Mathematics

The language of patterns, structure, and abstract thought

Foundations

Khan Academy — Arithmetic & Algebra

Comprehensive foundation in basic mathematics

Interactive Course Beginner

MIT OpenCourseWare — Single Variable Calculus

Complete calculus course with lectures and problem sets

Video Lectures Intermediate

3Blue1Brown — Essence of Linear Algebra

Visual and intuitive introduction to linear algebra

Video Series Intermediate

Pure Mathematics

Book of Proof by Richard Hammack

Introduction to mathematical proofs and reasoning

Free Textbook Intermediate

Abstract Algebra — Harvard Extension

Groups, rings, fields, and algebraic structures

Online Course Advanced

Real Analysis — MIT OCW

Rigorous treatment of limits, continuity, and convergence

Course Materials Advanced

Applied Mathematics

Differential Equations — Paul's Online Math Notes

Comprehensive guide to ordinary and partial differential equations

Tutorial Intermediate

Numerical Analysis — Cleve Moler

Computational methods and numerical algorithms

Book & Software Advanced

Special Topics

Number Theory — Art of Problem Solving

Properties of integers, primes, and modular arithmetic

Interactive Intermediate

Topology Without Tears — Sidney Morris

Introduction to point-set topology

Free Textbook Advanced

Graph Theory — Douglas West

Networks, paths, and combinatorial structures

Textbook Intermediate

Problem Solving & Practice

Project Euler

Mathematical and computational problem solving challenges

Problem Archive All Levels

Brilliant.org — Mathematics

Interactive problem-solving platform for mathematical thinking

Interactive Platform All Levels