Khan Academy
Free, self-paced lessons and exercises from arithmetic through calculus and beyond.
Free, self-paced lessons and exercises from arithmetic through calculus and beyond.
86
Awesome Math
A curated list of awesome mathematics resources
This page lists names, links and short descriptions. The original list on GitHub is the source and belongs to its authors.
Start Here >Learning Platforms
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.
Start Here >Proof and Problem Solving
Basic Concepts of Mathematics
Elias Zakon.
Book of Proof
Richard Hammack (Virginia Commonwealth University).
In 2 lists
How to Prove It: A Structured Approach (3rd Edition)
Paid textbook by Daniel J. Velleman.
Start Here >Video Courses and Series
Brandon Foltz
Video courses in statistics, probability, and quantitative methods with worked examples.
StatQuest
Introductory video explanations of statistics, probability, and machine learning.
3Blue1Brown
Visual explanations of core mathematics, including calculus, linear algebra, and differential equations.
NPTEL
University lecture courses from Indian institutes covering mathematics and related technical subjects.
Numberphile
Popular mathematics videos featuring mathematicians discussing problems, ideas, and curiosities.
PatrickJMT
Worked-example videos for algebra, calculus, and other introductory college topics.
Professor Leonard
Full lecture series in precalculus, calculus, and differential equations for college students.
Precalculus - College Algebra/Trigonometry
Full course playlist.
Calculus 1
Full course playlist.
Calculus 2
Full course playlist.
Calculus 3
Full course playlist.
Differential Equations
Full course playlist.
To The Point Math
Short reviews of common algebra and calculus topics.
MIT OpenCourseWare
MIT course recordings and video lectures, including full mathematics courses.
Mathologer
Visual videos on recreational mathematics and selected advanced topics.
The Math District
Free guides and videos covering prealgebra, algebra, geometry, trigonometry, statistics, calculus, and technical mathematics.
Start Here >Questions and Answers
Mathematics Stack Exchange
Community questions and answers about mathematics problems and proofs.
In 2 lists
MathOverflow
Questions and answers for professional mathematicians.
In 2 lists
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.
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).
In 2 lists
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.
In 2 lists
The Math Behind Artificial Intelligence
Tiago Capelo Monteiro (freeCodeCamp).
In 4 listsDetails
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.
General Mathematics
Paul's Online Math Notes
Free notes, examples, and practice problems for algebra, calculus, and differential equations, by Paul Dawkins at Lamar University.
In 2 lists
UBC CLP Calculus Textbooks
Free textbooks, problem books, and source files for a four-course university sequence in differential, integral, multivariable, and vector calculus.
In 2 lists
Foundations and Logic >Logic
Introduction to Logic
Michael Genesereth, Eric J. Kao (Stanford University).
An Introduction to Formal Logic
P.D. Magnus (University at Albany).
forall x: Calgary (An Introduction to Formal Logic)
P.D. Magnus and Tim Button, remixed by Aaron Thomas-Bolduc and Richard Zach (Open Logic Project).
In 3 lists
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.
In 2 lists
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.
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.
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.
In 2 lists
Homotopy Type Theory
Open textbook on homotopy type theory, univalent foundations, and higher-dimensional structures.
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
Community-maintained mathematical library for Lean 4, with formalized theories, proof tactics, programming infrastructure, and generated documentation.
Mathematics in Lean
Free textbook with examples and exercises for mathematicians learning Lean 4 and mathlib.
Theorem Proving in Lean 4
Free official textbook on dependent type theory, propositions, tactics, inductive types, type classes, and constructing verified proofs in Lean 4.
Natural Number Game
Interactive Lean 4 game that introduces theorem proving through guided exercises about natural numbers.
Isabelle
General-purpose interactive theorem prover with higher-order logic and set-theory environments for formalizing mathematics and computer science.
Archive of Formal Proofs
Refereed collection of Isabelle proof libraries, examples, and scientific developments maintained against current Isabelle releases.
Rocq Prover
Open-source interactive theorem prover and dependently typed programming language for mechanized mathematics and verified software.
Mathematical Components
Rocq libraries and tools for large-scale formalized mathematics, including substantial developments in algebra and analysis.
Metamath
Minimal formal language and proof verifier with explicit, inspectable proofs built from simple foundations.
Courses Using Lean
Maintained, filterable index of university courses that teach Lean or use it for mathematics, logic, programming, and formal verification.
