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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
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
- Introduction to Algebraic Number Theory - F. Oggier
- 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)
- Algebraic methods - F. Oggier
- Abstract Algebra : Theory and Applications - Thomas W. Judson, Robert A. Beezer (Austin State University)
- An undergraduate course in Abstract Algebra - Robert Howlett
Group theory
- Notes on Group Theory - Mark Reeder
- Group theory - J.S. Milne
- Notes on finite group theory - Peter J. Cameron
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
Ring theory
- Foundations of Module and Ring Theory - Robert Wisbauer (University of Düsseldorf)
Galois theory
- An Introduction to Galois Theory - Andrew Baker (University of Glasgow)
- Fields and Galois Theory - J.S. Milne
- Galois theory - Miles Reid
Analysis
Real analysis
- An Introduction to Real Analysis - John K. Hunter (University of California at Davis)
- Introduction to real analysis - William F. Trench (Trinity University, Texas)
- Basic Analysis: Introduction to Real Analysis - Jirí Lebl
- Elementary Real Analysis - Thomson, Bruckner
- Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University)
- Real analysis - C. McMullen
- From Calculus to Analysis - Steen Pedersen
- Real analysis for graduate students - Richard F. Bass
- Modern Real Analysis - William P. Ziemer (Indiana University)
Harmonic analysis
- Harmonic Analysis Lecture Notes - Richard S. Laugesen (University of Illinois at Urbana–Champaign)
- Harmonic Analysis - W. Schlag
- Lecture Notes: Fourier Transform and its Applications - Brad Osgood
- Fourier Analysis - Lucas Illing
Complex analysis
- Introduction to Complex Analysis - Michael Taylor
- An Introduction to Complex Analysis and Geometry - John P. D'Angelo (University of Illinois)
- A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
- A Guide to Complex Variables - Steven G. Krantz
- Complex Analysis - Charles Walkden
- Complex Analysis - Christian Berg
- Complex Variables - R. B. Ash, W.P. Novinger
- Complex Analysis - Christer Bennewitz
- Complex Analysis - Donald E. Marshall
- A concise course in complex analysis and Riemann surfaces - Wilhelm Schlag
Functional analysis
- An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo)
- Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University)
- Functional analysis lecture notes - T.B. Ward (University of East Anglia)
- Functional analysis - Alexander C. R. Belton
- Topics in Real and Functional Analysis - Gerald Teschl
- Functional Analysis - Christian Remling
Measure theory
- An introduction to measure theory - Terence Tao (UCLA)
- Lecture Notes on Measure Theory and Functional Analysis - P. Cannarsa, T. D’Aprile
- Lecture Notes in Measure Theory - Christer Borell
- A Crash Course on the Lebesgue Integral and Measure Theory - Steve Cheng
- Measure Theory - John K. Hunter (University of California at Davis)
- Measure and Integration - Dietmar A. Salamon (ETH Zürich)
- Lecture notes: Measure Theory - Bruce K. Driver
Ordinary Differential Equations
- Ordinary Differential Equation - Alexander Grigorian (University of Bielefeld)
- Ordinary Differential Equations: Lecture Notes - Eugen J. Ionascu
- Ordinary Differential Equations - Peter Philip
- Ordinary Differential Equations - Gabriel Nagy
- Ordinary Differential Equations and Dynamical Systems - Gerald Teschl
Partial differential equations
- Notes on Partial Differential Equations - John K. Hunter (University of California at Davis)
- Partial Differential Equations: Lecture Notes - Erich Miersemann (Leipzig University)
Combinatorics
- Basic Combinatorics - Carl G. Wagner (University of Tennessee)
- Applied Combinatorics - Mitchel T. Keller, William T. Trotter
- Notes on Combinatorics - Peter J. Cameron
- Analytic Combinatorics - Philippe Flajolet, Robert Sedgewick
Graph theory
- Graph Theory: Lecture Notes - Christopher Griffin
- Graph Theory - Reinhard Diestel
Geometry and topology
- Fundamentals of Geometry - Oleg A. Belyaev
Differential geometry
- Introduction to differential geometry - Joel W. Robbin, Dietmar A. Salamon
- Notes on Differential Geometry and Lie Groups - Jean Gallier (University of Pennsylvania)
- Topics in Differential Geometry - Peter W. Michor
- Lectures on Differential Geometry - Wulf Rossmann
- An Introduction to Riemannian Geometry - Sigmundur Gudmundsson (Lund University)
Algebraic geometry
- A Brief Introduction to Algebraic Geometry - R.C. Churchill
- Introduction to Algebraic Geometry - Igor V. Dolgachev
- Foundations of Algebraic Geometry - Ravi Vakil
- Algebraic Geometry - Jean Gallier, Stephen S. Shatz (University of Pennsylvania)
- Algebraic Geometry - J.S. Milne
- Algebraic Geometry - Andreas Gathmann (University of Kaiserslautern)
Topology
Algebraic topology
Probability and statistics
-
Statistical Learning Theory - Percy Liang
Numerical Analysis
Computer algebra
Websites
Learning platforms
Questions and answers
- Mathematics Stack Exchange
- MathOverflow - for professional mathematicians
Encyclopedia
Misc
Books
- Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)