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

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

Lecture Notes

Foundations of Mathematics

Transition To Pure Rigour Math

Basic Concepts of Mathematics - Elias Zakon
Book of Proof - Richard Hammak (Virginia Commonwealth University)

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

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
Predictive Arithmetic - Edward Nelson
Proofs and Concepts: the fundamentals of abstract mathematics - Joy Morris, Dave Morris
Mathematical Reasoning: Writing and Proof - Ted Sundstrom
Logic and Proof - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn
QED - an interactive textbook - Terence Tao
Open Logic Textbook - collaborative effort, main contributors listed here

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
An Introduction to the Theory of Numbers - Leo Moser
Yet Another Introductary Number Theory Textbook - Jonathan A. Poritz
Elementary Number Theory - David M. Burton

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)
A Course In Algebraic Number Theory - Robert Ash

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

A Course in Universal Algebra - S. Burris, H.P. Sankappanavar
A Course in Commutative Algebra - Robert Ash
First Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910)
Second Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911)
Algebra: An Elementary Text-Book, Part I - G. Chrystal (1904)
Algebra: An Elementary Text-Book, Part II - G. Chrystal (1900)
Understanding Algebra - James W. Brennan

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
Elements of Abstract and Linear Algebra - E.H. Connell (University of Miami)
Abstract Algebra: The Basic Graduate Year - Robert Ash
Abstract Algebra: Harvard Extension (Archived) - Benedict Gross
Abstract Algebra: Harvard Extension Videos - Benedict Gross

Group Theory

Notes on Group Theory - Mark Reeder
Group Theory - J.S. Milne
Notes on Finite Group Theory - Peter J. Cameron
Group Theory - Pedrag Civitanovic

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
MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks - Juan Klopper
Linear Algebra - Jim Hefferon
Elementary Linear Algebra - Keith Matthews
A First Courses in Linear Algebra - Rob Breezer
Linear Algebra - David Cherney, Tom Denton, Andrew Waldron
Introduction to vectors and tensors, Vol 1: linear and multilinear algebra - Ray M Bowen, C. C. Wang
Introduction to vectors and tensors, Vol 2: vector and tensor analysis - Ray M Bowen, C. C. Wang
Introduction to Applied Linear Algebra - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
Linear Algebra Done Wrong - Sergei Treil
Immersive Linear Algebra - J. Ström, K. Åström, and T. Akenine-Möller
Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff
Linear Algebra, Infinite Dimensions, and Maple - James Herod

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
Galois Theory - Ian Stewart

Lie Algebras

Lie Algebras - Shlomo Sternberg

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
generatingfunctionology - Herbert Wilf

Graph Theory

Graph Theory: Lecture Notes - Christopher Griffin
Graph Theory - Reinhard Diestel

Geometry and Topology

Fundamentals of Geometry - Oleg A. Belyaev
A=B - M. Petkovsek, H. Wilf, D. Zeilberger
Elements - Euclid
Euclid's Elements Redux - Daniel Callahan
Mathematical Illustrations - Bill Casselman
Byrne's Euclid - Oliver Byrne
Plane Geometry - George Wentworth and David Eugene Smith (1913)
Planes and Spherical Trigonometry - George Wentworth and David Eugene Smith (1915)
Coordinate Geometry - Henry Buchard Fine and Henry Dallas Thompson (1911)
Analytic Geometry - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922)

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)
The Geometry and Topology of Three-Manifolds - W. Thurston
Semi-Riemann Geometry and General Relativity - Shlomo Sternberg

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)
The Stacks Project - Maintained by Aise Johan de Jong (Columbia)

Topology

Elementary Applied Topology - Robert Ghrist (UPenn)
Introduction to Topology
Introduction to Topology - Alex Küronya
Introductory Topology - Jim L. Brown
General Topology - Pierre Schapira (Paris VI University)
Elementary Topology Problem Textbook
General Topology - Jesper M. Møller
Topology Topics

Algebraic Topology

Algebraic Topology - Allen Hatcher
A Concise Course in Algebraic Topology - J. P. May
Introduction to Algebraic Topology - Martin Cadek
Algebra and Topology - Pierre Schapira (Paris VI University)
Lecture Notes in Algebraic Topology - James F. Davis, Paul Kirk (Indiana University)
Algebraic Topology - Michael Starbird
Lecture Notes on Algebraic Topology - Jie Wu

Analysis

Real Analysis

MIT OpenCourseWare Lectures on Calculus - G. Strang
Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler
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 - Jiří Lebl
Elementary Real Analysis - Thomson, Bruckner
Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University)
Real Analysis - C. McMullen
Real Analysis for Graduate Students - Richard F. Bass
Modern Real Analysis - William P. Ziemer (Indiana University)
Mathematical Analysis Vol I - Elias Zakon
Mathematical Analysis Vol II - Elias Zakon
Advanced Calculus - Lynn Loomis, Schlomo Sternberg
Analysis of Functions of a Single Variable - Lawerence Baggett
The Calculus of Functions of Several Variables - Dan Sloughter
A ProblemText in Advanced Calculus - John M. Erdman
Calculus and Linear Algebra. Vol. 1 - Wilfred Kaplan, Donald J. Lewis
Calculus and Linear Algebra. Vol. 2 - Wilfred Kaplan, Donald J. Lewis
Introduction to Calculus I and II - J.H. Heinbockel
Active Calculus - Matt Boelkins
Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis" - George M. Bergman
Calculus Made Easy - Silvanus P. Thompson (1910)
Elements of Differential and Integral Calculus - William Anthony Granville (1911)
Precalculus - Carl Stitz, Jeff Zeager

