Theory
1,949 items in 14 lists
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Notes on Combinatorics webspace.maths.qmul.ac.uk
Peter J. Cameron.
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Introduction to Applied Linear Algebra web.stanford.edu
Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA).
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Statistical Learning Theory web.stanford.edu
Percy Liang.
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A ProblemText in Advanced Calculus web.pdx.edu
John M. Erdman.
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Lecture Notes on Operator Algebras web.pdx.edu
Free graduate notes by John M. Erdman on Hilbert-space operators, Banach algebras, spectral theory, C*-algebras, compact operators, and K-theory.
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Surreal Numbers and Games web.mit.edu
Introductory notes on Conway's surreal numbers and their connection with combinatorial game theory.
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Basic Combinatorics web.math.utk.edu
Carl G. Wagner (University of Tennessee).
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Predictive Arithmetic web.math.princeton.edu
Edward Nelson.
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General Topology web.math.ku.dk
Jesper M. Møller.
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Evan Chen web.evanchen.cc
MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more.
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Introduction to Probability vfu.bg
Dimitri P. Bertsekas, John N. Tsitsiklis (MIT).
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Differential Equations users.math.msu.edu
Gabriel Nagy.
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Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods user.math.uni-bremen.de
Specialized notes by Alfred Schmidt and Arsen Narimanyan on adaptive finite element methods.
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Metamath us.metamath.org
Minimal formal language and proof verifier with explicit, inspectable proofs built from simple foundations.
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Lectures in Basic Computational Numerical Analysis uknowledge.uky.edu
Archived University of Kentucky textbook by J. M. McDonough, focused on computational methods for differential equations.
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Paul's Online Math Notes tutorial.math.lamar.edu
Free notes, examples, and practice problems for algebra, calculus, and differential equations, by Paul Dawkins at Lamar University.
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Algebraic Statistics tore.tuhh.de
Karl-Heinz Zimmermann.
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The Math District themathdistrict.com
Free guides and videos covering prealgebra, algebra, geometry, trigonometry, statistics, calculus, and technical mathematics.
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Interactive Linear Algebra textbooks.math.gatech.edu
Dan Margalit and Joseph Rabinoff.
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Elementary Real Analysis textbooks.aimath.org
Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner.
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A First Course in Linear Algebra textbooks.aimath.org
Robert A. Beezer.
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A First Course in Complex Analysis textbooks.aimath.org
Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka.
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AIM Open Textbook Initiative textbooks.aimath.org
Open mathematics textbooks organized by course and evaluated by the American Institute of Mathematics editorial board.
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An Introduction to Measure Theory terrytao.files.wordpress.com
Terence Tao (UCLA).
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QED - an interactive textbook teorth.github.io
Terence Tao.
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Mathematical Reasoning: Writing and Proof tedsundstrom.com
Ted Sundstrom.
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Talking Maths in Public talkingmathsinpublic.uk
Biennial conference for mathematics communicators in the United Kingdom.
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Categories and Groupoids tac.mta.ca
P. J. Higgins.
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Abelian Categories tac.mta.ca
Peter Freyd.
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Abstract and Concrete Categories: The Joy of Cats tac.mta.ca
Jiri Adamek, Horst Herrlich, George E. Strecker.
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Toposes, Triples and Theories tac.mta.ca
Michael Barr, Charles Wells.
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Basic Concepts of Enriched Category Theory tac.mta.ca
G. M. Kelly.
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The Calculus of Functions of Several Variables synechism.org
Dan Sloughter.
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SymPy sympy.org
Python library for symbolic algebra, calculus, equation solving, matrices, and code generation.
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Symbolab symbolab.com
Online solver with step-by-step solutions, graphing, calculators, and practice tools. Some solution steps and study features require a paid plan.
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Precalculus stitz-zeager.com
Carl Stitz, Jeff Zeager.
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Statistical Thinking for the 21st Century statsthinking21.org
Russell A. Poldrack.
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UCLA Statistical Methods and Data Analytics stats.oarc.ucla.edu
Tutorials and examples for R, Stata, SAS, and SPSS.
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Statistics Done Wrong statisticsdonewrong.com
Alex Reinhart.
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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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The Stacks Project stacks.math.columbia.edu
Maintained by Aise Johan de Jong (Columbia).
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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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