- Fermat's Last Theorem - BBC Online - Horizon
About Andrew Wiles and the solving of FLT - with a link to a long programme transcript.
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- FermiEffect.com - Alice Caton
Links to biographies of Enrico Fermi and his granddaughters, computers and chaos theory, Fermi questions, and the Fermi paradox.
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- Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications - Pierre Del Moral
Description of a published book on Feynman-Kac path measures and their genealogical and interacting particle interpretations, with a range of applications including statistical physics, biology, and advanced engineering sciences. The site features PostScript
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- FFTW - Matteo Frigo and Steven G. Johnson
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data. Download FFTW; read about its features; subscribe to its mailing list for announcements.
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- A Field Guide to the Orbifolds (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
Tongue-in-cheek hints for learning how to classify the 17 types of symmetry patterns in the Euclidean plane. "...information presented in this section has been gleaned from a cryptic manuscript discovered among the personal papers of John Conway after
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- The Fields Institute for Research in Mathematical Sciences - The Fields Institute for Research in Mathematical Sciences
The Institute's mandate includes programs devoted to leading-edge research in the mathematical sciences, advancement in mathematics education, enhanced graduate and post-doctoral training opportunities, and developing partnerships with industry to encourage
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- Fields Medals and Rolf Nevanlinna Prizes - The International Mathematical Union (IMU)
Information about these mathematics awards, with lists of recipients.
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- The Fifth Taxicab Number is 48988659276962496 - David W. Wilson
An article on the search for the smallest integer that can be expressed as a sum of two positive cubes in 5 distinct ways, up to order of summands. The nth taxicab number is the least number which can be expressed as a sum of two positive cubes in n distinct
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- Figshare
"Get credit for all your research" with Figshare, which allows researchers to publish their data in a citable, searchable and sharable manner. Figshare's creative commons licensing especially facilitates the sharing of null results, thereby avoiding publication
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- Financial Mathematics, Financial Engineering and Risk Management Workshop - FinMath.com @ Chicago
All about Mathematical Finance and Derivatives - new books, journals, seminars, conferences, workshops.
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- Find OpenCourseWare with OCW Search - Pierre Far
An independent search engine that indexes all the course materials published freely online by universities that participate in the OpenCourseWare (OCW) initiative, including the Massachusetts Institute of Technology (MIT) and Stanford University. Search
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- Fine Structure Constant, alpha - James G. Gilson
Solution to a 20th century mystery: Feynman's conjecture of a relation between alpha, the fine structure constant, and pi. Includes the formula for alpha and some of its consequences.
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- Finite Canonical Commutation Relations - Bill Hammel
A working paper on finite canonical commutation relations (FCCR) nxn matrices as local kinematical replacement for CCR, and construction of REPS of CCR by pxp matrices over Galois fields. Contents include truncated creation and annihilation operators,
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- The Finite Element Circus - Richard S. Falk, Rutgers University
A regular conference devoted to the theory and applications of the finite element method, and related areas of numerical analysis and partial differential equations. Dates and locations, talks and poems, and a mailing list.
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- Finite Element Mesh Generation - Robert Schneiders
Mesh generation is an interdisciplinary area within numerical analysis that includes mathematicians, computer scientists, and engineers from many disciplines. This page is intended to build a bridge between theory and applications. People and research
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- Finite Rank Torsion Free Modules Over Dedekind Domains - E. Lee Lady; University of Hawaii
A book that discusses abelian group theory as not just another variety of group theory but the study of modules over principal ideal domains, a highly specialized branch of commutative ring theory. Postscript and DVI versions. Chapters: Modules Over Commutative
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- Finnish Mathematical Society (SMY)
A society for mathematics professionals and students. Introduction and membership information. More information is available in Finnish.
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- First occurrences of square-free gaps and an algorithm for their computation
- Louis Marmet
This page reports the results of a search for first occurrences of square-free gaps using an algorithm based on the sieve of Eratosthenes. The source code is supplied.
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- Flexagon - Magnus Enarsson
"A flexagon is a polygon folded from paper with a very remarkable quality: you can turn it inside out to make it reveal hidden surfaces." History, including the original discovery of the tri-hexaflexagon by Arthur H. Stone, as he folded strips of paper
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- Fluid Mechanics, Chaos and Mixing - Julio M. Ottino, Chemical Engineering Dept., Northwestern University
Research Interests of the Chaos and Mixing Group include: Granular Flows and Solid-Solid Mixing; Competition Between Chaos and Order; Liquid-Liquid Mixing; Mixing in 3-D Flows; Mixing in Cell Culture Systems; Solid-Liquid Mixing; and Geometric Aspects
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- FlyBase: A Database of the Drosophila Genome - Berkeley & European Drosophila Genome Projects
A searchable database of maps, genes, transposons, aberrations, stocks; genome projects, references, people, and images (body parts).
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- fMath: Mathematics on Web - Ionel Alexandru
fMath is a free Flash and Javascript library for displaying mathematics on the web: display equations in your site, edit the equations online, display graphs in your site.
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- Folding and Unfolding - Eric Demaine
A series of pages detailing research and findings in origami, including: fold and cut, folding silhouettes and wrapping polyhedra, map folding, unfolding polyhedra, folding polygons into polytopes, linkages, protein folding, hinged dissections, hyperbolic
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- FOLDOC: Free On-line Dictionary of Computing - Denis Howe
A searchable dictionary of acronyms, jargon, programming languages, tools, architectures, operating systems, networking, theory, mathematics, telecoms, institutions, companies, projects, products, history, in fact anything to do with computing - and broad
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- Forget 'Back to Basics.' It's Time for 'Forward to (the New) Basics.' - Keith Devlin (Devlin's Angle)
What is the best way to prepare our children for life in the twenty-first century? The first thing to realize is that the nation needs only 3 or 4 percent of the population to be highly skilled in mathematics. Of the remainder, hardly any will ever need
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- Formula Sheet - Timothy Setterfield
Formula Sheet gets images of formulae or copies them to LaTeX or Microsoft Word, and lets you upload, organize, share, render, and store them all in one place.
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- Formulator MathML Suite - Hermitech Laboratory
MathML authoring and educational software, video processing and digital signage. MathML editors can insert clean mathematical notation into your documents or web pages, and the educational component can be used to print jigsaw puzzles, dominoes, and more.
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- 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 four-coloring 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, 20-22 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, non-standard 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 q-series 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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- 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 high-performance 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 non-trivial 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 three-year 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 e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alg-geom, funct-an, dg-ga, q-alg, auto-fms, cd-hg, MAGNUS, Several Complex
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- Frustration Solitaire - Doyle, Grinstead, Snell
A paper on the rank-derangement 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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- Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras - Gerald Albrecht
The introductory section of a paper collecting some of the author's mathematical thoughts. Some problems are still open, and the literature about this specific subject is very scarce. The complete paper is available as a PDF file.
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