 Jazzing Up Euclid's Algorithm  Ivars Peterson (MathTrek)
Early in 2000, the journal Computing in Science & Engineering (CISE) published a list of the top 10 algorithms of the century. Many of the selections are now familiar, finely tuned, heavily used tools. The Metropolis algorithm for Monte Carlo methods,
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 Jon Kleinberg's Homepage  Jon Kleinberg, Department of Computer Science, Cornell University
Read Kleinberg's research on algorithms that exploit the combinatorial structure of networks and information. His work includes techniques for analyzing and modeling link structure in the World Wide Web and related information networks; discrete optimization
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 Karla Hoffman
A specialist in operations research and combinatorial optimization. Papers in PDF, PostScript, or HTML formats include articles on airline scheduling, set covering, and the traveling salesman problem. Resume and curriculum vitae and syllabus, project,
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 The Klein Project
Revisiting the intent of Felix Klein's Elementary Mathematics from an Advanced Standpoint on the centenary of its publication, this IMU/ICMIcommissioned project aims to produce a book for upper secondary teachers that communicates the breadth and vitality
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 Knight's Tour  Gunno Törnberg
Describes two methods for finding Knight's Tours (paths for a chess knight to visit every square on a chessboard), backtracking and Warnsdorff's Rule. Java applets demonstrate both methods.
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 LEDA Research  Michael Seel
LEDA is a library of the data types and algorithms of combinatorial computing. Try the OverTheNet Demo which allows you to play with some computational geometry algorithms provided by LEDA; download commercial or research packages and licenses; read
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 Lesson Plan Search  Google
Free math lesson plans that make use of Google Earth, Google Calendar, Exploring Computational Thinking, and other products and projects of the search engine company: Telling time & Google Calendar; Human Dimensions Project; Median of Latitude Data;
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 Levitated  Jared Tarbell
"Visual poetry and science fun narrated in an object oriented graphic environment." See, in particular, the generators in sketches and applications; and "open source," a library of fractals, cellular automata, spacefilling algorithms, "autofixing words,"
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 Liz's Research Interests  Liz Bradley, Department of Computer Science, University of Colorado
Artificial intelligence projects include Chaography, a pair of tools that use mathematics to generate choreographic variations: Chaographer, which uses a chaotic mapping to generate variations on a musical piece; and MotionMind, which uses machine learning
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 Marc Chamberland
A mathematician at Grinnell College interested in differential equations and dynamical systems. Resources for the 3x + 1 problem and the Jacobian Conjecture include papers to download in PostScript format and information and proceedings for related conferences.
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 Mathematical constants and computation  Xavier Gourdon and Pascal Sebah
How famous mathematical constants were computed in the past, and current ways of obtaining them: pi, e, the logarithmic constant, square root of 2, Euler's constant, and Apery's constant. Also algorithms (arbitrary precision computation; FFT based multiplication
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 Mathematical Entertainment  Eric Hiob, British Columbia Institute of Technology
Instructions for building a pinball table that demonstrates Pascal's Triangle. Also, notes on the Travelling Salesman Problem; Finding Areas Using the Monte Carlo Method; Important Numbers (pi and e); the Inside or Outside Problem; and the Roller Coaster
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 Mathematical Problems  Torsten Sillke
Some in German, most in English. Topics include graph theory, number theory, combinatorics (enumerations), geometry, algorithms and complexity, recreational mathematics, tiling and packing, dissections, probability, algebra, analysis. Also links to "MathNews"
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 Mathematics and Statistics: Academic Press  Elsevier
This imprint of Elsevier offers over 100 print and eBook titles in mathematics and statistics.
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 Mathematics  John Savard
A collection of essays and illustrations: pentagonal tilings, infinity (Cantor's theory of transfinite numbers), rotations of the dodecahedron, Archimedean solids, the fourth dimension (regular polytopes), Gödel's proof and the halting problem, and
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 Math Exercises
Interactive exercises, lessons, and worksheets to practice knowledge of whole numbers, integers, divisibility, fractions, exponents and powers, percentages, proportional reasoning, linear equations, quadratic equations, monomials, polynomials, special
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 Math Is Power Math Puzzles  National Action Council for Minorities in Engineering (NACME)
Six Shockwave games. CodeBreaker requires using trial and error to deduce the correct string of colored circles, given feedback on position and quantity. In Space Tag, two players take turns moving on a grid, one of them attempting to occupy the other's
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 The Math Less Traveled  Brent Yorgey
A blog "dedicated to exploring beautiful mathematics." Posts, which date back to March, 2006, have included "Proof by animation," "The Nuclear Pennies Game," "Recounting the Rationals," "Predicting Pi," "Square roots with pencil and paper," "Irrationality
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 The MathSite  David Gale
Hear, see, and do the pure mathematics of polygon dissections ("Dissecting Triangles and Squares") or the applied mathematics of sorting algorithms ("Sorting Bricks and Sticks"). Requires Flash and Java plugins.
