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Updated students lecture notes, adding _Fabrice Baudoin_, and changing the title to _Researchers lecture notes_, As he is a professor
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Awesome Math 
A curated list of awesome mathematics resources.
Contents
- Contents
- General Resources
- Lecture Notes
- Students Lecture Notes
- License
General Resources
Learning Platforms
- Khan Academy
- Coursera
- MIT OpenCourseWare
- edX
- Brilliant
- WooTube
- Mathigon
- Calculus.org
- Ximera : free interactive mathematics textbooks (Ohio State University)
- Dzdx.xyz
Learn to Learn
Youtube Series
Tools
- Symbolab
- Desmos
- Math Words
- Wolfram Alpha
- Maxima
- Sympy
- Sagemath
- Unit Converter
- GeoGebra
- Macaulay2
- Singular
- GNU Octave
- Magma
- Maple
- Matlab
- Wolfram Mathematica
- Free Math
- xhub
Questions and Answers
- Mathematics Stack Exchange
- MathOverflow - for professional mathematicians
Encyclopedia
Books
- Calculus: Basic Concepts for High Schools - L.V. Tarasov
- Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)
- Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)
- Wikibooks
- Online Mathematics Textbooks
- Beginning and Intermediate Algebra
- Free Mathematics Books
- Trigonometry
Blogs
- 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)
- Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull)
- 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
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
- Toposes, Triples and Theories - Michael Barr, Charles Wells
- Abelian Categories - Peter Freyd
- Categories and Groupoids - P. J. Higgins
- Basic Concepts of Enriched Category Theory - G. M. Kelley
- Abstract and Concrete Categories: The Joy of Cats - Jiri Adamek, Horst Herrlich, George Strecker
- Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (MIT)
- Category Theory in Context - Emily Riehl (John Hopkins University)
Type Theory
- Proofs and Types - Jean-Yves Girard
- Intuitionistic Type Theory - Per Martin-Lof
- Type Theory and Functional Programming - Simon Thompson
- Programming in Martin-Lof’s Type Theory - Bengt Nordstrom, Kent Petersson, Jan M. Smith
Homotopy Type Theory
Surreal Numbers
- Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness - D. E. Knuth
- An Introduction to Surreal Numbers - Gretchen Grimm
- Surreal Numbers and Games
- Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich
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
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
- MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks - Juan Klopper
- 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
- Discrete Differential Geometry - Keenan Crane
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
Researchers 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.
- Fabrice Baudoin - Connecticut. 2014 ~ 2019. Covers Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more; Both research and lecture notes.
License
To the extent possible under law, Cyrille Rossant has waived all copyright and related or neighboring rights to this work.