 The Expected Number of Rising Sequences After a Shuffle [PDF]  Peter Doyle
A paper taking up Brad Mann's derivation of his simple expression for the expected number of rising sequences in a deck after a shuffle, which involved lengthy gymnastics with binomial coefficients. Doyle provides a short derivation. A PostScript file
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 Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces  David W. Henderson; Cornell University
A book that presents a series of problems. Most of the chapters start intuitively and are accessible to a general reader with no particular mathematics background; however, the discussions were written for mathematics majors and mathematics teachers and
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 Experimental Mathematics  A. K. Peters, Ltd.
A refereed journal devoted to experimental aspects of mathematical research. Browse full articles or abstracts, in PostScript of DVI, dating back to 1992's Volume 1. Also, read the journal's statement of philosophy and publishability criteria, subscription
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 Experimentàlis Hunlap (hun meg nem) a Titkos Tudományokról  Ferenc Molnár
New geometric discovery (site is in Hungarian).
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 Expert Choice
Analytic Hierarchy Process (AHP) and other decision support software for strategic planning and operations research.
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 Explaining Mathematics  Joel Feinstein
Ideas and praxis by a lecturer at the University of Nottingham (UK). Feinstein's blog posts, which date to December, 2008, have included "How and why we do proofs" and "Problems using LaTeX seminar class with pdflatex" and "Feedback on the use of IT in
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 Explicit Approaches to Modular Abelian Varieties  William Stein
Stein's Ph.D. thesis (Berkeley, 2000). An investigation of the Birch and SwinnertonDyer conjecture, which ties together the constellation of invariants attached to an abelian variety. The author attempts to verify this conjecture for certain specific
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 Exploring the Space of Cellular Automata  Langton, Hayden, Gutowitz, Carr, Fraser
Cellular automata (CA) are discrete space/time logical universes, obeying their own local physics according to given rules. Space in CA is partitioned into discrete volume elements called "cells" and time progresses in discrete steps. Each cell of space
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 Extended Finite Element Methods, Level Set Methods and Meshless Methods in Computational Mechanics  Stéphane Bordas
Describes my research in computational mechanics, geomechanics, fracture mechanics, meshless and extended finite element methods, plasticity, and aerospace castings.
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 The Extreme Science and Engineering Discovery Environment
Supercomputers, collections of data, new tools, and other integrated advanced digital resources and services for scientific research. See, in particular, the Education and Outreach Service of the Extreme Science and Engineering Discovery Environment (XSEDE),
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 Factasia: Mathematics  Roger Bishop Jones
Math essays organized into three categories: general (threads in the web of mathematics and reuse and abstraction); real numbers (a logical development, some history, and computing with reals); and history (a short history of rigour in mathematics, classical
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 FA Functional Analysis (Front for the Mathematics ArXiv)  Univ. of California, Davis
Functional Analysis preprints, from the 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. Search by keyword or browse by topic.
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 Famous Curves Applet Index  MacTutor Math History Archive
From Astroid, Cardiod, Catenary, and Cayley's Sextic to the Trisectrix of Maclaurin, Tschirnhaus' Cubic, Watt's Curve, the Witch of Agnesi  and many more  click on the name of a curve to experiment with some of its associated curves.
(Your browser
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 Famous Curves Index  MacTutor Math History Archive
Links to pages illustrating more than 60 mathematical curves, with information on their history and associated curves. Anyone with the Mathematical MacTutor system or a Javaenabled browser can investigate these curves and their associated curves interactively.
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 Fano Varieties and Extremal Laurent Polynomials  Coates, Tom; Corti, Alessio; Galkin, Sergey; Golyshev, Vasily; Kasprzyk, Al
This research collaboration blogs about the creation of a directory of all possible shapes and geometric building blocks in the universe  the equivalent of a periodic table of the elements for three, four, and fivedimensional shapes. Along the way,
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 Fast Marching Methods and Level Set Methods  J. A. Sethian, University of CaliforniaBerkeley
Fast Marching Methods and Level Set Methods are numerical techniques that can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together. The techniques have a wide range of applications, including
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 The FBI Fingerprint Compression Standard  Chris Brislawn
A summary, with examples, of the Federal Bureau of Investigation's image coding standard for digitized fingerprints, developed and maintained by the FBI, Los Alamos National Lab, and the National Institute for Standards and Technology. The standard is
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 Federal Geographic Data Committee (FGDC)  Federal Geographic Data Committee (FGDC)
An interagency committee that promotes the coordinated use, sharing, and dissemination of geospatial data on a national basis. Search for data in the National Spatial Data Clearinghouse; browse related information in registered Clearinghouse Websites,
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 Feigenbaum's Constant  Anders Skovsted Buch
A picture showing a fraction of the Feigenbaum tree.
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 FElt (Finite ELemenT)
A free system for finite element analysis; this site provides an overview of some of its features. Contents: general overview of the FElt system components; example problems that demonstrate what kinds of problems FElt can solve, how FElt can help you
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 Fermat Computer Algebra System  Robert H. Lewis
Fermat is a computer algebra system that does graphing, and symbolic and numerical calculations. Fast and economical of space, the main version is oriented toward polynomial and matrix algebra over the rationals and finite fields; Smith normal form; polynomial
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 Fermat Project Description  Hanson, Kaplan, Heng; Center for Innovative Computer Applications (CICA)
Images, movies, videos, publications, presentations. An animation presents a popularized introduction to Fermat's Last Theorem. Threedimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical
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 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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 FeynmanKac Formulae: Genealogical and Interacting Particle Systems with Applications  Pierre Del Moral
Description of a published book on FeynmanKac 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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 The Feynman Lectures on Physics  California Institute of Technology
Free online edition of the book by Richard Feynman, Robert B. Leighton, and Matthew Sands, based on the Nobel Prize winner's lectures presented in the early 1960s at Caltech. Volume I mainly addresses mechanics, radiation, and heat; Volume II, electromagnetism
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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
Tongueincheek 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 leadingedge research in the mathematical sciences, advancement in mathematics education, enhanced graduate and postdoctoral 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 squarefree gaps and an algorithm for their computation
 Louis Marmet
This page reports the results of a search for first occurrences of squarefree 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 trihexaflexagon 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 SolidSolid Mixing; Competition Between Chaos and Order; LiquidLiquid Mixing; Mixing in 3D Flows; Mixing in Cell Culture Systems; SolidLiquid 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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 The Flyspeck Project  Tom Hales
In pursuit of a formal proof of the Kepler Conjecture. The Flyspeck Project uses the Objective CAML programming language to investigate the density of a packing of congruent spheres in three dimensions. Start with the fact sheet.
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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 Online 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 twentyfirst 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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 A Formula Based Approach to Arithmetic Coding  Arun (Siara Logics [cc])
An explanation of the mathematical foundation of arithmetic coding. With comparisons to Huffman coding and ShannonFano coding, feedback from public forums, and screenshots of spreadsheets showing the placement of letters in compressed value.
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