 The Distribution of the Knight  the Theoretical Research Institute
For every given starting point in the knight's tour problem, evaluate every
possible path that visits each square exactly once, and then count how many
solutions exist. Illustrations and calculations of the distribution of solutions
and dead ends across
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 Divide and conquer for quantum computers  Ivars Peterson  Science News Online
In theory, quantum computations can be speeded up significantly by letting many quantum computers work together in parallel on data encoded as particles in an entangled quantum state.
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 Divine Proportions: Rational Trigonometry and Geometry  N. J. Wildberger, Wild Egg Books
Divine Proportions describes a new way of thinking about trigonometry and Euclidean geometry. It shows how to develop both subjects in a completely algebraic, or rational, way, without any need for transcendental concepts or functions. As a result the
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 Divisibility Criteria  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A definition of some divisibility criteria, and their derivation from modulo arithmetic, with links to related pages.
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 Division by Three [PDF]  John Conway, Peter Doyle
A formal proof that it is possible to divide by three. This assertion is easy to prove using the axiom of choice, but becomes a much more difficult problem if the axiom of choice is not allowed (as is the case here). From this proof, and the much simpler
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 Division by Zero  Dave Richeson
A blog about "math, puzzles, teaching, and academic technology." Posts, which date back to September of 2008 and sometimes introduce original applets, have included "Volumes of ndimensional balls," "Albrecht Dürer's ruler and compass constructions,"
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 Divisor Plot  Jeffrey Ventrella
"We hear of primes described as the 'building blocks' of all numbers. Let's turn that concept on [its] head. Instead, let's think of primes as the negative spaces behind complex objects. Imagine a series of picket fences stacked in front of each other.
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 Divulgaciones Matemáticas  La Universidad del Zulia
Archives of the biannual Spanishlanguage research journal dating back to 1993. Most issues contain research papers (artículos de investigación), articles about teaching (artículos sobre enseñanza), expository and historical
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 DIY Calculator  Clive (Max) Maxfield and Alvin Brown
Order the book How Computers Do Math, or preview its table of contents. The book's interactive laboratories guide you in the creation of a simple calculator program to run on your DIY Calculator; its accompanying CDROM contains a virtual "DoitYourself
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 D. J. Bernstein
Courses, research articles (in dvi format), and a list of available software, listed by a professor of mathematics and computer science at the University of Illinois. Pages are also listed by topic. Also at ftp://koobera.math.uic.edu/www/djb.html.
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 Dmitry Gokhman
Papers (Hardy fields; Differential fields of complex germs; Applied mathematics), Class lecture notes and summaries, code (IGF, LibPS 2, Python, Perl, TeXtool 2.12a), courses, translations, guests.
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 DNA Adds Up  Ivars Peterson (MathLand)
Calculating that 0 + 0 = 0, 1 + 0 = 1, and 0 + 1 = 1 is normally no big deal. When the calculations are done in the lab using DNA molecules, however, these elementary manipulations look considerably more interesting. In the July 12 [1996] Science, a team
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 DNA, Computers, and Killer Apps  Ivars Peterson (MathLand)
When computer scientists look at DNA, they see information storage and processing. They view the four bases of DNA as something akin to the zeros and ones of the binary code by which computers store and process information. They look for algorithms, theorems,
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 Documenta Mathematica  Ulf Rehmann
Documenta Mathematica is open to all mathematical fields and is refereed in the traditional manner. Tables of contents for past issues are available in dvi.gz, dvi, and ps.gz formats, and you can view or download entire volumes.
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 Dodecahedron Measures  Paul Kunkel
An investigation of the formulas of the surface area and volume for the dodecahedron. With icosahedron extensions.
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 Does March Madness need a timeout?  J. Travis  Science News Online
Suggestions about the effects of circadian rhythms, daily cycles of physiological activity that every organism experiences, and changes in time zone (causing 'jet lag'), on sports teams.
