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A curated list of awesome mathematics resources
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Jan 26, 2023
Youtube Series
Dec 16, 2022
Tools
Nov 16, 2022
Analysis / Measure Theory
- An Introduction to Measure Theory - Terence Tao (UCLA)
Aug 02, 2022
Learning Platforms
May 18, 2022
Numerical Analysis / Stochastic processes
- Introduction to Numerical Analysis - Doron Levy (University of Maryland)
- Numerical Analysis for Engineers - Douglas Wilhelm Harder
Apr 19, 2022
Learning Platforms
Mar 16, 2022
Mathematical Physics / Stochastic processes
Feb 18, 2022
Magazines
- Quanta Magazine - Features latest research breakthroughs in an accessible style for non-experts.
- Bulletin of the American Mathematical Society - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.
- Notices of the American Mathematical Society - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.
- European Mathematical Society Magazine - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.
- Mathematics Today by Institute of Mathematics and its Applications - News, opinions, and articles related to mathematics, so the reader stays updated.
- Crux Mathematicorum by Canadian Mathematical Society - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions.
Jan 27, 2022
Learning Platforms
Jan 19, 2022
Misc
- Fabrice Baudoin's Notes - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more.
Dec 30, 2021
Foundations of Mathematics / Logic
- Computability - An introduction to recursive function theory - Nigel Cutland (University of Hull)
Dec 06, 2021
Tools
Nov 12, 2021
Tools
Nov 05, 2021
Books
Aug 19, 2021
Geometry and Topology / Algebraic Geometry
- A Brief Introduction to Algebraic Geometry - R.C. Churchill
Aug 04, 2021
Learning Platforms
- Ximera : free interactive mathematics textbooks (Ohio State University)
Jun 17, 2021
Geometry and Topology / Differential Geometry
- Discrete Differential Geometry - Keenan Crane
Jun 04, 2021
Analysis / Complex Analysis
- A Concise Course in Complex Analysis and Riemann Surfaces - Wilhelm Schlag
Apr 09, 2021
Tools
Apr 08, 2021
Tools
Mar 13, 2021
Learning Platforms
Mar 10, 2021
Foundations of Mathematics / Logic
- Introduction to Logic - Michael Genesereth, Eric Kao (Stanford University)
Number Theory / Surreal Numbers
- Elementary Number Theory - W. Edwin Clark (University of South Florida)
- Number Theory: A Contemporary Introduction - Pete L. Clark
Mar 05, 2021
Geometry and Topology / Topology
Analysis / Complex Analysis
- Introduction to Complex Analysis - Michael Taylor
Jan 08, 2021
Mathematical Physics / Stochastic processes
- 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.
Jan 04, 2021
Foundations of Mathematics / Transition To Pure Rigour Math
- Book of Proof - Richard Hammak (Virginia Commonwealth University)
Oct 03, 2020
Algebra / Analytic Number Theory
- Understanding Algebra - James W. Brennan
Analysis / Real Analysis
- Precalculus - Carl Stitz, Jeff Zeager
Analysis / Harmonic Analysis
- Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications - Julius O. Smith III (Stanford University)
Oct 01, 2020
Tools
Foundations of Mathematics / Type Theory
- Programming in Martin-Lof’s Type Theory - Bengt Nordstrom, Kent Petersson, Jan M. Smith
Sep 15, 2020
Foundations of Mathematics / Logic
- Open Logic Textbook - collaborative effort, main contributors listed here
Foundations of Mathematics / Category Theory
- Category Theory in Context - Emily Riehl (John Hopkins University)
Aug 06, 2020
Foundations of Mathematics / Logic
- QED - an interactive textbook - Terence Tao
Aug 04, 2020
Misc
- Recreations in Math - H. E. Licks (1917)
- Magic Squares and Cubes - W. S. Andrews (1917)
Algebra / Analytic Number Theory
- 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)
Geometry and Topology / Graph Theory
- 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)
Analysis / Real Analysis
- Calculus Made Easy - Silvanus P. Thompson (1910)
- Elements of Differential and Integral Calculus - William Anthony Granville (1911)
Analysis / Ordinary Differential Equations
- Differential Equations - H. B. Phillips (1922)
Aug 03, 2020
Learning Platforms
Misc
- Convex Optimization - Stephen Boyd and Lieven Vandenberghe
Foundations of Mathematics / Logic
- Logic and Proof - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn
