Courses & Tutorials
Awesome Math – Massive Collection of Resources
Contents
- Contents
- General Resources
- Lecture Notes
General Resources
Learning Platforms
Learn to Learn
Youtube Series
Tools
- Symbolab
- Desmos
- Math Words
- Wolfram Alpha
- Sympy
- Sagemath
- Unit Converter
- GeoGebra
- Macaulay2
- Singular
- GNU Octave
- Magma
- Maple
- Matlab
- Wolfram Mathematica
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)
- 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
- 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
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
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