Theory
1,949 items in 14 lists
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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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Theorem Proving in Lean 4 lean-lang.org
Free official textbook on dependent type theory, propositions, tactics, inductive types, type classes, and constructing verified proofs in Lean 4.
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Lean lean-lang.org
Open-source interactive theorem prover and programming language based on dependent type theory, used for formal mathematics and software verification.
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A Brief Introduction to Algebraic Geometry ksda.ccny.cuny.edu
R.C. Churchill.
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Khan Academy khanacademy.org
Free, self-paced lessons and exercises from arithmetic through calculus and beyond.
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Abstract Algebra: Theory and Applications judsonbooks.org
Thomas W. Judson.
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Odds and Ends: Introducing Probability & Decision with a Visual Emphasis jonathanweisberg.org
Jonathan Weisberg.
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Group Theory jmilne.org
J.S. Milne.
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Fields and Galois Theory jmilne.org
J.S. Milne.
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Algebraic Number Theory jmilne.org
J.S. Milne.
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Algebraic Geometry jmilne.org
J.S. Milne.
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Basic Analysis: Introduction to Real Analysis jirka.org
Jiří Lebl.
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Notes on Diffy Qs: Differential Equations for Engineers jirka.org
Jiří Lebl.
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NIST Handbook of Statistical Methods itl.nist.gov
Resource on practical statistics directed towards scientists and engineers.
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Isabelle isabelle.in.tum.de
General-purpose interactive theorem prover with higher-order logic and set-theory environments for formalizing mathematics and computer science.
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Archive of Formal Proofs isa-afp.org
Refereed collection of Isabelle proof libraries, examples, and scientific developments maintained against current Isabelle releases.
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Information Theory, Inference, and Learning Algorithms inference.org.uk
David J. C. MacKay.
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Mathematics Today by Institute of Mathematics and its Applications ima.org.uk
News, opinions, and articles related to mathematics, so the reader stays updated.
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ILoveMaths ilovemaths.com
Mathematics lessons and activities for Indian classes 6 to 12.
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The Chaos Textbook: Mathematics in the age of the computer hypertextbook.com
Glenn Elert.
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Homotopy Type Theory hottheory.files.wordpress.com
Open textbook on homotopy type theory, univalent foundations, and higher-dimensional structures.
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Lecture Notes on Statistical Theory homepages.math.uic.edu
Undergraduate notes by Ryan Martin on estimation, likelihood, hypothesis testing, and Bayesian statistics, with some R examples.
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Linear Algebra hefferon.net
Jim Hefferon.
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The Elements of Statistical Learning hastie.su.domains
Trevor Hastie, Robert Tibshirani, Jerome Friedman.
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Linear Methods of Applied Mathematics harrell.math.gatech.edu
Evans M. Harrell II, James V. Herod (Georgia Tech).
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Think DSP greenteapress.com
Allen B. Downey.
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A Crash Course on the Lebesgue Integral and Measure Theory github.gold-saucer.org
Steve Cheng.
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Probability and Statistics Cookbook github.com
Matthias Vallentin (UC Berkeley).
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GeoGebra geogebra.org
Interactive mathematics suite for geometry, graphing, algebra, spreadsheets, statistics, and calculus.
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A Concise Course in Complex Analysis and Riemann Surfaces gauss.math.yale.edu
Wilhelm Schlag.
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Free Math freemathapp.org
Free, open-source software for recording, organizing, and reviewing digital mathematics homework without solving the problems automatically.
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Foundations of Signal Processing fourierandwavelets.org
Martin Vetterli, Jelena Kovacevic, Vivek K Goyal.
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forall x: Calgary (An Introduction to Formal Logic) forallx.openlogicproject.org
P.D. Magnus and Tim Button, remixed by Aaron Thomas-Bolduc and Richard Zach (Open Logic Project).
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Fundamentals of Numerical Computation fncbook.com
Online textbook by Tobin Driscoll and Richard Braun with Julia, MATLAB, and Python editions covering core numerical methods for linear systems, approximation, root finding, ODEs, and PDEs.
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Introduction to Algebraic Number Theory feog.github.io
F. Oggier.
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Algebraic Methods feog.github.io
F. Oggier.
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An Introduction to Formal Logic fecundity.com
P.D. Magnus (University at Albany).
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Feedback Systems: An Introduction for Scientists and Engineers fbsbook.org
Free textbook by Karl J. Åström and Richard M. Murray on modeling, feedback, stability, performance, state feedback, and control design.
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Active Calculus faculty.gvsu.edu
Matt Boelkins.
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Research and Lecture Notes fabricebaudoin.blog
Advanced notes by Fabrice Baudoin on stochastic analysis, differential geometry, and Dirichlet spaces.
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European Mathematical Society Magazine euromathsoc.org
The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items.
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Error Correction Zoo errorcorrectionzoo.org
Maintained reference database of classical, quantum, and hybrid error-correcting codes, with definitions, relationships, and references.
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Encyclopedia of Mathematics encyclopediaofmath.org
Reference articles on mathematical concepts, theorems, biographies, and applications.
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Wikibooks en.wikibooks.org
Community-authored collection of open mathematics textbooks and instructional books.
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An Introduction to Probability and Random Processes ellerman.org
Gian-Carlo Rota, Kenneth Baclawski.
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An Introduction to Statistical Signal Processing ee.stanford.edu
Robert M. Gray, Lee D. Davisson.
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edX edx.org
University and professional mathematics courses, with audit and paid options varying by course.
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