XDJ 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 GENERAL RESOURCES LEARNING PLATFORMS Khan Academy Coursera MIT OpenCourseWare edX Brilliant WooTube Mathigon Calculus.org Ximera Free interactive mathematics textbooks (Ohio State University) QUESTIONS AND ANSWERS Mathematics Stack Exchange MathOverflow For professional mathematicians ENCYCLOPEDIA Encyclopedia of Mathematics Planetmath ProofWiki Wolfram Mathworld YOUTUBE SERIES Brandon Foltz 3blue1brown NPTEL Prof. Leonard Crash Course Harvard MIT TOOLS Symbolab Desmos Math Words Wolfram Alpha Maxima Sympy Sagemath GeoGebra Macaulay2 Singular GNU Octave Magma Maple Matlab Wolfram Mathematica Free Math BLOGS BetterExplained Maintained by Kalid Azad ILoveMaths For grades 6 thru 12 in K-12 system 3blue1brown Animated Maths Mathsisfun Simple text lightweight site for students up to high school 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) 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 Logic and Proof Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn QED – an interactive textbook Terence Tao Open Logic Textbook contributors listed here CATEGORY THEORY Introduction to Category Theory and Categorical Logic Thomas Streicher 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 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 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 Algebraic Number Theory J.S. Milne 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) ABSTRACT ALGEBRA 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 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 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 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 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 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 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 General Topology Pierre Schapira (Paris VI University) Elementary Topology Problem Textbook General Topology Jesper M. Møller Topology Topics ALGEBRAIC TOPOLOGY A Concise Course in Algebraic Topology J. P. May Introduction to Algebraic Topology Martin Cadek Algebraic Topology Michael Starbird 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 Lecture Notes in Real Analysis Eric T. Sawyer (McMaster University) 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) 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 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 Functional Analysis: Lecture Notes Jeff Schenker (Michigan State University) 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 Lecture Notes on Measure Theory and Functional Analysis P. Cannarsa, T. D’Aprile Lecture Notes in Measure Theory Christer Borell 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 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)
XDJ 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 Dimitri P. Bertsekas, John N. Tsitsiklis (MIT) A Short Introduction to Probability Dirk P. Kroese (University of Queensland) 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 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 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 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 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 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.