Awesome Math

A curated list of awesome mathematics resources.

All resources are freely available except those with a 💲 icon.

Contents

• Contents
• General Resources
  • Learning Platforms
  • Learn to Learn
  • Youtube Series
  • Tools
  • Questions and Answers
  • Encyclopedia
  • Books
  • Magazines
  • Blogs
  • Meetings and Conferences
  • Misc
• Branches of Mathematics
  • Foundations of Mathematics
    • Transition To Pure Rigour Math
    • Set Theory
    • Logic
    • Category Theory
    • Type Theory
    • Homotopy Type Theory
    • Surreal Numbers
  • Number Theory
    • Algebraic Number Theory
    • Analytic Number Theory
  • Algebra
    • Abstract Algebra
    • Group Theory
    • Linear Algebra
    • Ring Theory
    • Galois Theory
    • Lie Algebras
  • Combinatorics
    • Graph Theory
  • Geometry and Topology
    • Differential Geometry
    • Algebraic Geometry
    • Algebraic Statistics
    • Topology
    • Algebraic Topology
  • Analysis
    • Real Analysis
    • Harmonic Analysis
    • Complex Analysis
    • Functional Analysis
    • Measure Theory
    • Ordinary Differential Equations
    • Partial Differential Equations
    • Chaos Theory
  • Probability and Statistics
    • Probability Theory
    • Statistics
    • Statistical Learning
    • Stochastic processes
  • Numerical Analysis
  • Signal processing
  • Mathematics for Computer Science
  • Mathematical Biology
  • Mathematical Physics
• Students Lecture Notes
• Related Awesome Lists
• License

General Resources

Learning Platforms

• Khan Academy
• Coursera
• MIT OpenCourseWare
• edX
• Brilliant
• WooTube
• Mathigon
• Calculus.org
• Ximera : free interactive mathematics textbooks (Ohio State University)
• Almost Fun
• Oxford Mathematics
• Math Academy
• Derivative Calculus Solver — A step-by-step differentiation tool focusing on the chain rule and substitution logic.

Learn to Learn

• Understanding Mathematics

Youtube Series

• Brandon Foltz
• StatQuest
• 3Blue1Brown
• NPTEL
• Numberphile
• PatrickJMT
• Professor Leonard
• Precalculus - College Algebra/Trigonometry
• Calculus 1
• Calculus 2
• Calculus 3
• Differential Equations
• To The Point Math
• Crash Course
• Harvard
• MIT OpenCourseWare
• Mathologer
• The Math District
• Mathematical Monk
• The Math Sorcerer

Tools

• Symbolab
• Desmos
• Math Words
• Wolfram Alpha
• Maxima
• Sympy
• Sagemath
• MathFlow - C# math expression library with symbolic computation (differentiation, simplification, equation solving)
• Unit Converter
• GeoGebra
• Macaulay2
• Singular
• GNU Octave
• Magma
• Maple
• Matlab
• Wolfram Mathematica
• Free Math
• xhub
• CopyPasteMathjax
• Finance calculators
• Mathcheap
• Midpoint Calculator
• Quartiles Calculator
• Corca Editor
• RunMat - Runtime for MATLAB-syntax array math with automatic CPU/GPU execution.
• Structural Engineering Tools (SEPCO Engineering) - Free online calculators for beam diagrams, Canadian steel section properties, and pressure conversions.

Questions and Answers

• Mathematics Stack Exchange
• MathOverflow - for professional mathematicians

Encyclopedia

• Encyclopedia of Mathematics
• Planetmath
• ProofWiki
• Wolfram Mathworld
• The On-Line Encyclopedia of Integer Sequences - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.
• 💲 The Princeton Companion to Mathematics - Timothy Gowers (Professor, Fields medallist), June Barrow-Green (Professor), and Imre Leader (Professor).
• 💲 Encyclopedia of Distances (4th Edition) - Michel Marie Deza, Elena Deza.

Books

• Calculus: Basic Concepts for High Schools - L.V. Tarasov
• Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)
• Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)
• Wikibooks
• Online Mathematics Textbooks
• Beginning and Intermediate Algebra
• Free Mathematics Books
• Trigonometry
• Math for Frontend Web Dev
• Grokking Statistics
• The Math Behind Artificial Intelligence - Tiago Capelo Monteiro (freeCodeCamp)

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 - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions.

Blogs

• BetterExplained - Maintained by Kalid Azad
• ILoveMaths - For grades 6 thru 12 in K-12 system
• 3blue1brown - Animated Maths
• Mathsisfun simple text lightweight site for students up to highschool
• MathematicsIsAScience - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)

Meetings and Conferences

• MathsJam - monthly local recreational maths/puzzle meetups and an annual gathering in Staffordshire, England
• Talking Maths in Public - a conference for maths communicators, running every two years, usually in the UK
• Bridges - an annual conference on mathematical connections in art, music, architecture, and culture. The 2025 meeting is in Eindhoven, Netherlands.

Misc

• Areas of mathematics on Wikipedia
• Paul's Online Math Notes - Paul Dawkins (Lamar University)
• List of electronic textbooks - Marcel B. Finan (Arkansas Tech University)
• Topology Atlas
• Recreations in Math - H. E. Licks (1917)
• Magic Squares and Cubes - W. S. Andrews (1917)
• Convex Optimization - Stephen Boyd and Lieven Vandenberghe
• Fabrice Baudoin's Notes - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more.

Branches of Mathematics

Content Format \ 📖 Books \ 🎥 Videos \ 📝 Lecture notes, slides, articles, papers

Foundations of Mathematics

Transition To Pure Rigour Math

• 📝 Basic Concepts of Mathematics - Elias Zakon
• 📝 Book of Proof - Richard Hammak (Virginia Commonwealth University)
• 📖 How to Prove It: A Structured Approach (3rd Edition) - Daniel J. Velleman (Professor).

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

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