 Foundations of Computational Mathematics
The FoCM's primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer. The meetings are unified
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 Foundations of Mathematics  Alex Sakharov
A collection of links to materials related to Foundations of Mathematics, organized as a book contents page, and intended to be a guide for studying the subject and a comprehensive Web reference. Naive Set Theory; Paradoxes; Formal Systems; Axiomatization;
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 Four Coloring Maps  Mario Stefanutti
Personal notes and ideas from a computer software engineer in pursuit of a "very easy pencil and paper proof of the four color problem." Posts, which date back to January, 2011, have included "Four color theorem: slow motion maps" and "Counting maps."
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 The Four Color Theorem  Robertson, Sanders, Seymour, Thomas; Georgia Tech
A brief summary of a new proof of the Four Color Theorem, with a fourcoloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas, illustrated using a map of the United States. Contents: History; Why a new proof?; Outline
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 Fractal Geometry: Mathematical Techniques, Algorithms and Applications  The Institute of Mathematics and its Applications (IMA)
The IMA conference on Fractal Geometry, 2022 September 2000, a forum for discussing the mathematical basis of fractal geometry, and the computer implementation of fractal algorithms and their applications to modelling and analysing complex processes
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 Fractal Image Encoding  Yuval Fisher; Institute for Nonlinear Science, University of California at San Diego
A page with links to a variety of information and resources on fractal image encoding and related topics: Bibliographies and Other References; Books  including Fisher's own Fractal Image Compression: Theory and Application to Digital Images; Conferences
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 Fractal Metaphysics Home Page  Christopher Sunami
A clearinghouse of (serious) materials on the web focused on the relationship between fractal geometry, chaos theory, and metaphysics. Essays, related sites, galleries, and recommended reading.
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 Fractal Music: Research, Publications, and Compositions by Harlan Brothers  Harlan J. Brothers
In 2003, Benoit Mandelbrot suggested to Harlan Brothers that he undertake a rigorous treatment of the subject of fractal music. Here is an overview of Brothers’ subsequent research, including papers, definitions, and examples.
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 Fractals (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
An extensive list of links to sites with information about fractals, classified by level and type of resource.
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 Fractals (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on fractals.
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 Fractional Tree Calculator  Henryk Trappmann
Fractional trees are a new kind of number (extra to quaternions, octonions, nonstandard reals, Conway numbers, etc.), an algebraic generalization of fractional numbers. Experiment with this web application
to get a first impression.
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 Frank Garvan
Frank Garvan is a mathematics professor at the University of Florida. His combinatorics research articles are available for download in PostScript and .dvi formats. A Maple package for qseries may also be downloaded. One may also find the syllabi
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 Frédéric Chyzak's Mgfun Project
Mgfun is a group of Maple packages intended for calculations with multivariate generating functions, in particular for their symbolic summation
and integration, and for the proof of special function and combinatorial identities. These packages include
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 Freakonometrics  Arthur Charpentier
Blog by a Montreal professor of actuarial science "addicted to R." Posts, which date back to March, 2007, have included "Dynamic dependence ordering for Archimedean copulas and distorted copulas," "Pricing catastrophe options in incomplete markets," "Estimation
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 Frederic Chyzak
Frederic Chyzak researches combinatorics and computer algebra, specifically holonomic functions. His thesis and other articles are available as abstracts and as PostScript files. Slides for a series of talks on holonomic functions and computer algebra
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 Free Complex Matrix and Vector classes  Abdon Pijpelink
Two C++ classes: implementations of a matrix and a vector of complex numbers. Free for everyone.
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 Freely Available Software for the Solution of Linear Algebra Problems  Jack Dongarra
Software for highperformance computers, available in source form for problems in numerical linear algebra, specifically dense, sparse direct and iterative systems and sparse iterative eigenvalue problems.
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 Free Mathematics Books  FreeTechBooks.com
Links to free mathematics books and lecture notes. Mostly in PDF and Postscript format.
