Math
Mathematics: proofs, geometry, calculus, linear algebra, probability, statistics, and math explained visually.
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Analytic Number Theory mathematik.uni-muenchen.de
Otto Forster (LMU Munich).
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Introduction to Modern Algebra mathcs.clarku.edu
David Joyce (Clark University).
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Euclid's Elements (David Joyce edition) mathcs.clarku.edu
Complete web edition with diagrams, commentary, and references by David Joyce.
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Math Academy mathacademy.com
Paid adaptive platform with diagnostic assessment and mastery-based courses from fourth-grade mathematics through university topics.
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Math AI Seminar math.washington.edu
University of Washington research seminar on formalization, theorem proving, mathematical AI, and machine-learning applications in mathematics, with a multi-year event archive.
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A Course in Universal Algebra math.uwaterloo.ca
Free online edition of Stanley Burris and H. P. Sankappanavar's graduate text on universal algebra.
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Applied Stochastic Processes in science and engineering math.uwaterloo.ca
Matt Scott (University of Waterloo).
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An Introduction to Functional Analysis math.uwaterloo.ca
Laurent W. Marcoux (University of Waterloo).
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Elementary Number Theory math.utoledo.edu
W. Edwin Clark (University of South Florida).
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A=B math.upenn.edu
Marko Petkovšek, Herbert Wilf, and Doron Zeilberger on algorithms for proving hypergeometric identities.
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Elementary Applied Topology math.upenn.edu
Robert Ghrist (UPenn).
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Introduction to Numerical Analysis math.umd.edu
Undergraduate notes by Doron Levy on root finding, interpolation, approximation, numerical differentiation, and quadrature.
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A Concise Course in Algebraic Topology math.uchicago.edu
J. P. May.
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The CRing Project math.uchicago.edu
Open-source work-in-progress textbook introducing commutative algebra for readers with elementary abstract algebra, with an emphasis on foundations for algebraic geometry.
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Linear Algebra math.ucdavis.edu
David Cherney, Tom Denton, Andrew Waldron.
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Measure Theory math.ucdavis.edu
John K. Hunter (University of California at Davis).
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An Introduction to Real Analysis math.ucdavis.edu
John K. Hunter (University of California at Davis).
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An Introduction to Set Theory math.toronto.edu
William A. R. Weiss.
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Foundations of Algebraic Geometry math.stanford.edu
Ravi Vakil.
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Modern Real Analysis math.purdue.edu
William P. Ziemer (Indiana University).
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Functional Analysis math.ou.edu
Christian Remling.
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Introduction to Algebraic Topology math.muni.cz
Martin Cadek.
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Elements of Abstract and Linear Algebra math.miami.edu
E.H. Connell (University of Miami).
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Category Theory for Computing Science math.mcgill.ca
Michael Barr, Charles Wells.
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Complex Analysis math.ku.dk
Christian Berg.
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Category Theory in Context math.jhu.edu
Emily Riehl (Johns Hopkins University).
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Mathematical Biology math.hkust.edu.hk
Jeffrey Chasnov.
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Introduction to Topology math.colostate.edu
Free introductory notes associated with Renzo Cavalieri's Colorado State University topology course and compiled by students. Covers point-set topology, compactness, connectedness, surfaces, Euler characteristic, and the fundamental group.
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Lecture Notes in Measure Theory math.chalmers.se
Christer Borell.
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Linear Algebra Done Wrong math.brown.edu
Sergei Treil.
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Introduction to Topology math.bme.hu
Alex Küronya.
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Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis" math.berkeley.edu
George M. Bergman.
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Partial Differential Equations math.berkeley.edu
Lawrence C. Evans's concise survey of modern PDE theory from analytical, qualitative, and computational viewpoints.
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Lectures on Algebraic Statistics math.berkeley.edu
Mathias Drton, Bernd Sturmfels, Seth Sullivant.
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An Introduction to Riemannian Geometry matematik.lu.se
Sigmundur Gudmundsson (Lund University).
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Topics in Differential Geometry mat.univie.ac.at
Peter W. Michor.
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Theory of Statistics mason.gmu.edu
Advanced, actively revised text by James E. Gentle on probability, statistical models, estimation, testing, and asymptotic theory.
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Maple maplesoft.com
Paid computer algebra and numerical mathematics system for symbolic computation, visualization, and programming.
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Magma magma.maths.usyd.edu.au
Subscription-based computer algebra system for research in algebra, number theory, algebraic geometry, and combinatorics.
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Macaulay2 macaulay2.com
Research system for algebraic geometry and commutative algebra with specialized computational packages.
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Introduction to Stochastic Processes - Lecture Notes ma.utexas.edu
Gordan Žitković (University of Texas).
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Introduction to Logic logic.stanford.edu
Michael Genesereth, Eric J. Kao (Stanford University).
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Convergence of Stochastic Processes link.springer.com
Paid textbook by David Pollard.
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All of Statistics: A Concise Course in Statistical Inference link.springer.com
Larry Wasserman.
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Linear Algebra Done Right linear.axler.net
Sheldon Axler.
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Graph Theory : Interactive Algorithm Visualizer | Graph Theory Learning Platform learngraphtheory.org
Hadjoudj Mohammed Islam.
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Mathematics in Lean leanprover-community.github.io
Free textbook with examples and exercises for mathematicians learning Lean 4 and mathlib.
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Lean-related Conferences and Events leanprover-community.github.io
Maintained calendar and archive of conferences, workshops, and tutorials about Lean, mathlib, and formalized mathematics.
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Courses Using Lean leanprover-community.github.io
Maintained, filterable index of university courses that teach Lean or use it for mathematics, logic, programming, and formal verification.
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LeanDojo v2 leandojo.org
Open-source framework and benchmark data for training, evaluating, and deploying AI-assisted theorem provers for Lean 4.
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