Theory
1,949 items in 14 lists
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Quantum Field Theory davidtong.org
David Tong's Cambridge master's-level lecture notes, problem sheets, HTML text, and recorded lectures on classical fields, quantization, Dirac fields, and quantum electrodynamics.
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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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Graph Theory cs.unibo.it
Reinhard Diestel.
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Type Theory and Functional Programming cs.kent.ac.uk
Simon Thompson.
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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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Notes on Differential Geometry and Lie Groups cis.upenn.edu
Jean Gallier (University of Pennsylvania).
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Algebraic Geometry cis.upenn.edu
Jean Gallier, Stephen S. Shatz (University of Pennsylvania).
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Chaos: Classical and Quantum chaosbook.org
Maintained technical webbook on dynamical systems, periodic orbits, deterministic chaos, statistical mechanics, and quantum chaos.
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Introduction to Probability chance.dartmouth.edu
Charles M. Grinstead, J. Laurie Snell.
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Chalkdust Magazine chalkdustmagazine.com
Independent magazine for mathematically curious readers, with free expository articles, interviews, puzzles, and downloadable issues.
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Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications ccrma.stanford.edu
Julius O. Smith III (Stanford University).
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How to Prove It: A Structured Approach (3rd Edition) cambridge.org
Paid textbook by Daniel J. Velleman.
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A Guide to Complex Variables cambridge.org
Paid textbook by Steven G. Krantz.
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Algebraic Statistics for Computational Biology cambridge.org
Paid textbook edited by Lior Pachter and Bernd Sturmfels.
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Calculus Made Easy calculusmadeeasy.org
Silvanus P. Thompson (1910).
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Complex Analysis cain.math.gatech.edu
G. Cain (Georgia Tech).
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Online Mathematics Textbooks cain.math.gatech.edu
Index of freely available mathematics textbooks maintained at Georgia Tech.
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Multivariable Calculus cain.math.gatech.edu
G. Cain, J. Herod (Georgia Tech).
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Byrne's Euclid c82.net
Interactive web edition of Oliver Byrne's color-coded presentation of Euclid's first six books.
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Open Logic Textbook builds.openlogicproject.org
collaborative effort, main contributors listed here.
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Brilliant brilliant.org
Interactive, problem-based lessons in foundational mathematics, probability, and related quantitative subjects.
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Bridges bridgesmathart.org
Annual conference on mathematical connections in art, music, architecture, and culture.
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Lecture Notes in Algebraic Topology bookstore.ams.org
Paid textbook by James F. Davis and Paul Kirk.
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An Introduction to Complex Analysis and Geometry bookstore.ams.org
Paid textbook by John P. D'Angelo.
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b=M²L bm2l.github.io
Barcelona Mathematics and Machine Learning colloquia on the interaction between mathematics and machine learning, with multi-year editions and recorded talks.
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Group Theory birdtracks.eu
Predrag Cvitanović.
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BetterExplained betterexplained.com
Maintained by Kalid Azad.
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Logic and Proof avigad.github.io
Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn.
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Galois Theory arxiv.org
Tom Leinster (University of Edinburgh).
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Foundations of Constructive Probability Theory arxiv.org
Yuen-Kwok Chan.
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Seven Sketches in Compositionality: An Invitation to Applied Category Theory arxiv.org
Brendan Fong and David I. Spivak (MIT).
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Harmonic Analysis Lecture Notes arxiv.org
Richard S. Laugesen (University of Illinois at Urbana-Champaign).
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Theory of Statistics archive.math.arizona.edu
Graduate notes by Joseph C. Watkins on measure-based probability, decision theory, estimation, testing, and hierarchical models.
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Lectures on Statistics archive.math.arizona.edu
Free text by William G. Faris covering inference, Bayesian methods, regression, principal components, and linear models.
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Intuitionistic Type Theory archive-pml.github.io
Per Martin-Lof.
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Functional Analysis: Lecture Notes apps.math.msu.edu
Jeff Schenker (Michigan State University).
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Applied Combinatorics appliedcombinatorics.org
Mitchel T. Keller, William T. Trotter.
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AMS Open Math Notes ams.org
Free course notes, textbooks, and research expositions hosted by the American Mathematical Society.
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Notices of the American Mathematical Society ams.org
Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research.
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Bulletin of the American Mathematical Society ams.org
Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic.
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Almost Fun almostfun.org
Free interactive middle- and high-school mathematics lessons, practice problems, and teacher resources from a nonprofit organization.
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Analytic Combinatorics algo.inria.fr
Philippe Flajolet, Robert Sedgewick.
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Algebraic Geometry agag-gathmann.math.rptu.de
Andreas Gathmann (RPTU).
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Stochastic Processes adembo.su.domains
Amir Dembo (Stanford University).
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