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 Donald Coxeter, Mathematician and Geometer  Great Canadian Scientists (GCS)
Harold Scott MacDonald Coxeter, Professor Emeritus, Math Dept., Univ. of Toronto, is best known for his work in hyperdimensional geometries and regular polytopes  geometric shapes that extend into the 4th dimension and beyond. In 1926 he discovered a
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 Don Hatch's Home Page  Don Hatch
Hyperbolic tessellations shown in various stages of truncation, and represented by their Schlafli symbols. Java applets explore hyperbolic tessellations, a magic Rubik'slike cube in four dimensions, polygon reciprocation (dual), modern portfolio theory
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 Don Knuth's Home Page  Donald E. Knuth, Stanford University
From the author of The Art of Computer Programming. "Computer Musings" chronologically documents Knuth's informal lectures at Stanford. It also links to Musings Online, digitized versions of videos from the lecture series that included Dancing Links;
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 Doodling and Miracles  Cut the Knot!, Alexander Bogomolny
Almost 100 years ago, Frank Morley proved a curious theorem from elementary geometry that had remained unknown until 1899. With time, the theorem became known in mathematical folklore as Morley's Miracle (Morley's Trisector Theorem is a more mundane term.)
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 The DOR: Home of the Direct Opposite Reverse  David P. Sterner
Sterner developed this shape, which he calls a geometric "missing link", and has applications as a lens.
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 Doron Zeilberger's Electronic Headquarters
Doron Zeilberger researches combinatorics using computer programs. The site is notable for his Opinions page; these opinions are wideranging but touch upon mathematics education, the use of computers, and the value of incomplete proofs. All of Zeilberger's
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 DOSE  G. B. Rubalsky
Determine Optimal Stocks Efficiently (DOSE) stands for the two software products DOSETRADE and DOSESERVICE, solving optimal inventory control problems for
trading enterprises and tech service enterprises. Both products work under Windows 95 and later,
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 Do software engineers need mathematics?  Keith Devlin (Devlin's Angle)
Software engineers don't use their college mathematics, but they make use of their college mathematics education every day. Brains are perhaps the world's best examples of an adaptive system. When we subject the human brain to an extended educational
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 Do the Math  Slate
A topical series about math in culture, politics, psychology, and other popular themes, many written by math professor Jordan Ellenberg. Articles, which date back to June, 2001, have included "Barry Bonds and the Placebo Effect," "Algebra for Adulterers,"
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 DotNumerics  José Antonio De SantiagoCastillo
DotNumerics is a Numerical Library for .NET written in C#. It provides routines for: Linear Algebra (CSLapack, CSBlas, CSEispack), Differential Equations, and Optimization.
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 Dot Patterns and Sierpinski Gasket  Cut the Knot!, Alexander Bogomolny
How many ways are there to define the Sierpinski gasket (also, the Sierpinski triangle)? The author has counted a respectable 9 but would be happy to learn of more. An applet with rows of digits or circles with colors corresponding to the digits shows
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 Dots and Boxes  Ivars Peterson (MathTrek)
The familiar pencilandpaper game of DotsandBoxes can be played on several different levels of sophistication. Elwyn Berlekamp posits that the game can be played on at least four different levels. "Players at any level consistently beat players at
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 Double Bubble Conjecture Proved (Math Chat)  Frank Morgan, MAA Online
Four mathematicians have announced a mathematical proof of the Double Bubble Conjecture: that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. In an address to the Undergraduate Mathematics Conference
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 Doug's Home Page  Douglas J. Ingalls
Includes mathematical interests such as images of fractal applications of Newton's Method and Gibb's Phenomena, with related programs in FORTRAN and BASIC, a discussion of the apparent depth problem in optics, and how multiple decisions can be reduced
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 Downloadable Preprints  Dept. of Applied Mathematics and Statistics, Stony Brook
Abstracts of papers (1991) written by faculty and students in the department. Complete papers are available in PostScript, and can be downloaded from this site. They are also available via anonymous ftp. Recent Ph.D. Theses are also available.
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 Downloads  Mac  Mathematics  CNET Download.com
Search this site to find a particular piece of software for the Mac, or browse their mathematics listings.