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 FreeScience.info  Claudio Attaccalite
Mathematics section of a site providing free scientific books, mostly in PDF format.
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 Friedman Numbers  Erich Friedman
A Friedman number is a number that can be written in some nontrivial way using its digits, the operations +  * / ^ and concatenation of digits. For example, 25 and 126 are Friedman numbers, since 25 = 5^2, and 126 = 6 * 21. Page includes a list of all
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 FRISCO  A Framework for Integrated Symbolic/Numeric Computation  The Numerical Algorithms Group Ltd, Oxford UK
A threeyear project funded by the European Commission under the Esprit Reactive LTR Scheme, its aim to develop highly efficient, versatile polynomial solvers for industrial users. Much of the software produced during the project is available for download,
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 Front for the Mathematics ArXiv  Univ. of California, Davis
U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex
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 Frustration Solitaire  Doyle, Grinstead, Snell
A paper on the rankderangement problem, which asks for the number of permutations of a deck of cards such that each card is replaced by a card of a different rank, and which arises when computing the probability of winning the game of 'frustration solitaire'.
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 FullText Electronic Journals  TriUniversity Group of Libraries, Ontario, Canada
A collection useful for browsing the contents of a particular journal and for locating a specific article given the article citation (article title, author, journal title, volume, date published). (You cannot search by subject, so if you do not have
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 functionspaces  eGroups
Subscribe to and join a free discussion about functionspaces and related topics. From eGroups' Math discussion groups.
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 Fundamentals of Geometry  Oleg A. Belyaev
A work in progress to create a free online book on geometryfrom exposition of elementary absolute geometry based on Hilbert's axioms to more advanced topics. The site contains a current draft of the book. This text is also intended to provide math background
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 The Funnel Cosmology  Vladimir Trifonov; American Mathematical Society (AMS)
Haar Measure and Geodesics in Funnel Cosmology  direct computation of the geodesics in the funnel model. Cosmological shape, dark matter, accelerating expansion, etc.
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 Fuzzy Machine Learning Framework  Dmitry A. Kazakov
This fuzzy machine learning framework uses graph schemes, a variant of decision trees, to extend intuitionistic sets and represent not only uncertain, but also contradictory data within the same framework. The software provides both a library and a graphical
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 Fuzzy sets for Ada  Dmitry A. Kazakov
A free (GPL) implementation of fuzzy sets, intuitionistic fuzzy sets, fuzzy
numbers, linguistic variables and sets of linguistic variables.
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 Gallery of Mathematical Models  Arthur Sherman
"Gold standard" versions of published models, given as input files for xpp but also humanreadable ASCII files adaptable for use with other programs. BetaCell Models: Generic, CRAC Models I and II, SmolenKeizer, KeizerSmolen, ShermanKeizerRinzel
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 Gallery of Pseudospheres  Robert McLachlan
A short version of an article by Robert McLachlan, "A gallery of constantnegativecurvature surfaces," (Mathematical Intelligencer, Fall 1994, 3137) about "pseudospherical" surfaces, equally "saddleshaped" at each point, extensively studied in the
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 Gallica  Bibliothèque nationale de France
Une sélection de documents numérisés qui montrent la diversité des collections manuscrites de la Bibliothèque nationale de France: les oeuvres de Joseph Liouville, Augustin Cauchy, Joseph Fourier, Henri Poincaré, Janos
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 Galois Field Package for Mathematica  Ryoh FujiHara; University of Tsukuba
An explanation of the concept and design of the Galois field package. Start Up and Declarations; Variables; Mixed operations with integers or constants of the base field; Implemented functions; How to get the Package and its Manual.
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 Gambit  Theodore Turocy, Director
An opensource collection of tools for doing computation in game theory. Gambit lets you build, analyze, and explore game models.