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
Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)

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
Complex Analysis - G. Cain (Georgia Tech)
Complex Analysis - Juan Carlos Ponce Campuzano

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
Theory of Functions of a Real Variable - Shlomo Sternberg
Functional Analysis - Lawerence Baggett

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

Difference Equations To Differential Equations - Dan Sloughter
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
Notes on Differential Equations - Bob Terrell
Elementary Differential Equations - William F. Trench
Elementary Differential Equations With Boundary Value Problems - William F. Trench
Notes on Diffy Qs: Differential Equations for Engineers - Jiří Lebl
Differential Equations - H. B. Phillips (1922)

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)
Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)

Probability and Statistics

Probability Theory

Introduction to Probability - Charles M. Grinstead, J. Laurie Snell
Introduction to Probability - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)
A Short Introduction to Probability - Dirk P. Kroese (University of Queensland)
Probability: Theory and Examples - Rick Durrett
Probability and Statistics Cookbook - Matthias Vallentin (UC Berkeley)
The Only Probability Cheatsheet You'll Ever Need - William Chen
An Introduction to Probability and Random Processes - Gian-Carlo Rota, Kenneth Baclawski
Foundations of Constructive Probability Theory - Yuen-Kwok Chan

Statistics

Lecture Notes on Statistical Theory - Ryan Martin (University of Illinois)
Introduction to Statistics and Data Analysis for Physicists - Gerhard Bohm, Günter Zech
Probability and Mathematical Statistics - Prasanna Sahoo (University of Louisville)
Lectures on Statistics - William G. Faris
Statistical Theory - Adolfo J. Rumbos
Theory of Statistics - James E. Gentle (George Mason University)
Theory of Statistics - Joseph C. Watkins (University of Arizona)
Glossary of Data Modeling - AI Access
Statistics Papers - List of statistics papers curated by the Institute for Digital Research and Education (IDRE) at UCLA on methods such as bootstrap and factor invariance.
NIST Handbook of Statistical Methods - Resource on practical statistics directed towards scientists and engineers.
Concepts and Applications of Inferential Statistics - Richard Lowry
Rough set data analysis: A road to non-invasive knowledge discovery - Ivo Düntsch, Günther Gediga
Statistical Thinking for the 21st Century - Russell A. Poldrack
Odds and Ends: Introducing Probability & Decision with a Visual Emphasis - Jonathan Weisberg
Seeing Theory - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang
Statistics Done Wrong - Alex Reinhart
All of Statistics: A Concise Course in Statistical Inference - Larry Wasserman

Statistical Learning

An Introduction to Statistical Learning with Applications in R - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
The Elements of Statistical Learning - Trevor Hastie, Robert Tibshirani, Jerome Friedman
Statistical Learning Theory - Percy Liang
Reinforcement Learning: An Introduction - Richard S. Sutton, Andrew G. Barto

Stochastic processes

Lectures on Stochastic Processes - K. Ito (Tata Institute of Fundamental Research, Bombay)
Probability and Stochastic Processes with Applications - Oliver Knill (Harvard University)
Stochastic Processes - Amir Dembo (Stanford University)
Lecture Notes on Stochastic Processes - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin)
Introduction to Stochastic Processes - Lecture Notes - Gordan Žitković (University of Texas)
Applied Stochastic Processes in science and engineering - Matt Scott (University of Waterloo)
An Introduction to Stochastic Processes in Continuous Time - Flora Spieksma (Leiden University)
Markov Chains and Mixing Times - David A. Levin, Yuval Peres, Elizabeth L. Wilmer
Convergence of Stochastic Processes - David Pollard

Numerical Analysis

Introduction to Numerical Analysis - Doron Levy (University of Maryland)
A Concise Introduction to Numerical Analysis - Douglas N. Arnold (University of Minnesota)
Numerical Analysis - L. Ridgway Scott
Lectures In Basic Computational Numerical Analysis - J. M. McDonough (University of Kentucky)
Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods - Alfred Schmidt, Arsen Narimanyan
Numerical Analysis for Engineers - Douglas Wilhelm Harder

Signal processing

Introduction to Signal Processing - Sophocles J. Orfanidis (Rutgers University)
Foundations of Signal Processing - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal
An Introduction to Statistical Signal Processing - Robert M. Gray, Lee D. Davisson
Think DSP - Allen B. Downey
Linear algebra, signal processing, and wavelets. A unified approach. - Øyvind Ryan (University of Oslo)

Mathematics for Computer Science

Mathematics for Computer Science - Eric Lehman, F. Thomson Leighton, Albert R. Meyer
Algorithms and Complexity - H. Wilf
Lecture Notes on Optimization - Pravin Varaiya
Information Theory, Inference, and Learning Algorithms - David J. C. MacKay
The Chaos Textbook: Mathematics in the age of the computer - Glenn Elert

Mathematical Biology

Mathematical Biology - Jeffrey Chasnov

Mathematical Physics

Introduction to Continuum Mechanics - Ray. M. Bowen
Mathematical Tools for Physics - James Nearing
Mechanism of the Heavens (1831) - Mary Somerville

Students Lecture Notes

Evan Chen - MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more.
Dexter Chua - Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more.

License

To the extent possible under law, Cyrille Rossant has waived all copyright and related or neighboring rights to this work.

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Tools

Questions and Answers

Encyclopedia

Books

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Misc

Lecture Notes

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

Topology

Algebraic Topology

Analysis

Real Analysis

Harmonic Analysis

Complex Analysis

Functional Analysis

Measure Theory

Ordinary Differential Equations

Partial Differential Equations

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

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