293 Free Mathematics Ebooks, Learning Platforms, Tools and Resources

Misc

1. Areas of mathematics on Wikipedia
2. Paul’s Online Math Notes
   Paul Dawkins (Lamar University)
3. List of electronic textbooks
   Marcel B. Finan (Arkansas Tech University)
4. Topology Atlas
5. Recreations in Math
   H. E. Licks (1917)
6. Magic Squares and Cubes
   W. S. Andrews (1917)
7. Convex Optimization
   Stephen Boyd and Lieven Vandenberghe

Lecture Notes

Foundations of Mathematics

Transition To Pure Rigour Math

1. Basic Concepts of Mathematics
   Elias Zakon
2. Book of Proof
   Richard Hammak (Virginia Commonwealth University)

Set Theory

1. Sets, Relations, Functions
   Ivo Düntsch, Günther Gediga
2. An Introduction to Set Theory
   William A. R. Weiss
3. Set Theory and Foundations of Mathematics
   Sylvain Poirier
4. Set Theory on the Stanford Encyclopedia of Philosophy

Logic

1. Introduction to Logic
   Michael Genesereth, Eric Kao (Stanford University)
2. An Introduction to Formal Logic
   P.D. Magnus (University at Albany)
3. A Problem Course in Mathematical Logic
   Stefan Bilaniuk (Trent University)
4. Mathematical Logic
   Helmut Schwichtenberg
5. Mathematical Logic
   Stephen G. Simpson (Pennsylvania State University)
6. Formal Logic
   Miguel Palomino
7. Predictive Arithmetic
   Edward Nelson
8. Proofs and Concepts: the fundamentals of abstract mathematics
   Joy Morris, Dave Morris
9. Logic and Proof
   Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn
10. QED – an interactive textbook
    Terence Tao
11. Open Logic Textbook
    contributors listed here

Category Theory

1. Introduction to Category Theory and Categorical Logic
   Thomas Streicher
2. Category Theory
   B. Pareigis
3. Category Theory for Computing Science
   Michael Barr, Charles Wells
4. Toposes, Triples and Theories
   Michael Barr, Charles Wells
5. Abelian Categories
   Peter Freyd
6. Categories and Groupoids
   P. J. Higgins
7. Basic Concepts of Enriched Category Theory
   G. M. Kelley
8. Abstract and Concrete Categories: The Joy of Cats
   Jiri Adamek, Horst Herrlich, George Strecker
9. Seven Sketches in Compositionality: An Invitation to Applied Category Theory
   Brendan Fong and David I. Spivak (MIT)
10. Category Theory in Context
    Emily Riehl (John Hopkins University)

Type Theory

1. Proofs and Types
   Jean-Yves Girard
2. Intuitionistic Type Theory
   Per Martin-Lof
3. Type Theory and Functional Programming
   Simon Thompson
4. Programming in Martin-Lof’s Type Theory
   Bengt Nordstrom, Kent Petersson, Jan M. Smith

Homotopy Type Theory

1. Homotopy Type Theory

Surreal Numbers

1. Surreal Numbers – How two ex-students turned on to pure mathematics and found total happiness
   D. E. Knuth
2. An Introduction to Surreal Numbers
   Gretchen Grimm
3. Surreal Numbers and Games

Number Theory

1. Elementary Number Theory: Primes, Congruences, and Secrets
   William Stein
2. Elementary Number Theory
   W. Edwin Clark (University of South Florida)
3. A Course on Number Theory
   Peter J. Cameron
4. A Computational Introduction to Number Theory and Algebra
   Victor Shoup
5. Number Theory: A Contemporary Introduction
   Pete L. Clark
6. An Introduction to the Theory of Numbers
   Leo Moser
7. Yet Another Introductary Number Theory Textbook
   Jonathan A. Poritz