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 GAMES Group  The University of Alberta
GAMES is a research group for Gameplaying, Analytical methods, Minimax search and Empirical Studies. It produces realtime programs for strategic game such as Amazons, Awari, Checkers, Chess, Domineering, Go, Hex, Lines of Action, Othello, Poker, RoShamBo,
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 Game Theory, Linear/NonLinear Programming  Math Forum
Links to some of the best Internet resources for game theory and linear or nonlinear programming: Web sites, software, Internet projects, publications, and public forums for discussion.
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 GAMS : Guide to Available Mathematical Software  National Institute of Standards and Technology (NIST)
A crossindex and virtual repository of mathematical software available to staff of the National Institute of Standards and Technology (NIST). Provides centralized access to abstracts, documentation, and source code of software modules that it catalogs.
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 GANG Discrete Library  Ian McIntosh; Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of discrete conformal maps as discrete integrable systems. A discrete conformal map is a map z : z^2 > p^1 with the property that the
crossratio of four adjacent points is constant... Illustrations show how a Riemann surface arises, considering
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 GANG Knot Library  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of Energy Minimizing Knots and Links. Select a knotimage or category to see more members of the knot's family. The catalog contains knots up to 8 crossings. 2,q torus knots and links; Rational link with two, three, and fourterm continued
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 GANG Symmetry Library  James M. Lawrence; Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
Symmetry detection software. Input file, sample output, graphs, and download. From the Center for Geometry Analysis Numerics and Graphics.
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 GAP: Groups, Algorithms, and Programming  GAP Group; UK, Germany, USA, Australia
A system for computational discrete algebra with particular emphasis on, but not restricted to computational group theory. GAP and its sources, including share packages, data library and a manual, are distributed freely, subject to conditions detailed
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 Gateway to Logic  Christian Gottschall; Dept. of Philosophy, Vienna
A collection of Webbased logic programs offering a number of logical functions. Client side processing (requires Java): sparse trees, alpha graphs (Peirce), Begriffsschrift notation (Frege), Polish notation, truth tables, normal forms, miscellaneous
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 Gb Home Page  Faugère
Faugère's GB package computes Gröbner basis of polynomials ideals and solves systems of algebraic equations. Best documentation is in French: GB est un systeme de Resolution de systeme d'equations algebriques.
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 Gene Abrams
Beamer files for seminars and colloquia on Leavitt path algebras, and activities related to mad veterinarian puzzles": "The Graph Menagerie: Abstract Algebra meets the Mad Veterinarian"; "The Graph Menagerie: Abstract algebra and the Mad Veterinarian"
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 General Algebraic Modeling System  GAMS
A highlevel modeling system for mathematical programming problems. It consists of a language compiler and a stable of integrated highperformance solvers. GAMS is tailored for complex, large scale modeling applications, and allows you to build large
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 Generalized Logistic Equation  Douglas J. Ingalls
A logistics equation is one of the simpler chaos equations. This site explores the property of the general equation with respect to immigration/emigration of the world's population. Includes graphs and a QBASIC program for generating logistic graphs.
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 The Generalized Theory of Life  Vyacheslav L. Kalmykov; Institute of Cell Biophysics, Russian Academy of Sciences
A paper that presents an integrally generalized theory or conceptualization of life that includes elements of an axiomatic approach and is physically interpretable, formulated as the result of attempts to invent a holistic system of creative synthetic
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 Genetic Algorithms Archive  Alan C. Schultz, Naval Research Laboratory
A repository for information related to research in genetic algorithms. Contents include: Calendar of ECrelated events; GAList Archive: back issues, source code, information; Links to other GArelated information; Links to EC research groups' home pages;
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 GeoLib: C++ and C# Computational Geometry Library  Matthew Minor, GeoLib
C++ and C# library with help and explanations for all agorithms and concepts used. Demo versions available.
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 Geometria descrittiva e modellazione 3d  Hasan Isawi
In Italian: Questo Sito vuole affrontare quella parte teorica della geometria
descrittiva tenendo conto della potenzialità degli odierni strumenti della
computer grafica.
Ovvero, in considerazione del fatto che una volta completata la costruzione
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