Math
Mathematics: proofs, geometry, calculus, linear algebra, probability, statistics, and math explained visually.
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Lecture Notes on Optimization people.eecs.berkeley.edu
Pravin Varaiya.
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Numerical Analysis (Second Edition) people.cs.uchicago.edu
Free second-edition textbook by L. Ridgway Scott on the theory and practice of numerical methods.
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Elementary Topology Problem Textbook pdmi.ras.ru
Oleg Viro.
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Proofs and Types paultaylor.eu
Jean-Yves Girard.
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OpenStax Mathematics openstax.org
Peer-reviewed, openly licensed textbooks for school and introductory college mathematics from Rice University.
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Elementary Algebra 2e openstax.org
Free one-semester textbook from OpenStax with web and PDF editions, worked examples, practice exercises, chapter reviews, and answer keys.
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OpenIntro Statistics openintro.org
Free introductory textbook for college courses and self-study, with datasets, labs, slides, videos, exercises, and accessible PDFs.
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Euclid's Elements Redux open.umn.edu
Open textbook by Daniel Callahan that presents Euclid with modern commentary and exercises.
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Discrete Mathematics: An Open Introduction open.umn.edu
Free fourth-edition undergraduate textbook by Oscar Levin, with inquiry activities, more than 750 exercises, solutions and hints, and coverage of proofs, graph theory, counting, sequences, and discrete structures.
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Waterloo Open Math open.math.uwaterloo.ca
Free university-level courseware with lessons, exercises, and immediate feedback from the University of Waterloo.
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Basic Concepts of Mathematics onlinebooks.library.upenn.edu
Elias Zakon.
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MIT OpenCourseWare ocw.mit.edu
Free MIT course materials, including notes, assignments, and exams for undergraduate and graduate mathematics.
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Calculus Open Textbook ocw.mit.edu
Gilbert Strang (MIT OpenCourseWare).
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Essential Coding Theory ocw.mit.edu
Free graduate MIT course on error-correcting codes, Hamming spaces, and the algebraic and complexity aspects of coding theory.
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Nonlinear Optimization ocw.mit.edu
Free graduate MIT course covering analytical and computational methods for unconstrained and constrained optimization.
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Mathematics for Computer Science ocw.mit.edu
Free MIT OpenCourseWare course with an open textbook, videos, notes, problem sets, and exams on proofs, discrete structures, counting, graphs, modular arithmetic, and discrete probability.
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Differential Geometry ocw.mit.edu
Rigorous undergraduate MIT OpenCourseWare course with lecture notes and problem sets centered on curves, surfaces, and curvature.
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Introduction to Representation Theory ocw.mit.edu
Free MIT course by Pavel Etingof with lecture notes and problem sets on representations of groups and algebras, categories, and quivers.
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Mathematics of Machine Learning ocw.mit.edu
Free graduate MIT course on the mathematical and statistical foundations of machine learning, with lecture notes, assignments, and problem-set solutions.
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Topics in Mathematics with Applications in Finance ocw.mit.edu
Free undergraduate MIT course covering bond mathematics, probability, portfolio methods, time series, stochastic processes, and quantitative finance.
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GNU Octave octave.org
Free environment for numerical computing, linear algebra, plotting, and MATLAB-compatible scripts.
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Introduction to Vectors and Tensors, Vol. 2: Vector and Tensor Analysis oaktrust.library.tamu.edu
Ray M. Bowen, C. C. Wang.
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Introduction to Vectors and Tensors, Vol. 1: Linear and Multilinear Algebra oaktrust.library.tamu.edu
Ray M. Bowen, C. C. Wang.
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NRICH nrich.maths.org
Free curriculum-linked problems, investigations, articles, and teacher guidance from the University of Cambridge for learners aged 3 to 18.
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nLab ncatlab.org
Collaborative research-level notes and expositions in category theory, homotopy theory, mathematical physics, and related areas.
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Lectures on Differential Geometry mysite.science.uottawa.ca
Wulf Rossmann.
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Introduction to Complex Analysis mtaylor.web.unc.edu
Michael Taylor.
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Mathematics Subject Classification 2020 msc2020.org
The standard subject taxonomy maintained by Mathematical Reviews and zbMATH.
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Lecture Notes in Real Analysis ms.mcmaster.ca
Eric T. Sawyer (McMaster University).
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Galois Theory mreid.warwick.ac.uk
Miles Reid.
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Mathematics for Machine Learning mml-book.github.io
Free textbook on the linear algebra, geometry, calculus, probability, and optimization needed to study machine learning.
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WooTube misterwootube.com
Video lessons by Eddie Woo covering secondary-school mathematics with an emphasis on conceptual understanding.
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Lecture Notes on Stochastic Processes mi.fu-berlin.de
Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin).
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Trigonometry mecmath.net
Michael Corral.
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Maxima maxima.sourceforge.io
Free computer algebra system for symbolic and numerical calculations, plotting, and scripting.
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Formal Logic maude.sip.ucm.es
Miguel Palomino.
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Wolfram Mathworld mathworld.wolfram.com
Reference articles on mathematical definitions, formulas, identities, and related concepts.
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MATLAB mathworks.com
Paid numerical computing environment by MathWorks.
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Lecture Notes: Measure Theory mathweb.ucsd.edu
Bruce K. Driver.
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On Stochastic Processes mathweb.tifr.res.in
K. Ito (Tata Institute of Fundamental Research).
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MathsJam mathsjam.com
Monthly local recreational mathematics and puzzle meetups, plus an annual gathering in the United Kingdom.
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Math Is Fun mathsisfun.com
Lightweight lessons and reference pages for school mathematics.
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MacTutor History of Mathematics Archive mathshistory.st-andrews.ac.uk
University of St Andrews archive of mathematician biographies, histories of mathematical topics, timelines, institutions, and related reference material.
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Complex Analysis maths.lth.se
Christer Bennewitz.
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Functional Analysis maths.lancs.ac.uk
Alexander C. R. Belton.
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An Introduction to Galois Theory maths.gla.ac.uk
Andrew Baker (University of Glasgow).
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Mathispower4u mathispower4u.com
More than 9,000 free, closed-captioned video lessons and worked examples organized from middle-school mathematics through calculus, linear algebra, differential equations, and statistics, by James Sousa.
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Mathigon mathigon.org
Interactive courses, activities, and visual explanations for school and early university mathematics.
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Mathematical Logic mathematik.uni-muenchen.de
Helmut Schwichtenberg.
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Category Theory mathematik.uni-muenchen.de
B. Pareigis.
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