 The Topological Zoo  The Geometry Center
For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each
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 Topology Atlas  Shakhmatov and Watson; York University, Toronto, Ontario, Canada
A multipurpose center for electronic distribution of information related to topology, the mathematical study of surfaces, sometimes called "rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely
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 Topology Enters Mathematics  MacTutor Math History Archives
Linked essay describing the development of topology as a mathematical discipline from Euler through the early 20th century, including 17 references (books/articles).
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 The Topology of Chaos: Alice in Stretch and Squeezeland  Robert Gilmore, Marc Lefranc
Web site around the book The Topology of Chaos: Alice in Stretch and Squeezeland, which is devoted to topological analysis, a relatively new technique for extracting from chaotic data the topological signatures that determine the stretching and squeezing
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 Toposes, Triples and Theories  Michael Barr and Charles Wells
A revised and corrected version of the original (1983) Grundlehren der math is available free for downloading. Formats: DVI, PDF, PostScript.
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 Touch3D
A commercial Macintosh program for 3Dmodeling, concept design, industrial design, quick prototyping, mockups, packaging, scale models, physical renderings, production preparation, and unfolding/unwrapping. Touch3D is a complete 3D modeling/unfolding
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 The Traveling Salesman Problem (TSP)  Vasek Chvátal
The problem: given a finite number of cities and the cost of travel between each pair of them, find the cheapest way of visiting them all and returning to your starting point. This site includes a link to TSPLIB, Gerhard Reinelt's library of some hundred
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk
Triangle generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Instructions for
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk, Carnegie Mellon University
A triangle that generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Created
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 Triangles and Simplices (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on triangles and their higherdimensional generalizations (simplices), with a particular interest in partitioning regions into triangles, tetrahedra, or higher dimensional simplices, for various applications
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 Tricki  Gowers, Timothy; Sisask, Olof; and Frolkin, Alex
A wiki "repository of mathematical knowhow" that encompasses techniques ranging from the very general to those that concern particular subareas of mathematics. Browse problemsolving ideas by technique: for finding algorithms and algorithmic proofs,
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 Triogram Models  Hansen, Kooperberg, Sardy
An electronic version of a paper that introduces the Triogram method for function estimation using piecewise linear, bivariate splines based on an adaptively constructed triangulation. Java applets are included and a PostScript version of the entire paper
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 TSPBIB (Traveling Salesman Problem)  Pablo Moscato
A comprehensive listing of papers, source code, preprints, technical reports, etc., available on the Internet about the Traveling Salesman Problem (TSP) and some associated problems such as Fractal TSP Instances and VRP Instances, with links to software
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 TtH: a TeX to HTML translator  Ian H. Hutchinson
TtH translates TeX source that uses the Plain macro package, or LaTeX, into a near equivalent in HTML. It supports builtup fractions through HTML tables and mathematical symbols via the common extension tag [font face="symbol"] This enables semantically
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 TTMath  big online calculator  Tomasz Sowa
This big numbers library for C++ programming language performs mathematical operations with unsigned/signed integers and floating point numbers.
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 Turbulence, Chaos and Disordered Systems
A research group at the Eindhoven University of Technology in the Netherlands investigating turbulence, selforganization, chaos, and complexity in fluids. Descriptions of projects and full text of related thesis projects.
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 tutOR  Moshe Sniedovich and Angie Byrne
An online Operations Research (OR) tutorial system developing tutorial modules for specific OR topics, generic web tools to facilitate the construction of the OR modules, and research of the WWW technologies pertaining to this project. Modules for investigating
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 Twistors  What Are They?  Fedja Hadrovic
Notes briefly introducing the basic definitions of twistor theory, which might provide an "elegant formalism for both general relativity and quantum theory. Roger Penrose was first led to the concept of twistors in his investigation of the structure of
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 UC Berkeley Mathematics Department
Department info; a collection of the Berkeley [Ph.D.] preliminary exams; undergraduate study hints and survival guide; Notherian Ring (women in mathematics at Berkeley  includes WWW sites of interest to women mathematicians or grad students); Center
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 UC Berkeley Wavelet Group  Univ. of California at Berkeley
People, papers and publications.
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 UCLA Statistics Series: Preprints  Dept. of Statistics, University of California at Los Angeles (UCLA)
Papers on statistics that have been or will be submitted for publication.
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 UK Mirror Service  Joint Information Systems Committee, Higher Education Funding Councils, UK
Formerly HENSA, this national software archive service benefits the higher education and research community in the UK, funded by the Joint Information Systems Committee of the Higher Education Funding Councils. It maintains copies of electronic archives
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 UMI's Online Dissertation Services  Bell & Howell Information and Learning Company
UMI publishes and archives dissertations and theses; sells copies on demand; and maintains the definitive bibliographic record for over 1.4 million doctoral dissertations and master's theses. Information on preparing a dissertation for publication; finding
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 Uncertain Reasoning Group  Mathematical Logic  Dept. of Mathematics, Manchester Univ., U.K.
Homepage for a research group that investigates uncertain knowledge, how to represent it, and how to reason with it intelligently. People, research topics, seminars, Web resources.
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 Undergraduate Research Project in Random Tilings  Propp, Wilson
This project investigates different regions of random tilings of nxn squares with 1x2 dominoes: square, hexagon, fortress, dungeon, and Aztec diamond (the set of lattice squares completely inside a square tilted 45 degrees, discovering that the dominoes
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 The Uniform Polyhedra  Roman Maeder
A shortened version of the notebook Polyhedra.ma from Illustrated Mathematics [Gloor/Amrhein/Maeder95]. Uniform polyhedra have regular faces and congruent vertices. Allowing for nonconvex faces and vertex figures, there are 75 such polyhedra, as well
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 Union of Bulgarian Mathematicians (UBM)
A voluntary, creative, nonpolitical organisation whose purpose is to bring together people who are interested in Mathematics and Computer science or are involved in activities related to those fields. Contact info, meetings.