Algebra / Linear Algebra
- Interactive Linear Algebra - Dan Margalit and Joseph Rabinoff
- Linear Algebra, Infinite Dimensions, and Maple - James Herod
Geometry and Topology / Graph Theory
- Byrne's Euclid - Oliver Byrne
Analysis / Complex Analysis
- Complex Analysis - Juan Carlos Ponce Campuzano
Probability and Statistics / Probability Theory
- Foundations of Constructive Probability Theory - Yuen-Kwok Chan
Probability and Statistics / Statistics
- 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
Mathematics for Computer Science / Stochastic processes
Jul 16, 2020
Blogs
- MathematicsIsAScience - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA)
Jul 02, 2020
Signal processing / Stochastic processes
- Think DSP - Allen B. Downey
Oct 16, 2019
Algebra / Galois Theory
- Galois Theory - Ian Stewart
Oct 15, 2019
Foundations of Mathematics / Type Theory
- Type Theory and Functional Programming - Simon Thompson
Oct 14, 2019
Foundations of Mathematics / Type Theory
- Proofs and Types - Jean-Yves Girard
- Intuitionistic Type Theory - Per Martin-Lof
Aug 02, 2019
Algebra / Linear Algebra
- Immersive Linear Algebra - J. Ström, K. Åström, and T. Akenine-Möller
May 23, 2019
Tools
May 06, 2019
Algebra / Abstract Algebra
- Introduction to Abstract Algebra - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University)
Apr 09, 2019
Foundations of Mathematics / Category Theory
- Category Theory for Computing Science - Michael Barr, Charles Wells
Algebra / Abstract Algebra
- Abstract Algebra: Harvard Extension (Archived) - Benedict Gross
- Abstract Algebra: Harvard Extension Videos - Benedict Gross
Algebra / Linear Algebra
- Linear Algebra Done Wrong - Sergei Treil
Analysis / Real Analysis
- Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis" - George M. Bergman
Analysis / Functional Analysis
- Theory of Functions of a Real Variable - Shlomo Sternberg
Apr 02, 2019
Learning Platforms
Blogs
- Mathsisfun simple text light weight site for students upto highschool
Nov 30, 2018
Geometry and Topology / Topology
- Elementary Applied Topology - Robert Ghrist (UPenn)
Nov 19, 2018
Geometry and Topology / Algebraic Geometry
- The Stacks Project - Maintained by Aise Johan de Jong (Columbia)
Oct 19, 2018
Foundations of Mathematics / Category Theory
- 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)
Jul 08, 2018
Tools
Jun 07, 2018
Algebra / Linear Algebra
- Introduction to Applied Linear Algebra - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA)
May 31, 2018
Misc
Probability and Statistics / Stochastic processes
- Convergence of Stochastic Processes - David Pollard
Mar 04, 2018
Foundations of Mathematics / Set Theory
- Sets, Relations, Functions - Ivo Düntsch, Günther Gediga
Foundations of Mathematics / Logic
- Predictive Arithmetic - Edward Nelson
- Proofs and Concepts: the fundamentals of abstract mathematics - Joy Morris, Dave Morris
- Mathematical Reasoning: Writing and Proof - Ted Sundstrom
Foundations of Mathematics / Category Theory
- 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
Number Theory / Surreal Numbers
- Yet Another Introductary Number Theory Textbook - Jonathan A. Poritz
Algebra / Abstract Algebra
- Abstract Algebra : Theory and Applications - Thomas W. Judson, Robert A. Beezer (Austin State University)
Algebra / Group Theory
- Group Theory - Pedrag Civitanovic
Algebra / Linear Algebra
- 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
Geometry and Topology / Differential Geometry
- Semi-Riemann Geometry and General Relativity - Shlomo Sternberg
Analysis / Real Analysis
- Basic Analysis: Introduction to Real Analysis - Jiří Lebl
- 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
Analysis / Functional Analysis
- Functional Analysis - Lawerence Baggett
Analysis / Ordinary Differential Equations
- Difference Equations To Differential Equations - Dan Sloughter
- Notes on Differential Equations - Bob Terrell
- Elementary Differential Equations - William F. Trench
- Elementary Differential Equations With Boundary Value Problems - William F. Trench
Probability and Statistics / Statistics
- Rough set data analysis: A road to non-invasive knowledge discovery - Ivo Düntsch, Günther Gediga
Mathematics for Computer Science / Stochastic processes
- 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
Mathematical Biology / Stochastic processes
- Mathematical Biology - Jeffrey Chasnov