Lean-related Conferences and Events
Maintained calendar and archive of conferences, workshops, and tutorials about Lean, mathlib, and formalized mathematics.
Algebra
Elementary Algebra 2e
Free one-semester textbook from OpenStax with web and PDF editions, worked examples, practice exercises, chapter reviews, and answer keys.
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).
Algebraic Methods
F. Oggier.
Abstract Algebra: Theory and Applications
Thomas W. Judson.
In 2 lists
Elements of Abstract and Linear Algebra
E.H. Connell (University of Miami).
In 2 lists
Abstract Algebra: Harvard Extension
Benedict Gross.
Abstract Algebra: Harvard Extension Videos
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.
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.
In 2 lists
Interactive Linear Algebra
Dan Margalit and Joseph Rabinoff.
Linear Algebra Done Right
Sheldon Axler.
In 2 lists
Algebra >Group Theory
Group Theory
J.S. Milne.
In 2 lists
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.
In 2 lists
Galois Theory
Miles Reid.
Galois Theory
Ian Stewart.
Galois Theory
Tom Leinster (University of Edinburgh).
Surreal Numbers and Games
Introductory notes on Conway's surreal numbers and their connection with combinatorial game theory.
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.
In 2 lists
Introduction to Representation Theory
Free MIT course by Pavel Etingof with lecture notes and problem sets on representations of groups and algebras, categories, and quivers.
Number Theory
Elementary Number Theory
W. Edwin Clark (University of South Florida).
A Course on Number Theory
Peter J. Cameron.
Yet Another Introductory Number Theory Textbook
Jonathan A. Poritz.
Number Theory >Algebraic Number Theory
Introduction to Algebraic Number Theory
F. Oggier.
Algebraic Number Theory
J.S. Milne.
In 2 lists
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
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.
In 2 lists
generatingfunctionology
Herbert Wilf.
In 2 lists
A=B
Marko Petkovšek, Herbert Wilf, and Doron Zeilberger on algorithms for proving hypergeometric identities.
Combinatorics and Discrete Mathematics >Graph Theory
Graph Theory: Lecture Notes
Christopher Griffin.
Graph Theory
Reinhard Diestel.
Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform
Hadjoudj Mohammed Islam.
Geometry and Topology
Fundamentals of Geometry
Free geometry text by Oleg A. Belyaev.
Euclid's Elements (David Joyce edition)
Complete web edition with diagrams, commentary, and references by David Joyce.
Euclid's Elements Redux
Open textbook by Daniel Callahan that presents Euclid with modern commentary and exercises.
Mathematical Illustrations
Bill Casselman's guide to creating clear mathematical diagrams and illustrations.
Byrne's Euclid
Interactive web edition of Oliver Byrne's color-coded presentation of Euclid's first six books.
Geometry and Topology >Differential Geometry
Introduction to Differential Geometry
Joel W. Robbin, Dietmar A. Salamon.
Notes on Differential Geometry and Lie Groups
Jean Gallier (University of Pennsylvania).
Topics in Differential Geometry
Peter W. Michor.
Lectures on Differential Geometry
Wulf Rossmann.
An Introduction to Riemannian Geometry
Sigmundur Gudmundsson (Lund University).
The Geometry and Topology of Three-Manifolds
W. Thurston.
Semi-Riemann Geometry and General Relativity
Shlomo Sternberg.
In 2 lists
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
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.
In 2 lists
Algebraic Geometry
Andreas Gathmann (RPTU).
The Stacks Project
Maintained by Aise Johan de Jong (Columbia).
Geometry and Topology >General Topology
General Topology
Stephen Willard.
Elementary Applied Topology
Robert Ghrist (UPenn).
Introduction to Topology
Free introductory notes associated with Renzo Cavalieri's Colorado State University topology course and compiled by students. Covers point-set topology, compactness, connectedness, surfaces, Euler characteristic, and the fundamental group.
Introduction to Topology
Alex Küronya.
General Topology
Pierre Schapira (Sorbonne University).
Elementary Topology Problem Textbook
Oleg Viro.
General Topology
Jesper M. Møller.
Geometry and Topology >Algebraic Topology
Algebraic Topology
Allen Hatcher.
In 2 lists
A Concise Course in Algebraic Topology
J. P. May.
Introduction to Algebraic Topology
Martin Cadek.