Algebraic Number Theory

1. Algebraic Number Theory
   J.S. Milne
2. A Course In Algebraic Number Theory
   Robert Ash

Analytic Number Theory

1. Introduction to Analytic Number Theory
   A.J. Hildebrand (University of Illinois)
2. Elements of Analytic Number Theory
   P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
3. Analytic Number Theory
   Otto Forster (LMU Munich)
4. Analytic Number Theory – Lecture Notes based on Davenport’s book
   Andreas Strömbergsson

Algebra

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

Abstract Algebra

1. Introduction to Modern Algebra
   David Joyce (Clark University)
2. Abstract Algebra : Theory and Applications
   Thomas W. Judson, Robert A. Beezer (Austin State University)
3. An Undergraduate Course in Abstract Algebra
   Robert Howlett
4. Elements of Abstract and Linear Algebra
   E.H. Connell (University of Miami)
5. Abstract Algebra: The Basic Graduate Year
   Robert Ash
6. Abstract Algebra: Harvard Extension (Archived)
   Benedict Gross
7. Abstract Algebra: Harvard Extension Videos
   Benedict Gross

Group Theory

1. Group Theory
   J.S. Milne
2. Notes on Finite Group Theory
   Peter J. Cameron

Linear Algebra

1. Fundamentals of Linear Algebra
   James B. Carrell
2. Linear Algebra and Matrices
   Martin Fluch
3. Vector Space Theory
   Robert Howlett
4. Linear Algebra
   Jim Hefferon
5. Linear Algebra
   Jim Hefferon
6. Elementary Linear Algebra
   Keith Matthews
7. A First Courses in Linear Algebra
   Rob Breezer
8. Linear Algebra
   David Cherney, Tom Denton, Andrew Waldron
9. Introduction to vectors and tensors, Vol 1: linear and multilinear algebra
   Ray M Bowen, C. C. Wang
10. Introduction to vectors and tensors, Vol 2: vector and tensor analysis
    Ray M Bowen, C. C. Wang
11. Introduction to Applied Linear Algebra
    Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
12. Linear Algebra Done Wrong
    Sergei Treil
13. Immersive Linear Algebra
    J. Ström, K. Åström, and T. Akenine-Möller
14. Interactive Linear Algebra
    Dan Margalit and Joseph Rabinoff
15. Linear Algebra, Infinite Dimensions, and Maple
    James Herod

Ring Theory

1. Foundations of Module and Ring Theory
   Robert Wisbauer (University of Düsseldorf)

Galois Theory

1. Fields and Galois Theory
   J.S. Milne
2. Galois theory
   Miles Reid
3. Galois Theory
   Ian Stewart

Lie Algebras

1. Lie Algebras
   Shlomo Sternberg

Combinatorics

1. Basic Combinatorics
   Carl G. Wagner (University of Tennessee)
2. Applied Combinatorics
   Mitchel T. Keller, William T. Trotter
3. Notes on Combinatorics
   Peter J. Cameron
4. Analytic Combinatorics
   Philippe Flajolet, Robert Sedgewick
5. generatingfunctionology
   Herbert Wilf

Graph Theory

1. Graph Theory: Lecture Notes
   Christopher Griffin
2. Graph Theory
   Reinhard Diestel

Geometry and Topology

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

Differential Geometry

1. Introduction to Differential Geometry
   Joel W. Robbin, Dietmar A. Salamon
2. Topics in Differential Geometry
   Peter W. Michor
3. Lectures on Differential Geometry
   Wulf Rossmann
4. An Introduction to Riemannian Geometry
   Sigmundur Gudmundsson (Lund University)
5. The Geometry and Topology of Three-Manifolds
   W. Thurston
6. Semi-Riemann Geometry and General Relativity
   Shlomo Sternberg
7. Discrete Differential Geometry
   Keenan Crane

Algebraic Geometry

1. A Brief Introduction to Algebraic Geometry
   R.C. Churchill
2. Introduction to Algebraic Geometry
   Igor V. Dolgachev
3. Foundations of Algebraic Geometry
   Ravi Vakil
4. Algebraic Geometry
   Jean Gallier, Stephen S. Shatz (University of Pennsylvania)
5. Algebraic Geometry
   J.S. Milne
6. The Stacks Project
   Maintained by Aise Johan de Jong (Columbia)

