awesome-math

Awesome Math

Awesome Math is a curated list of high-quality resources for learning, teaching, and doing mathematics. It covers pure mathematics, applied mathematics, computation, formal proof, and the use of AI in mathematics.

Most resources are free to access. Paid resources may be included when they are widely respected, unusually useful, and hard to replace. Access limits should be stated in the entry.

Read the contribution guidelines before suggesting a resource.

Contents

• Start Here
  • Learning Platforms
  • Proof and Problem Solving
  • Video Courses and Series
  • Questions and Answers
  • Reference Works
  • Broad Course Notes
• General Mathematics
• Foundations and Logic
  • Logic
  • Set Theory
  • Type Theory
  • Category Theory
  • Formal Mathematics and Theorem Proving
• Algebra
  • Abstract Algebra
  • Linear Algebra
  • Group Theory
  • Ring and Field Theory
  • Commutative Algebra
  • Representation Theory
• Number Theory
  • Algebraic Number Theory
  • Analytic Number Theory
• Combinatorics and Discrete Mathematics
  • Graph Theory
• Geometry and Topology
  • Differential Geometry
  • Algebraic Geometry
  • General Topology
  • Algebraic Topology
• Analysis
  • Real Analysis
  • Complex Analysis
  • Functional Analysis
  • Operator Theory
  • Harmonic Analysis
  • Measure Theory
• Differential Equations and Dynamical Systems
  • Ordinary Differential Equations
  • Partial Differential Equations
  • Ergodic Theory and Chaos
• Probability and Statistics
  • Probability
  • Stochastic Processes
  • Statistics
  • Statistical Learning
  • Algebraic Statistics
• Numerical and Computational Mathematics
  • Numerical Analysis
• Optimization, Operations Research, and Control
  • Control Theory
• Mathematical Physics
• Interdisciplinary Mathematics
  • Mathematics for Computer Science
  • Mathematics for Machine Learning
  • Information and Coding Theory
  • Mathematical Finance
  • Mathematical Biology
  • Signal Processing
• Mathematical Practice
  • AI for Mathematics
  • Mathematical Software and Tools
• History and Mathematics Education
• Community and Further Reading
  • Journals and Magazines
  • Blogs
  • Meetings and Conferences
  • Related Curated Lists

Start Here

Learning Platforms

• Khan Academy - Free, self-paced lessons and exercises from arithmetic through calculus and beyond.
• Coursera - University and industry mathematics courses, with access and payment varying by course.
• MIT OpenCourseWare - Free MIT course materials, including notes, assignments, and exams for undergraduate and graduate mathematics.
• edX - University and professional mathematics courses, with audit and paid options varying by course.
• Brilliant - Interactive, problem-based lessons in foundational mathematics, probability, and related quantitative subjects.
• WooTube - Video lessons by Eddie Woo covering secondary-school mathematics with an emphasis on conceptual understanding.
• Mathispower4u - More than 9,000 free, closed-captioned video lessons and worked examples organized from middle-school mathematics through calculus, linear algebra, differential equations, and statistics, by James Sousa.
• Mathigon - Interactive courses, activities, and visual explanations for school and early university mathematics.
• Ximera - Free interactive mathematics textbooks from Ohio State University.
• Almost Fun - Free interactive middle- and high-school mathematics lessons, practice problems, and teacher resources from a nonprofit organization.
• Oxford Mathematics - Lectures and public talks from the University of Oxford, including accessible explanations of advanced topics.
• Math Academy - Paid adaptive platform with diagnostic assessment and mastery-based courses from fourth-grade mathematics through university topics.
• OSSU Math - Free, prerequisite-ordered self-study curriculum modeled on the mathematics requirements of an undergraduate degree.
• Waterloo Open Math - Free university-level courseware with lessons, exercises, and immediate feedback from the University of Waterloo.

Proof and Problem Solving

• Basic Concepts of Mathematics - Elias Zakon.
• Book of Proof - Richard Hammack (Virginia Commonwealth University).
• How to Prove It: A Structured Approach (3rd Edition) - Paid textbook by Daniel J. Velleman.

Video Courses and Series

• Brandon Foltz - Video courses in statistics, probability, and quantitative methods with worked examples.
• StatQuest - Introductory video explanations of statistics, probability, and machine learning.
• 3Blue1Brown - Visual explanations of core mathematics, including calculus, linear algebra, and differential equations.
• NPTEL - University lecture courses from Indian institutes covering mathematics and related technical subjects.
• Numberphile - Popular mathematics videos featuring mathematicians discussing problems, ideas, and curiosities.
• PatrickJMT - Worked-example videos for algebra, calculus, and other introductory college topics.
• Professor Leonard - Full lecture series in precalculus, calculus, and differential equations for college students.
  • Precalculus - College Algebra/Trigonometry - Full course playlist.
  • Calculus 1 - Full course playlist.
  • Calculus 2 - Full course playlist.
  • Calculus 3 - Full course playlist.
  • Differential Equations - Full course playlist.
  • To The Point Math - Short reviews of common algebra and calculus topics.
• MIT OpenCourseWare - MIT course recordings and video lectures, including full mathematics courses.
• Mathologer - Visual videos on recreational mathematics and selected advanced topics.
• The Math District - Free guides and videos covering prealgebra, algebra, geometry, trigonometry, statistics, calculus, and technical mathematics.

Questions and Answers

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

Reference Works

• Mathematics Subject Classification 2020 - The standard subject taxonomy maintained by Mathematical Reviews and zbMATH.

• Encyclopedia of Mathematics - Reference articles on mathematical concepts, theorems, biographies, and applications.

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

• nLab - Collaborative research-level notes and expositions in category theory, homotopy theory, mathematical physics, and related areas.

• Wolfram Mathworld - Reference articles on mathematical definitions, formulas, identities, and related concepts.

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

• AIM Open Textbook Initiative - Open mathematics textbooks organized by course and evaluated by the American Institute of Mathematics editorial board.

• AMS Open Math Notes - Free course notes, textbooks, and research expositions hosted by the American Mathematical Society.

• OpenStax Mathematics - Peer-reviewed, openly licensed textbooks for school and introductory college mathematics from Rice University.

• The Princeton Companion to Mathematics - Paid reference edited by Timothy Gowers, June Barrow-Green, and Imre Leader.

• Encyclopedia of Distances (4th Edition) - Paid reference by Michel Marie Deza and Elena Deza.

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

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

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

• Online Mathematics Textbooks - Index of freely available mathematics textbooks maintai