Algebra and Topology
Pierre Schapira (Sorbonne University).
Lecture Notes in Algebraic Topology
Paid textbook by James F. Davis and Paul Kirk.
Analysis >Real Analysis
Calculus Open Textbook
Gilbert Strang (MIT OpenCourseWare).
Elementary Calculus: An Approach Using Infinitesimals
Professor H. Jerome Keisler.
An Introduction to Real Analysis
John K. Hunter (University of California at Davis).
Introduction to Real Analysis
William F. Trench (Trinity University, Texas).
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.
In 2 lists
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.
Calculus Made Easy
Silvanus P. Thompson (1910).
Precalculus
Carl Stitz, Jeff Zeager.
Analysis >Complex Analysis
Introduction to Complex Analysis
Michael Taylor.
An Introduction to Complex Analysis and Geometry
Paid textbook by John P. D'Angelo.
A First Course in Complex Analysis
Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka.
A Guide to Complex Variables
Paid textbook by Steven G. Krantz.
Complex Analysis
Charles Walkden.
Complex Analysis
Christian Berg.
Complex Variables
R. B. Ash, W.P. Novinger.
Complex Analysis
Christer Bennewitz.
Complex Analysis
Donald E. Marshall.
A Concise Course in Complex Analysis and Riemann Surfaces
Wilhelm Schlag.
Complex Analysis
G. Cain (Georgia Tech).
Complex Analysis
Juan Carlos Ponce Campuzano.
Analysis >Functional Analysis
An Introduction to Functional Analysis
Laurent W. Marcoux (University of Waterloo).
Functional Analysis: Lecture Notes
Jeff Schenker (Michigan State University).
Functional Analysis
Alexander C. R. Belton.
Functional Analysis
Christian Remling.
Theory of Functions of a Real Variable
Shlomo Sternberg.
In 2 lists
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).
Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications
Julius O. Smith III (Stanford University).
In 2 lists
Analysis >Measure Theory
An Introduction to Measure Theory
Terence Tao (UCLA).
Lecture Notes in Measure Theory
Christer Borell.
Measure Theory
John K. Hunter (University of California at Davis).
Measure and Integration
Dietmar A. Salamon (ETH Zürich).
Lecture Notes: Measure Theory
Bruce K. Driver.
Differential Equations and Dynamical Systems >Ordinary Differential Equations
Ordinary Differential Equation
Alexander Grigorian (University of Bielefeld).
Ordinary Differential Equations: Lecture Notes
Eugen J. Ionascu.
Differential Equations
Gabriel Nagy.
Ordinary Differential Equations and Dynamical Systems
Gerald Teschl.
Elementary Differential Equations
William F. Trench.
Elementary Differential Equations With Boundary Value Problems
William F. Trench.
In 2 lists
In 2 lists
Differential Equations and Dynamical Systems >Partial Differential Equations
Notes on Partial Differential Equations
John K. Hunter (University of California at Davis).
Linear Methods of Applied Mathematics
Evans M. Harrell II, James V. Herod (Georgia Tech).
Partial Differential Equations
Lawrence C. Evans's concise survey of modern PDE theory from analytical, qualitative, and computational viewpoints.
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.
In 2 lists
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.
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).
In 2 lists
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.
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.
Statistical Thinking for the 21st Century
Russell A. Poldrack.
Odds and Ends: Introducing Probability & Decision with a Visual Emphasis
Jonathan Weisberg.
In 2 lists
Seeing Theory
Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang.
In 3 lists
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.
In 2 lists
Probability and Statistics >Statistical Learning
An Introduction to Statistical Learning
Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani.
In 3 lists
The Elements of Statistical Learning
Trevor Hastie, Robert Tibshirani, Jerome Friedman.
Statistical Learning Theory
Percy Liang.
In 3 lists
Reinforcement Learning: An Introduction
Richard S. Sutton, Andrew G. Barto (2nd edition).
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.
Algebraic Statistics for Computational Biology
Paid textbook edited by Lior Pachter and Bernd Sturmfels.
Numerical and Computational Mathematics >Numerical Analysis
Introduction to Numerical Analysis
Undergraduate notes by Doron Levy on root finding, interpolation, approximation, numerical differentiation, and quadrature.
Numerical Analysis (Second Edition)
Free second-edition textbook by L. Ridgway Scott on the theory and practice of numerical methods.
