Awesome maths

A curated list of awesome mathematics resources.

Foundations of mathematics

Set theory

• 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
• Set Theory on Wikibooks

Logic

• Introduction to logic - Michael Genesereth, Eric Kao (Stanford University)
• An introduction to formal logic - P.D. Magnus (University at Albany)
• A problem course in mathematical logic - Stefan Bilaniuk (Trent University)
• Language, proof, and logic - Jon Barwise, John Etchemendy
• Mathematical logic - Helmut Schwichtenberg
• Mathematical logic - Stephen G. Simpson (Pennsylvania State University)
• Formal logic - Miguel Palomino

Homotopy type theory

• Homotopy type theory

Number 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: A Contemporary Introduction - Pete L. Clark
• Introduction to Algebraic Number Theory
• Algebraic Number Theory - J.S. Milne
• Algebraic Number Theory Course Notes - Matthew Baker (Georgia Tech)

Algebra

Analysis

Combinatorics

Geometry and topology

Probability and statistics

Numerical Analysis

Computer algebra

Websites

Learning platforms

• Khan Academy
• Coursera
• Wikibooks

Questions and answers

• Mathematics Stack Exchange
• MathOverflow - for professional mathematicians

Encyclopedia

• Encyclopedia of Mathematics
• Wolfram Mathworld
• Planetmath

Misc

• Areas of mathematics on Wikipedia