, 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.

Jan 23, 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.

Aug 27, 2025

Mathematical Practice / Mathematical Software and Tools

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

Aug 16, 2025

Combinatorics and Discrete Mathematics / Graph Theory

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

Jul 18, 2025

Algebra / Abstract Algebra

• Algebraic Methods - F. Oggier.

Number Theory / Algebraic Number Theory

• Introduction to Algebraic Number Theory - F. Oggier.

Dec 30, 2024

Algebra / Linear Algebra

• Linear Algebra Done Right - Sheldon Axler.

Nov 16, 2024

Community and Further Reading / Journals and Magazines

• Quanta Magazine - Features latest research breakthroughs in an accessible style for non-experts.

Nov 08, 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 11, 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 15, 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 11, 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.

Foundations and Logic / Logic

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

• Predictive Arithmetic - Edward Nelson.

• QED - an interactive textbook - Terence Tao.

Foundations and Logic / Type Theory

• Intuitionistic Type Theory - Per Martin-Lof.

• Type Theory and Functional Programming - Simon Thompson.

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

Algebra / Abstract Algebra

• Abstract Algebra: Harvard Extension Videos - Benedict Gross.

Algebra / Linear Algebra

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

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

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

• Linear Algebra Done Wrong - Sergei Treil.

• Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff.

Number Theory / Representation Theory

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

Combinatorics and Discrete Mathematics / Analytic Number Theory

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

Geometry and Topology / Graph Theory

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

Geometry and Topology / Differential Geometry

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

Geometry and Topology / Algebraic Geometry

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

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

Geometry and Topology / General Topology

• Elementary Applied Topology - Robert Ghrist (UPenn).

Analysis / Real Analysis

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

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

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

• Precalculus - Carl Stitz, Jeff Zeager.

Analysis / Complex Analysis

• Introduction to Complex Analysis - Michael Taylor.

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

• Complex Analysis - Juan Carlos Ponce Campuzano.

Analysis / Functional Analysis

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

Analysis / Harmonic Analysis

• 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).

Analysis / Measure Theory

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

• 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 / Probability

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

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

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).

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.

Probability and Statistics / Statistical Learning

• Statistical Learning Theory - Percy Liang.

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.

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.

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

Interdisciplinary Mathematics / Mathematics for Computer Science

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

Interdisciplinary Mathematics / Signal Processing

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

• Think DSP - Allen B. Downey.

Jul 05, 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.

Apr 29, 2023

Start Here / Video Courses and Series

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

Jan 25, 2023

Start Here / Video Courses and Series

• 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.

Jan 23, 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.

• MIT OpenCourseWare - MIT course recordings and video lectures, including full mathematics courses.

• Mathologer - Visual videos on recreational mathematics and selected advanced topics.

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

• 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 04, 2021

Start Here / Learning Platforms

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

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.

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 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 03, 2020

Start Here / Learning Platforms

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

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.

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.

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 30, 2017

Community and Further Reading / Blogs

• BetterExplained - Maintained by Kalid Azad.

Feb 11, 2017

Start Here / Reference Works

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

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.