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 METIS: Family of Multilevel Partitioning Algorithms  George Karypis
A family of programs for partitioning unstructured graphs and hypergraphs and computing fillreducing orderings of sparse matrices. Includes serial and parallel graph partitioning and sparse matrix ordering and serial hypergraph partitioning.
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 Michael Singer
Differential (and difference) Galois theorist, algorithmic analyst, and computer algebraist, and professor at North Carolina State University. Available here: books and papers, some in PDF, PostScript, or .dvi versions; course notes for Computational
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 Modulef: Methods and Tools for Scientific Computing  Michel Bernadou
The MODULEF project was dissolved on December 31, 1995. The members of this project created the GAMMA project and the MOSTRA preproject. Activity report of the project (1995) (French  abstract in English), research reports of the project, videos and
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 Monte Carlo Simulation Excel AddIn  Luciano Machain
An addin for Microsoft Excel, distributed as "emailware". SimulAr adds probability distribution functions to spreadsheets for performing Monte Carlo simulation and risk analysis under uncertainty conditions. Possibility of correlating variables. Fitting
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 Music by John Greschak  John Greschak
Platonic Dice: Dodecahedron, Platonic Dice: Hexahedron, Pentominoes, The Tower of Hanoi, and other music compositions based upon the mathematical properties of various objects. Listen with RealAudio or Midi.
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 My Speed Cubing Page  Jessica Fridrich
"Intended for those of you who can already solve [Rubik's] cube in a few minutes and want to get really fast." Content includes "20 years of speed cubing (a short historical narrative)," "Finger shortcuts," "Move algorithms to your subconsciousness,"
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 NEOS Guide (NetworkEnabled Optimization System)  The Optimization Technology Center
A thumbnail sketch, outlines of the major algorithms, and pointers to software packages on optimization and its various subdisciplines: integer programming, stochastic programming, network programming, bound constrained, nonlinearly constrained, linear
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 Neural network music composition by prediction  Michael C. Mozer
Exploring the benefits of psychophysical constraints and multiscale processing. In algorithmic music composition, a simple technique involves selecting notes sequentially according to a transition table that specifies the probability of the next note
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 A New Kind of Science  The Wolfram Institute, LLC
A forthcoming book by Stephen Wolfram (creator of Mathematica) arguing that the "rules" science searches for should include algorithms like those used in computer programs, not just mathematical equations. Site includes a summary, table of contents,
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 New York Group Theory Cooperative at CCNY
Genetic algorithms, open problems and preprints in combinatorial and geometric group theory, meetings, links, and MAGNUS, a free (GPL) graphically oriented system, based on Tcl/Tk, for computational group theory designed to allow for exploration and experimentation
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 Noga Alon
Noga Alon researches combinatorics, graph theory, their applications to theoretical computer science, combinatorial geometry and number theory, and the relationship of combinatorial algorithms and circuit complexity. Some of his papers, along with a
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 Numerical Problems (Algorithm Design Manual)  Steven S. Skiena
A chapter from the Algorithm Design Manual, by Steven S. Skiena. Specific algorithms: Solving Linear Equations; Bandwidth Reduction; Matrix Multiplication; Determinants and Permanents; Constrained and Unconstrained Optimization; Linear Programming; Random
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 Occam Press  Peter Schorer
"The skeptical mathematician is invited to improve upon the current implementations of the 3x + 1 strategy...." In addition to the Collatz conjecture, Schorer offers a simple proof of Fermat's Last Theorem, articles on Occam's Razor and programming,
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 Olimpíada Brasileira de Matemática  Sociedade Brasileira de Matemática (SBM)
The Olimpíada Brasileira de Matemática (OBM) is a competition open to all students enrolled in Brazil's fundamental or middle studies. Browse or download archived exam problems and solutions dating back to 1997. Read news about olympiads, or the journal
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 Open Problems  Jeff Erickson
Open problems, mostly in geometry, including folding, combinatorial, and algorithmic problems. Contents include: Existence Problems: Does Object X exist?
