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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
Category theory
- Introduction to category theory and categorical logic - Thomas Streicher
- An introduction to Category Theory - Harold Simmons
- Category Theory - Steve Awodey (Carnegie Mellon University)
- Category Theory - B. Pareigis
- Category Theory for Computing Science - Michael Barr, Charles Wells
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
Algebraic number theory
- Introduction to Algebraic Number Theory
- Algebraic Number Theory - J.S. Milne
- Algebraic Number Theory Course Notes - Matthew Baker (Georgia Tech)
Analytic number theory
- Introduction to Analytic Number Theory - A.J. Hildebrand (University of Illinois)
- Elements of analytic number theory - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
- Analytic Number Theory - Otto Forster (LMU Munich)
- Analytic number theory - Lecture notes based on Davenport’s book - Andreas Strömbergsson
Algebra
Abstract algebra
- Introduction to Abstract Algebra - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)
- Introduction to Modern Algebra - David Joyce (Clark University)
- Abstract Algebra : Theory and Applications - Thomas W. Judson, Robert A. Beezer (Austin State University)
- An undergraduate course in Abstract Algebra - Robert Howlett
Linear algebra
- Fundamentals of linear algebra - James B. Carrell
- Linear algebra and matrices - Martin Fluch
- Vector space theory - Robert Howlett
- Linear Algebra - Jim Hefferon
- Linear algebra - Peter Petersen
Galois theory
- An Introduction to Galois Theory - Andrew Baker (University of Glasgow)
- Fields and Galois Theory - J.S. Milne
- Galois theory - Miles Reid
Group theory
Ring theory
Field theory
Analysis
Combinatorics
Graph theory
Geometry and topology
Algebraic geometry
Probability and statistics
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Statistical Learning Theory - Percy Liang
Numerical Analysis
Computer algebra
Websites
Learning platforms
Questions and answers
- Mathematics Stack Exchange
- MathOverflow - for professional mathematicians