Math
Mathematics: proofs, geometry, calculus, linear algebra, probability, statistics, and math explained visually.
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Harvard Statistics 110: Probability stat110.hsites.harvard.edu
Free probability course with a textbook, lecture videos, exercises, and an optional edX version by Joe Blitzstein.
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Functional Analysis spot.colorado.edu
Lawerence Baggett.
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Analysis of Functions of a Single Variable spot.colorado.edu
Lawerence Baggett.
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The Geometry and Topology of Three-Manifolds slmath.org
W. Thurston.
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Graph Theory: Lecture Notes sites.psu.edu
Christopher Griffin.
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Complex Analysis sites.math.washington.edu
Donald E. Marshall.
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Mathematics and AI sites.math.washington.edu
University of Washington Fall 2025 graduate course with public slides, Lean examples, projects, and readings on machine learning, formalization, autoformalization, mathematical discovery, and ethics.
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Probability: Theory and Examples sites.math.duke.edu
Rick Durrett (5th edition).
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Introduction to Algebraic Geometry sites.lsa.umich.edu
Igor V. Dolgachev.
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Commutative Algebra Notes sites.lsa.umich.edu
Free graduate course notes by Mel Hochster, from an introductory course through advanced topics such as Cohen-Macaulay rings, multiplicities, and étale maps.
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Algebraic Number Theory Course Notes sites.google.com
Matthew Baker (Georgia Tech).
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Singular singular.uni-kl.de
Computer algebra system for polynomial computations in commutative algebra, algebraic geometry, and singularity theory.
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AI for Mathematics and Theoretical Computer Science simons.berkeley.edu
Simons Institute and SLMath workshop archive with recorded talks on proof assistants, automated reasoning, machine learning, and mathematical discovery.
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A Computational Introduction to Number Theory and Algebra shoup.net
Victor Shoup.
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Mathematical Logic sgslogic.net
Stephen G. Simpson (Pennsylvania State University).
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Set Theory and Foundations of Mathematics settheory.net
Sylvain Poirier.
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Seeing Theory seeing-theory.brown.edu
Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang.
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Rocq Prover rocq-prover.org
Open-source interactive theorem prover and dependently typed programming language for mechanized mathematics and verified software.
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Book of Proof richardhammack.github.io
Richard Hammack (Virginia Commonwealth University).
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General Topology rexresearch1.com
Stephen Willard.
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Introduction to Continuum Mechanics rbowen.engr.tamu.edu
Ray M. Bowen.
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Introduction to Real Analysis ramanujan.math.trinity.edu
William F. Trench (Trinity University, Texas).
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Real Analysis for Graduate Students r-bass.scholar.uconn.edu
Richard F. Bass.
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Calculus and Linear Algebra. Vol. 2 quod.lib.umich.edu
Wilfred Kaplan, Donald J. Lewis.
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Calculus and Linear Algebra. Vol. 1 quod.lib.umich.edu
Wilfred Kaplan, Donald J. Lewis.
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An Introduction to Stochastic Processes in Continuous Time pub.math.leidenuniv.nl
Flora Spieksma (Leiden University).
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ProofWiki proofwiki.org
Collaborative repository of mathematical definitions, lemmas, and proofs.
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Probabilistic Machine Learning probml.github.io
Introductory and advanced books by Kevin Murphy, with free draft PDFs, code, figures, exercises, and teaching resources.
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Language, Proof, and Logic, Second Edition press.uchicago.edu
Paid textbook by Dave Barker-Plummer, Jon Barwise, and John Etchemendy.
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The Princeton Companion to Mathematics press.princeton.edu
Paid reference edited by Timothy Gowers, June Barrow-Green, and Imre Leader.
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Yet Another Introductory Number Theory Textbook poritz.net
Jonathan A. Poritz.
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Fundamentals of Geometry polly.phys.msu.ru
Free geometry text by Oleg A. Belyaev.
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Computability - An introduction to recursive function theory poincare.matf.bg.ac.rs
Nigel Cutland (University of Hull).
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Algebraic Topology pi.math.cornell.edu
Allen Hatcher.
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Complex Analysis personalpages.manchester.ac.uk
Charles Walkden.
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Mathematical Illustrations personal.math.ubc.ca
Bill Casselman's guide to creating clear mathematical diagrams and illustrations.
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Fundamentals of Linear Algebra personal.math.ubc.ca
James B. Carrell.
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UBC CLP Calculus Textbooks personal.math.ubc.ca
Free textbooks, problem books, and source files for a four-course university sequence in differential, integral, multivariable, and vector calculus.
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A Short Introduction to Probability people.smp.uq.edu.au
Dirk P. Kroese (University of Queensland).
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Elementary Calculus: An Approach Using Infinitesimals people.math.wisc.edu
Professor H. Jerome Keisler.
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Complex Variables people.math.sc.edu
R. B. Ash, W.P. Novinger.
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Semi-Riemann Geometry and General Relativity people.math.harvard.edu
Shlomo Sternberg.
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Lie Algebras people.math.harvard.edu
Shlomo Sternberg.
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Theory of Functions of a Real Variable people.math.harvard.edu
Shlomo Sternberg.
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Advanced Calculus people.math.harvard.edu
Lynn Loomis, Schlomo Sternberg.
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Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness people.math.harvard.edu
D. E. Knuth.
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Probability and Stochastic Processes with Applications people.math.harvard.edu
Oliver Knill (Harvard University).
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Abstract Algebra: Harvard Extension people.math.harvard.edu
Benedict Gross.
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Advanced Real Analysis people.math.harvard.edu
Curtis T. McMullen.
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Introduction to Differential Geometry people.math.ethz.ch
Joel W. Robbin, Dietmar A. Salamon.
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