Combinatorial Problems: How complex is Object X? Algorithmic Problems: How fast can Problem X be
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 Pentium Bug Revisited  Ivars Peterson (MathLand)
The incident that triggered a barrage of ridicule occurred in the fall of 1994, a few months after Intel had introduced its Pentium microprocessor. The furor started with an email message from Thomas R. Nicely, a mathematician at Lynchburg College in
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 Philippe Flajolet
Philippe Flajolet researches the analysis of algorithms, analytic combinatorics, computer algebra, asymptotic analysis, special functions, random structures, and natural languages. An extensive collection of his articles, and the first chapters of
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 Pi: A Source Book  J. Borwein, SpringerVerlag
A complete history of pi, with resources for teachers for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three classes: a selection of the mathematical
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 The Problem of the Knight: A Fast and Simple Algorithm  Arnd Roth
Download a Mathematica notebook that discusses different algorithms for solving the Knight's Tour problem, finding a path for the chess knight that visits every square once. For an Introduction, Implementation, and Examples, visit Roth's MaxPlanckInstitut
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 Problem Solving Island  Samuel A. Rebelsky
Challenging openended word problems on the topics of games, such as Blockade, Finger Multiplication, and The Word Pyramid; puzzles such as Error Correction, Error Detection, The Fake Coin, Friday the 13th, and Leap Birthdays; and problems based on figures,
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 Problems with a Point  Education Development Center, Inc. (EDC)
A collection of problems designed to help students in grades 612 learn new mathematical ideas by building on old ones. Varying in difficulty and approaches, these problems are useful for teachers, students, parents, math clubs, homeschoolers, and others.
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 Project Based Learning Pathways  David Graser
A blog about real life projects suitable for college math courses such as algebra, finite math, and business calculus. Most of these applied math projects include handouts, videos, and other resources for students, as well as a project letter. Graser,
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 Projet Folium
Folium est un ensemble organisé d'articles sur les mathématiques, du cours aux biographies de mathématiciens célèbres, en passant par les exos les plus classiques et les théorèmes les plus puissants. Articles
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 The Quake Project  The Department of Civil and Environmental Engineering and the School of Computer Science at Carnegie Mellon University; and the University of Southern California's Southern California Earthquake Center (SCEC)
An NSF and DARPAfunded project developing the capability for predicting, by computer simulation, the ground motion of large basins during strong earthquakes, and using this capability to study the seismic response of the Greater Los Angeles Basin. Research
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 Quite BASIC  Nikko Strom
A JavaScript environment for coding in the classic BASIC programming language. Math projects include the Fibonacci Sequence, Fibonacci Squares, the Sieve of Eratosthenes, and Mandelbrot; puzzles include the Towers of Hanoi and variations of the Eight
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 Robert J. Lang Origami  Robert J. Lang
Lang has catalogued and diagrammed over 400 models, combining aspects of the Western school of mathematical origami design with the Eastern emphasis upon line and form. Read about origami mathematics, which mathematically describe the underlying laws
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 Scrambled Grids  Ivars Peterson (MathTrek)
The socalled baker's map, or transformation, in dynamical systems theory. One special case: Start with a square. Stretch it to twice its original length
while making it half as wide. Cut the result in half, and stack one half on top of the other to
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 Selected Recent Publications  George W. Hart
Areas of Hart's research and pointers to further information, including a bibliography of his publications. Links to pages on: Multidimensional Analysis; Nonintrusive Appliance Load Monitoring; Telecommunications Network Management; Viterbi Algorithm
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 Séminaire Lotharingien de Combinatoire  Institut für Mathematik, Universität Wien, Vienna, Austria
A joint seminar in Combinatorics for the Universities of Bayreuth, Erlangen and Strasbourg, as well as the other Universities along the Lotharingian boundaries. The Seminar hosts an international electronic journal carrying the same name, with abstracts
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 Solving the Quintic by Iteration [PDF]  Peter Doyle, Curt McMullen
This paper, which appeared in Acta Mathematica, gives explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm
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 Teaching Contemporary Mathematics Conference  North Carolina School of Science and Mathematics (NCSSM)
Papers and talks presented at the conference. Download PDF files of Geometry and Programming: The Forgotten and the Avoided; Student Investigations in Algebra 2 and Precalculus; The Mantid: An Extended Data Problem; Errors and Power in Significance Tests;
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