Math
Mathematics: proofs, geometry, calculus, linear algebra, probability, statistics, and math explained visually.
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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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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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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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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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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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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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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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edX edx.org
University and professional mathematics courses, with audit and paid options varying by course.
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Galois Theory eclass.uoa.gr
Ian Stewart.
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Numerical Analysis for Engineers ece.uwaterloo.ca
University of Waterloo course with lectures, assignments, projects, and MATLAB material on numerical methods for engineers.
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Proofs and Concepts: the fundamentals of abstract mathematics deductivepress.ca
Joy Morris, Dave Morris.
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Dexter Chua dec41.user.srcf.net
Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more.
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Advanced Linear Algebra: Foundations to Frontiers cs.utexas.edu
Online text by Robert van de Geijn and Margaret Myers on algorithms for advanced numerical linear algebra.
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Discrete Differential Geometry cs.cmu.edu
Keenan Crane.
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Ordinary Differential Equations: Lecture Notes cs.bgu.ac.il
Eugen J. Ionascu.
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Coursera coursera.org
University and industry mathematics courses, with access and payment varying by course.
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Sets, Relations, Functions cosc.brocku.ca
Ivo Düntsch, Günther Gediga.
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Complex Analysis complex-analysis.com
Juan Carlos Ponce Campuzano.
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Crux Mathematicorum by Canadian Mathematical Society cms.math.ca
Challenging problems for secondary and undergraduate students, including an Olympiad Corner.
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Basics of Algebra, Topology, and Differential Calculus cis.upenn.edu
Jean Gallier (University of Pennsylvania).
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