Mathematical Physics / Stochastic processes
- Introduction to Continuum Mechanics - Ray. M. Bowen
- Mathematical Tools for Physics - James Nearing
- Mechanism of the Heavens (1831) - Mary Somerville
Mar 02, 2018
Foundations of Mathematics / Transition To Pure Rigour Math
- Basic Concepts of Mathematics - Elias Zakon
Number Theory / Surreal Numbers
- An Introduction to the Theory of Numbers - Leo Moser
Algebra / Linear Algebra
- A First Courses in Linear Algebra - Rob Breezer
Algebra / Lie Algebras
- Lie Algebras - Shlomo Sternberg
Geometry and Topology / Graph Theory
- Mathematical Illustrations - Bill Casselman
Analysis / Real Analysis
- Elementary Calculus: An Approach Using Infinitesimals - Professor H. Jerome Keisler
- Mathematical Analysis Vol I - Elias Zakon
- Mathematical Analysis Vol II - Elias Zakon
Probability and Statistics / Statistics
- Concepts and Applications of Inferential Statistics - Richard Lowry
Feb 11, 2018
Books
- Multivariable Calculus - G. Cain, J. Herod (Georgia Tech)
Number Theory / Algebraic Number Theory
- A Course In Algebraic Number Theory - Robert Ash
Algebra / Analytic Number Theory
- A Course in Universal Algebra - S. Burris, H.P. Sankappanavar
- A Course in Commutative Algebra - Robert Ash
Algebra / Abstract Algebra
- Elements of Abstract and Linear Algebra - E.H. Connell (University of Miami)
- Abstract Algebra: The Basic Graduate Year - Robert Ash
Algebra / Linear Algebra
- Elementary Linear Algebra - Keith Matthews
Combinatorics / Lie Algebras
- generatingfunctionology - Herbert Wilf
Geometry and Topology / Graph Theory
- A=B - M. Petkovsek, H. Wilf, D. Zeilberger
- Elements - Euclid
- Euclid's Elements Redux - Daniel Callahan
Geometry and Topology / Differential Geometry
- The Geometry and Topology of Three-Manifolds - W. Thurston
Analysis / Real Analysis
- MIT OpenCourseWare Lectures on Calculus - G. Strang
Analysis / Complex Analysis
- Complex Analysis - G. Cain (Georgia Tech)
Analysis / Partial Differential Equations
- Linear Methods of Applied Mathematics - E. Harrell, J. Herod (Georgia Tech)
Probability and Statistics / Probability Theory
- An Introduction to Probability and Random Processes - Gian-Carlo Rota, Kenneth Baclawski
Dec 21, 2017
Books
Nov 29, 2017
Probability and Statistics / Statistics
- Theory of Statistics - James E. Gentle (George Mason University)
Nov 17, 2017
Probability and Statistics / 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
Signal processing / Stochastic processes
- 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
- Linear algebra, signal processing, and wavelets. A unified approach. - Øyvind Ryan (University of Oslo)
Nov 10, 2017
Algebra / Linear Algebra
- Linear Algebra - Jim Hefferon
Aug 15, 2017
Blogs
- 3blue1brown - Animated Maths
Jun 30, 2017
Blogs
- BetterExplained - Maintained by Kalid Azad
- ILoveMaths - For grades 6 thru 12 in K-12 system
Jun 26, 2017
Books
Jun 22, 2017
Foundations of Mathematics / 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
- Conway names, the simplicity hierarchy and the surreal number tree - Philip Ehrlich
May 23, 2017
Foundations of Mathematics / Logic
- An Introduction to Formal Logic - P.D. Magnus (University at Albany)
- Language, Proof, and Logic - Jon Barwise, John Etchemendy
Algebra / Group Theory
- Notes on Group Theory - Mark Reeder
Algebra / Linear Algebra
- Linear Algebra and Matrices - Martin Fluch
Analysis / Real Analysis
- Real Analysis for Graduate Students - Richard F. Bass
- Modern Real Analysis - William P. Ziemer (Indiana University)
Analysis / Complex Analysis
- Complex Analysis - Donald E. Marshall
May 20, 2017
Books
- Calculus: Basic Concepts for High Schools - L.V. Tarasov
Apr 18, 2017
Probability and Statistics / Probability Theory
- Probability and Statistics Cookbook (⭐2.1k) - Matthias Vallentin (UC Berkeley)
Feb 11, 2017
Encyclopedia
Sep 25, 2016
Probability and Statistics / Statistical Learning
- Reinforcement Learning: An Introduction - Richard S. Sutton, Andrew G. Barto
Sep 15, 2016
Algebra / Linear Algebra
Sep 07, 2016
Learn to Learn
Aug 09, 2016
Probability and Statistics / Statistics
- NIST Handbook of Statistical Methods - Resource on practical statistics directed towards scientists and engineers.
Aug 04, 2016
Probability and Statistics / Statistics
- 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.