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 Univalg  eGroups, Inc.
Mailing list for use by the Universal Algebra community: subscribe here, or browse archive by month. (Universal Algebra is a technical branch of mathematics related to algebra and model theory.)
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 Universal Framework for Science and Engineering  Part 5: Category theory  Petr Ivankov
Software for use in Category Theory. The web site describes its function and operation.
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 The Universe of Discourse  Mark Dominus
Blog by the perl programmer who authored the book HigherOrder Perl and columns for The Perl Journal. Posts, which date back to November, 2005, have included "Fibonaccilike sequences," "More Liber Abaci," "The 3n+1 domain," "Biblical infallibility and
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 Université de Montréal  Département d'informatique et de recherche opérationnelle
In French, with some pages available in English as well: Fondé en 1966, le DIRO fut le second département d’informatique créé au Canada. La recherche de pointe de son corps professoral, l’ampleur de son activité académique et son rayonnement international
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 Unsolved Problems in Function Theory  Alexandre Eremenko
Files available in PDF format: Some constants studied by Littlewood; Meromorphic functions satisfying certain differential equations (E. Hille); Does every universe contain a place where you can stay at rest? (Lee Rubel); Holomorphic curves with few inflection
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 Unsolved Problems in Number Theory, Logic, and Cryptography  Tim Roberts
This site "concentrates only on problems which are easily understandable to the amateur.... explainable on a single screen (perhaps 200 words), using simple terminology." Read brief descriptions of open problems such as the Chromatic Number, the Collatz
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 Unstructured Grids (UG)  Institut für Computeranwendungen, UniversitU7auml;t Stuttgart
A flexible software tool for the numerical solution of partial differential equations on unstructured meshes in two and three space dimensions using multigrid methods. Its basic design is flexible enough to support many different discretization schemes.
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 Untangled  Mehta, Gayatri; Luo, Xiaozhong; et al.
Map and place logic blocks in this game to make more compact circuit layouts on a grid  and more efficient computer chips. Visually appealing graphs bring nodes closer to parents or children and untangle knots in graphs; behind the scenes, the accumulated
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 Using Sketchpad in Calculus  Doris Schattschneider, Moravian College
Three sketches about parametric equations of curves and a sketch about a (then) unsolved problem about perpendicular bisectors of quadrilaterals. Notes on Doris Schattschneider's presentation at the Sketchpad User's Group Meeting in Cincinatti in January
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 The Valuation Theory Home Page  FranzViktor Kuhlmann
A forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research. The home page offers: information about conferences and special events; names and email addresses of mathematicians working
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 Van der Waerden's Theorem  Nikolaos Konstantopoulos
The first steps of a computational approach, in multiple PDF documents.
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 Vasiliu Lucilius Homepage  Vasiliu Lucilius
Lucilius offers books of his research work in mathematics and mathematical physics.
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 Vector Land: An Introduction to 3D Vector Analysis  Paul Kirby
An online course offering Java applets and 3D graphics to teach 3D vectors and related topics such as 3D graphics programming and Newtonian mechanics. Contents: 3D Vectors; The Dot Product; The Cross Product; the Vector Equation of a Line; The Vector
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 VedicMaths.Org  Clive Middleton, Kenneth Williams, and Mark Gaskell
Learn about the ancient system of mathematics of the Vedas through interactive tutorials, research and teaching articles, recommended books and websites, a list of sutras translated from the original Sanskrit, a calendar of events, newsletter, and references
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 The Vertex Coloring Algorithm  Ashay Dharwadker
A polynomialtime algorithm for coloring the vertices of a graph with a new constructive proof of Brooks' theorem.
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 The Vertex Cover Algorithm  Ashay Dharwadker
A polynomialtime algorithm for finding minimal vertex covers in a graph.
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 Victor Shoup's Home Page
Download research papers on cryptographic protocols and on algorithms for solving problems in the area of number theory and algebra. The Courant Institute researcher freely offers a standard for publickey encryption, a simple LaTeX class for preparing
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 Video Mosaic Collaboration
"Watching students grow with math": this interactive collaboration portal integrates the Robert B. Davis Institute for Learning Video Collection (Rutgers University) — a video collection spanning two decades capturing mathematics learning experiences
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 Viewing Fourdimensional Objects in Three Dimensions  Barbara Hausmann; The Geometry Center
"Given that humans only visualize three dimensions, how is it possible to visualize four dimensional, or higher, objects? This question is the underlying idea of a short novel written over a hundred years ago by Edwin A. Abbot called Flatland. Flatland
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 Vignettes on automorphic forms, representations, Lfunctions, and number theory  Paul Garrett
Shoft downloadable "vignettes" in postscript format, and some with overviews in html. Also some vignettes on functional analysis.
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 Virtual Algebra Center  City College, CUNY
The home of the World Wide Algebra project. This international megaproject has several principal parts, including Algebraic Cryptography, The World of Groups, and The World of Polynomials. These include lists of open problems, conferences and seminars,
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 The Virtual Mathematics Center  Martindale's Graduate & Undergraduate Center
Preprints and online journals from a wide variety of math and science organizations; Online math dictionaries and encylopedias; mathematics courses, tutorials and databases; courses by subject; related mathematics information and databases.
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 Virtual Optima  Tony Hürlimann, Chris Hürlimann
A company offering consultancy, software (a linear programming language for mathematical optimization and modeling), and sport league schedules. It also offers a book of optimization problems, with sample problems available online.
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