Lectures in Basic Computational Numerical Analysis
Archived University of Kentucky textbook by J. M. McDonough, focused on computational methods for differential equations.
Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods
Specialized notes by Alfred Schmidt and Arsen Narimanyan on adaptive finite element methods.
Numerical Analysis for Engineers
University of Waterloo course with lectures, assignments, projects, and MATLAB material on numerical methods for engineers.
Advanced Linear Algebra: Foundations to Frontiers
Online text by Robert van de Geijn and Margaret Myers on algorithms for advanced numerical linear algebra.
Fundamentals of Numerical Computation
Online textbook by Tobin Driscoll and Richard Braun with Julia, MATLAB, and Python editions covering core numerical methods for linear systems, approximation, root finding, ODEs, and PDEs.
Optimization, Operations Research, and Control
Convex Optimization
A free textbook with slides, exercises, code, and course material by Stephen Boyd and Lieven Vandenberghe.
Nonlinear Optimization
Free graduate MIT course covering analytical and computational methods for unconstrained and constrained optimization.
CVXPY
Open-source Python modeling language for convex, geometric, quasiconvex, and related optimization problems.
In 2 lists
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
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.
In 2 lists
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.
In 3 lists
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.
In 2 lists
Interdisciplinary Mathematics >Signal Processing
Introduction to Signal Processing
Sophocles J. Orfanidis (Rutgers University).
Foundations of Signal Processing
Martin Vetterli, Jelena Kovacevic, Vivek K Goyal.
An Introduction to Statistical Signal Processing
Robert M. Gray, Lee D. Davisson.
Think DSP
Allen B. Downey.
Mathematical Practice >AI for Mathematics
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.
In 2 lists
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.
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.
In 2 lists
Wolfram Alpha
Computational knowledge engine for evaluating expressions, plotting functions, and answering structured queries. Some advanced features require a paid plan.
In 7 listsDetails
Maxima
Free computer algebra system for symbolic and numerical calculations, plotting, and scripting.
In 2 lists
SymPy
Python library for symbolic algebra, calculus, equation solving, matrices, and code generation.
In 2 lists
SageMath
Free mathematics software combining computer algebra, numerical computation, geometry, statistics, and visualization through Python.
In 2 lists
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.
In 2 lists
Wolfram Mathematica
Paid technical-computing system for symbolic and numerical mathematics, visualization, programming, and data analysis.
In 5 listsDetails
Free Math
Free, open-source software for recording, organizing, and reviewing digital mathematics homework without solving the problems automatically.
History and Mathematics Education
MacTutor History of Mathematics Archive
University of St Andrews archive of mathematician biographies, histories of mathematical topics, timelines, institutions, and related reference material.
NRICH
Free curriculum-linked problems, investigations, articles, and teacher guidance from the University of Cambridge for learners aged 3 to 18.
Community and Further Reading >Journals and Magazines
Quanta Magazine
Features latest research breakthroughs in an accessible style for non-experts.
Bulletin of the American Mathematical Society
Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.
Notices of the American Mathematical Society
Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.
European Mathematical Society Magazine
The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.
Mathematics Today by Institute of Mathematics and its Applications
News, opinions, and articles related to mathematics, so the reader stays updated.
Crux Mathematicorum by Canadian Mathematical Society
Challenging problems for secondary and undergraduate students, including an Olympiad Corner.
Chalkdust Magazine
Independent magazine for mathematically curious readers, with free expository articles, interviews, puzzles, and downloadable issues.
Community and Further Reading >Blogs
BetterExplained
Maintained by Kalid Azad.
In 4 lists
ILoveMaths
Mathematics lessons and activities for Indian classes 6 to 12.
3Blue1Brown
Animated explanations of mathematics by Grant Sanderson.
In 4 lists
Math Is Fun
Lightweight lessons and reference pages for school mathematics.
In 2 lists
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.
Related lists in Theory
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A curated list of Artificial Intelligence (AI) courses, books, video lectures and papers.
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Papers We Love
papers-we-love/papers-we-love
Papers from the computer science community to read and discuss.
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Awesome talks
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Awesome online talks and screencasts
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Awesome Audit Algorithms
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A curated list of algorithms and papers for auditing black-box algorithms.
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Awesome VLM Architectures
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Curated visual catalog of 155+ vision-language model (VLM/MLLM) architectures: papers, diagrams, training recipes, datasets, and a release timeline for multimodal AI…