Apr 26, 2016
Books
Apr 11, 2016
Misc
- Paul's Online Math Notes - Paul Dawkins (Lamar University)
- List of electronic textbooks - Marcel B. Finan (Arkansas Tech University)
Jan 25, 2016
Probability and Statistics / Statistics
- Glossary of Data Modeling - AI Access
Sep 05, 2015
Probability and Statistics / Probability Theory
- The Only Probability Cheatsheet You'll Ever Need - William Chen
Sep 02, 2015
Learning Platforms
Questions and Answers
- MathOverflow - for professional mathematicians
Encyclopedia
Books
- Basics of Algebra, Topology, and Differential Calculus - Jean Gallier (University of Pennsylvania)
Misc
Foundations of Mathematics / Set Theory
- An Introduction to Set Theory - William A. R. Weiss
Foundations of Mathematics / Logic
- 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
Foundations of Mathematics / Category Theory
- Introduction to Category Theory and Categorical Logic - Thomas Streicher
- An Introduction to Category Theory - Harold Simmons
Foundations of Mathematics / Homotopy Type Theory
Number Theory / Analytic Number Theory
- Elements of Analytic Number Theory - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk)
- Analytic Number Theory - Lecture Notes based on Davenport’s book - Andreas Strömbergsson
Algebra / Abstract Algebra
- Algebraic Methods - F. Oggier
- An Undergraduate Course in Abstract Algebra - Robert Howlett
Algebra / Group Theory
- Group Theory - J.S. Milne
- Notes on Finite Group Theory - Peter J. Cameron
Algebra / Linear Algebra
- Fundamentals of Linear Algebra - James B. Carrell
- Vector Space Theory - Robert Howlett
Algebra / Galois Theory
- Galois theory - Miles Reid
Combinatorics / Lie Algebras
- 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
Combinatorics / Graph Theory
- Graph Theory: Lecture Notes - Christopher Griffin
- Graph Theory - Reinhard Diestel
Geometry and Topology / Graph Theory
- Fundamentals of Geometry - Oleg A. Belyaev
Geometry and Topology / 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)
Geometry and Topology / Algebraic Geometry
- 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)
Geometry and Topology / Topology
- Introduction to Topology - Alex Küronya
- Introductory Topology - Jim L. Brown
- General Topology - Pierre Schapira (Paris VI University)
- General Topology - Jesper M. Møller
Geometry and Topology / 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
- Introduction to Real Analysis - William F. Trench (Trinity University, Texas)
- Real Analysis - C. McMullen
Analysis / Functional Analysis
- Functional Analysis Lecture Notes - T.B. Ward (University of East Anglia)
- Functional Analysis - Alexander C. R. Belton
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 / 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 - Joseph C. Watkins (University of Arizona)
Probability and Statistics / 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
Numerical Analysis / Stochastic processes
- 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
Aug 31, 2015
Foundations of Mathematics / Set Theory
- Set Theory and Foundations of Mathematics - Sylvain Poirier
Foundations of Mathematics / Category Theory
- Category Theory - Steve Awodey (Carnegie Mellon University)
- Category Theory - B. Pareigis
Number Theory / Surreal Numbers
- Elementary Number Theory: Primes, Congruences, and Secrets - William Stein
- A Course on Number Theory - Peter J. Cameron
- A Computational Introduction to Number Theory and Algebra - Victor Shoup
Number Theory / 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)
Number Theory / Analytic Number Theory
- Introduction to Analytic Number Theory - A.J. Hildebrand (University of Illinois)
- Analytic Number Theory - Otto Forster (LMU Munich)
Algebra / Abstract Algebra
- Introduction to Modern Algebra - David Joyce (Clark University)
Algebra / Ring Theory
- Foundations of Module and Ring Theory - Robert Wisbauer (University of Düsseldorf)
Algebra / Galois Theory
- An Introduction to Galois Theory - Andrew Baker (University of Glasgow)
- Fields and Galois Theory - J.S. Milne
Analysis / Real Analysis
- An Introduction to Real Analysis - John K. Hunter (University of California at Davis)
- Elementary Real Analysis - Thomson, Bruckner
- Lecture Notes in Real Analysis - Eric T. Sawyer (McMaster University)
Analysis / 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
Analysis / Complex Analysis
- 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
Analysis / Functional Analysis
- An Introduction to Functional Analysis - Laurent W. Marcoux (University of Waterloo)
- Functional Analysis: Lecture Notes - Jeff Schenker (Michigan State University)
- Topics in Real and Functional Analysis - Gerald Teschl
- Functional Analysis - Christian Remling
Analysis / 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
Analysis / Ordinary Differential Equations
- 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
Analysis / 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)
Probability and Statistics / Statistical Learning
- Statistical Learning Theory - Percy Liang