Theory
1,949 items in 14 lists
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Rocq Prover rocq-prover.org
Open-source interactive theorem prover and dependently typed programming language for mechanized mathematics and verified software.
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Book of Proof richardhammack.github.io
Richard Hammack (Virginia Commonwealth University).
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General Topology rexresearch1.com
Stephen Willard.
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Introduction to Continuum Mechanics rbowen.engr.tamu.edu
Ray M. Bowen.
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Introduction to Real Analysis ramanujan.math.trinity.edu
William F. Trench (Trinity University, Texas).
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Real Analysis for Graduate Students r-bass.scholar.uconn.edu
Richard F. Bass.
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Calculus and Linear Algebra. Vol. 2 quod.lib.umich.edu
Wilfred Kaplan, Donald J. Lewis.
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Calculus and Linear Algebra. Vol. 1 quod.lib.umich.edu
Wilfred Kaplan, Donald J. Lewis.
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Quanta Magazine quantamagazine.org
Features latest research breakthroughs in an accessible style for non-experts.
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An Introduction to Stochastic Processes in Continuous Time pub.math.leidenuniv.nl
Flora Spieksma (Leiden University).
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ProofWiki proofwiki.org
Collaborative repository of mathematical definitions, lemmas, and proofs.
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Probabilistic Machine Learning probml.github.io
Introductory and advanced books by Kevin Murphy, with free draft PDFs, code, figures, exercises, and teaching resources.
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Language, Proof, and Logic, Second Edition press.uchicago.edu
Paid textbook by Dave Barker-Plummer, Jon Barwise, and John Etchemendy.
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The Princeton Companion to Mathematics press.princeton.edu
Paid reference edited by Timothy Gowers, June Barrow-Green, and Imre Leader.
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Yet Another Introductory Number Theory Textbook poritz.net
Jonathan A. Poritz.
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Fundamentals of Geometry polly.phys.msu.ru
Free geometry text by Oleg A. Belyaev.
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Computability - An introduction to recursive function theory poincare.matf.bg.ac.rs
Nigel Cutland (University of Hull).
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Set Theory on the Stanford Encyclopedia of Philosophy plato.stanford.edu
Peer-reviewed overview of set theory with historical context and references.
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Algebraic Topology pi.math.cornell.edu
Allen Hatcher.
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Complex Analysis personalpages.manchester.ac.uk
Charles Walkden.
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Mathematical Illustrations personal.math.ubc.ca
Bill Casselman's guide to creating clear mathematical diagrams and illustrations.
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Fundamentals of Linear Algebra personal.math.ubc.ca
James B. Carrell.
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UBC CLP Calculus Textbooks personal.math.ubc.ca
Free textbooks, problem books, and source files for a four-course university sequence in differential, integral, multivariable, and vector calculus.
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A Short Introduction to Probability people.smp.uq.edu.au
Dirk P. Kroese (University of Queensland).
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Elementary Calculus: An Approach Using Infinitesimals people.math.wisc.edu
Professor H. Jerome Keisler.
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Complex Variables people.math.sc.edu
R. B. Ash, W.P. Novinger.
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Semi-Riemann Geometry and General Relativity people.math.harvard.edu
Shlomo Sternberg.
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Lie Algebras people.math.harvard.edu
Shlomo Sternberg.
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Theory of Functions of a Real Variable people.math.harvard.edu
Shlomo Sternberg.
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Advanced Calculus people.math.harvard.edu
Lynn Loomis, Schlomo Sternberg.
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Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness people.math.harvard.edu
D. E. Knuth.
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Probability and Stochastic Processes with Applications people.math.harvard.edu
Oliver Knill (Harvard University).
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Abstract Algebra: Harvard Extension people.math.harvard.edu
Benedict Gross.
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Advanced Real Analysis people.math.harvard.edu
Curtis T. McMullen.
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Measure and Integration people.math.ethz.ch
Dietmar A. Salamon (ETH Zürich).
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Introduction to Differential Geometry people.math.ethz.ch
Joel W. Robbin, Dietmar A. Salamon.
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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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Markov Chains and Mixing Times pages.uoregon.edu
David A. Levin, Yuval Peres, Elizabeth L. Wilmer.
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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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Mechanism of the Heavens (1831) openlibrary.org
Mary Somerville.
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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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The On-Line Encyclopedia of Integer Sequences oeis.org
Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane.
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