Topology

1. Elementary Applied Topology
   Robert Ghrist (UPenn)
2. Introduction to Topology
3. Introduction to Topology
   Alex Küronya
4. General Topology
   Pierre Schapira (Paris VI University)
5. Elementary Topology Problem Textbook
6. General Topology
   Jesper M. Møller
7. Topology Topics

Algebraic Topology

1. A Concise Course in Algebraic Topology
   J. P. May
2. Introduction to Algebraic Topology
   Martin Cadek
3. Algebraic Topology
   Michael Starbird

Analysis

Real Analysis

1. MIT OpenCourseWare Lectures on Calculus
   G. Strang
2. Elementary Calculus: An Approach Using Infinitesimals
   Professor H. Jerome Keisler
3. An Introduction to Real Analysis
   John K. Hunter (University of California at Davis)
4. Introduction to Real Analysis
   William F. Trench (Trinity University, Texas)
5. Basic Analysis: Introduction to Real Analysis
   Jiří Lebl
6. Lecture Notes in Real Analysis
   Eric T. Sawyer (McMaster University)
7. Real Analysis for Graduate Students
   Richard F. Bass
8. Modern Real Analysis
   William P. Ziemer (Indiana University)
9. Mathematical Analysis Vol I
   Elias Zakon
10. Mathematical Analysis Vol II
    Elias Zakon
11. Advanced Calculus
    Lynn Loomis, Schlomo Sternberg
12. Analysis of Functions of a Single Variable
    Lawerence Baggett
13. The Calculus of Functions of Several Variables
    Dan Sloughter
14. A ProblemText in Advanced Calculus
    John M. Erdman
15. Calculus and Linear Algebra. Vol. 1
    Wilfred Kaplan, Donald J. Lewis
16. Calculus and Linear Algebra. Vol. 2
    Wilfred Kaplan, Donald J. Lewis
17. Introduction to Calculus I and II
    J.H. Heinbockel
18. Active Calculus
    Matt Boelkins
19. Supplements to the Exercises in Chapters 1-7 of Walter Rudin’s “Principles of Mathematical Analysis”
    George M. Bergman
20. Calculus Made Easy
    Silvanus P. Thompson (1910)
21. Elements of Differential and Integral Calculus
    William Anthony Granville (1911)
22. Precalculus
    Carl Stitz, Jeff Zeager

Harmonic Analysis

1. Harmonic Analysis Lecture Notes
   Richard S. Laugesen (University of Illinois at Urbana–Champaign)
2. Lecture Notes: Fourier Transform and its Applications
   Brad Osgood
3. Fourier Analysis
   Lucas Illing
4. Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications
   Julius O. Smith III (Stanford University)

Complex Analysis

1. Introduction to Complex Analysis
   Michael Taylor
2. An Introduction to Complex Analysis and Geometry
   John P. D’Angelo (University of Illinois)
3. A First Course in Complex Analysis
   Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
4. A Guide to Complex Variables
   Steven G. Krantz
5. Complex Analysis
   Christian Berg
6. Complex Variables
   R. B. Ash, W.P. Novinger
7. Complex Analysis
   Christer Bennewitz
8. Complex Analysis
   Donald E. Marshall
9. A Concise Course in Complex Analysis and Riemann Surfaces
   Wilhelm Schlag
10. Complex Analysis
    G. Cain (Georgia Tech)
11. Complex Analysis
    Juan Carlos Ponce Campuzano

Functional Analysis

1. Functional Analysis: Lecture Notes
   Jeff Schenker (Michigan State University)
2. Functional Analysis
   Alexander C. R. Belton
3. Topics in Real and Functional Analysis
   Gerald Teschl
4. Functional Analysis
   Christian Remling
5. Theory of Functions of a Real Variable
   Shlomo Sternberg
6. Functional Analysis
   Lawerence Baggett

