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293 Free Mathematics Ebooks, Learning Platforms, Tools and Resources

293 Free Mathematics Ebooks, Learning Platforms, Tools and Resources
Archimedes is known as the Father of Mathematics. It is one of the ancient sciences developed in time immemorial. Algebra, geometry, calculus and statistics & probability are considered to be the 4 main branches of mathematics. It is also broadly divided into pure mathematics and applied mathematics. Applied mathematics can be applied to real world problems.

Which is the toughest branch of mathematics? Geometry and trigonometry are both basic. Algebra can get very difficult at the university level, especially in graduate programs when you start to generalize concepts to abstract algebra and then explore commutative algebra. Alternatively, math gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world and we use the world to understand math. The world is interconnected.

This post will further your knowledge in areas that all mathematicians will be interested in. Find out what resources you can read to learn more, and find a selection of useful links including a variety of ebooks, learning platforms, videos, tools and lecture notes on a wide array of topics, such as doing math foundation, set theory, logic, type theory, algebra and many many more.


  1. Calculus: Basic Concepts for High Schools
    L.V. Tarasov
  2. Basics of Algebra, Topology, and Differential Calculus
    Jean Gallier (University of Pennsylvania)
  3. Multivariable Calculus
    G. Cain, J. Herod (Georgia Tech)
  4. Wikibooks
  5. Online Mathematics Textbooks
  6. Beginning and Intermediate Algebra

General Resources

Learning Platforms

  1. Khan Academy
  2. Coursera
  3. MIT OpenCourseWare
  4. edX
  5. Brilliant
  6. WooTube
  7. Mathigon
  9. Ximera
    Free interactive mathematics textbooks (Ohio State University)

Questions and Answers

  1. Mathematics Stack Exchange
  2. MathOverflow
    For professional mathematicians


  1. Encyclopedia of Mathematics
  2. Planetmath
  3. ProofWiki
  4. Wolfram Mathworld

Youtube Series

  1. Brandon Foltz
  2. 3blue1brown
  3. NPTEL
  4. Prof. Leonard
  5. Crash Course
  6. Harvard
  7. MIT


  1. Symbolab
  2. Desmos
  3. Math Words
  4. Wolfram Alpha
  5. Maxima
  6. Sympy
  7. Sagemath
  8. GeoGebra
  9. Macaulay2
  10. Singular
  11. GNU Octave
  12. Magma
  13. Maple
  14. Matlab
  15. Wolfram Mathematica
  16. Free Math


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

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  2. Free Mathematics Ebooks – Algebra & Real Analysis – 2018
    These books are at the first-year graduate level or a little higher, depending on one’s university. The list includes basic & advanced algrebra and basic & advanced real analysis.
  3. Other free mathematics ebooks and resources


  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


    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


  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


  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
  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)


  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


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


  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.