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 Downloads  PC  Mathematics  CNET Download.com
Search this site to find a particular piece of software for the PC, or browse their mathematics listings.
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 DPGraph (Dynamic Photorealistic Graphing)  David Parker
Software that allows you to: display multiple simultaneous dynamic photorealistic 3D implicit equalities and inequalities, and intersections of their volumes; spin, slice, and view timedependent (moving) photorealistic surfaces in real time; and construct
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 DPlot Plotting Software for Scientists and Engineers  David Hyde
A general purpose XY plotting program that features multiple scaling types, including linear, logarithmic, and probability scales, as well as several specialpurpose plots: tripartite grids (shock spectra), grain size distribution plots, and polar plots.
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 Draft version of MSC2000  European Mathematical Society (EMS)
The proposed revision of the 1991 Mathematics Subject Classification (MSC), the classification used by the two reviewing journals Mathematical Reviews (MR) and Zentralblatt für Mathematik (Zbl) since the beginning of 1991. MSC2000 is the result of
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 Drawing Tools  Shai Duvdevani
A growing group of .NET C# programs intended to make life easier for highschool and university students studying subjects such as math, computers and electronics. Each of these programs features saving and loading, so that sharing a drawing of logical
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 Drayton Analytics
A provider of optimisationrelated software to the Australian operations research community, and economic consulting services to the utility industries.
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 DreamCalc for Windows  Andy Thomas
A freeware scientific calculator for Windows, intended to replace standard handheld calculators. Fully featured range of math, scientific, statistical & financial functions. Supports natural fractions, complex numbers, basen logic, unit conversions
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 Dream Frequency .com
CGI web applications to calculate the factors of a number, calculate the prime numbers below a number, test a number for primality, calculate a word's position in the alphabetically sorted list, convert hex to ASCII, or convert temperature from celsius
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 The Drills To Play  Cut the Knot!, Alexander Bogomolny
An exploration of a detail found at the beginning of Kurt Godel's biography by John Dawson, how repetition and practice constitute an integral and necessary part of the learning process; that, by implication, one first conceives an idea, then proves it
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 Dr Len Fisher: Opening the Door to Science  Len Fisher
Fisher concentrates on the science of the everyday and making science accessible. His latest book is Rock, Paper, Scissors: Game Theory in Real Life. The site contains excerpts from his books as well as descriptions of his talks, articles about his work,
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 Dr. Rich's Page o' Math
Math problems in algebra, trigonometry, and calculus, posted more or less monthly (past puzzles, with solutions, are on the Web).
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 Drums That Sound Alike  Ivars Peterson (MathLand)
Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normalmode vibrations. He outlines the progress made on Mark Kac's
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 Drunkard Walk  Vladimir Gusev
An applet illustrating the onedimensional drunkard walk algorithm, which describes the process of molecular diffusion in an equilibrium gas.
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 Dr. Vogel's Gallery of Calculus Pathologies  Thomas I. Vogel; Dept. of Mathematics, Texas A&M University
In learning calculus, students develop intuitive ideas of such concepts as limit, continuity, differentiability, and so on, useful in dealing with simple examples, but potentially a hindrance to deeper understanding of the basic concepts of mathematical
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 DS Dynamical Systems (Front for the Mathematics ArXiv)  Univ. of California, Davis
Dynamical Systems 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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 DSP First: A Multimedia Approach  McClellan, Schafter, & Yoder
The CDROM portion of the book, containing, for each chapter: Demos  quicktime movies, sound files, etc. that help reinforce the concepts introduced in the text; Labs  MATLAB based laboratory exercises for indepth study of certain concepts and ideas
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 Duke University Math Union  Jadrian Miles
The Duke University Math Union (DUMU) writes and hosts the annual Duke Math Meet. Download PDFs of problems and solutions from meets dating back to 1998.
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 Dynagraph  Rouben Rostamian, University of Maryland, Baltimore County
Dynagraph is a 3D plotting utility for the X Window System. It draws 3D curves and surfaces representing mathematical expressions and numerical data, and allows for interactive rotation, zooming, and other manipulations of the displayed images. Read the
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