Measure Theory

1. Lecture Notes on Measure Theory and Functional Analysis
   P. Cannarsa, T. D’Aprile
2. Lecture Notes in Measure Theory
   Christer Borell
3. Measure Theory
   John K. Hunter (University of California at Davis)
4. Measure and Integration
   Dietmar A. Salamon (ETH Zürich)
5. Lecture notes: Measure Theory
   Bruce K. Driver

Ordinary Differential Equations

1. Difference Equations To Differential Equations
   Dan Sloughter
2. Ordinary Differential Equation
   Alexander Grigorian (University of Bielefeld)
3. Ordinary Differential Equations: Lecture Notes
   Eugen J. Ionascu
4. Ordinary Differential Equations
   Gabriel Nagy
5. Ordinary Differential Equations and Dynamical Systems
   Gerald Teschl
6. Notes on Differential Equations
   Bob Terrell
7. Elementary Differential Equations
   William F. Trench
8. Elementary Differential Equations With Boundary Value Problems
   William F. Trench
9. Notes on Diffy Qs: Differential Equations for Engineers
   Jiří Lebl
10. Differential Equations
    H. B. Phillips (1922)

Partial Differential Equations

1. Notes on Partial Differential Equations
   John K. Hunter (University of California at Davis)
2. Partial Differential Equations: Lecture Notes
   Erich Miersemann (Leipzig University)
3. Linear Methods of Applied Mathematics
   E. Harrell, J. Herod (Georgia Tech)

Probability and Statistics

Probability Theory

1. Introduction to Probability
   Dimitri P. Bertsekas, John N. Tsitsiklis (MIT)
2. A Short Introduction to Probability
   Dirk P. Kroese (University of Queensland)
3. Probability and Statistics Cookbook
   Matthias Vallentin (UC Berkeley)
4. The Only Probability Cheatsheet You’ll Ever Need
   William Chen
5. An Introduction to Probability and Random Processes
   Gian-Carlo Rota, Kenneth Baclawski
6. Foundations of Constructive Probability Theory
   Yuen-Kwok Chan

Statistics

1. Lecture Notes on Statistical Theory
   Ryan Martin (University of Illinois)
2. Introduction to Statistics and Data Analysis for Physicists
   Gerhard Bohm, Günter Zech
3. Lectures on Statistics
   William G. Faris
4. Statistical Theory
   Adolfo J. Rumbos
5. Theory of Statistics
   James E. Gentle (George Mason University)
6. Theory of Statistics
   Joseph C. Watkins (University of Arizona)
7. Glossary of Data Modeling
   AI Access
8. NIST Handbook of Statistical Methods
   Resource on practical statistics directed towards scientists and engineers.
9. Concepts and Applications of Inferential Statistics
   Richard Lowry
10. Rough set data analysis: A road to non-invasive knowledge discovery
    Ivo Düntsch, Günther Gediga
11. Statistical Thinking for the 21st Century
    Russell A. Poldrack
12. Odds and Ends: Introducing Probability & Decision with a Visual Emphasis
    Jonathan Weisberg
13. Seeing Theory
    Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang
14. Statistics Done Wrong
    Alex Reinhart
15. All of Statistics: A Concise Course in Statistical Inference
    Larry Wasserman

Statistical Learning

1. An Introduction to Statistical Learning with Applications in R
   Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani
2. The Elements of Statistical Learning
   Trevor Hastie, Robert Tibshirani, Jerome Friedman
3. Statistical Learning Theory
   Percy Liang

Stochastic processes

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

Numerical Analysis

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

Signal processing

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

Mathematics for Computer Science

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

Mathematical Biology

1. Mathematical Biology
   Jeffrey Chasnov

Mathematical Physics

1. Introduction to Continuum Mechanics
   Ray. M. Bowen
2. Mathematical Tools for Physics
   James Nearing

Students Lecture Notes

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