 Decibels (Math Chat)  Frank Morgan, MAA Online
Challenge: The Christian Science Monitor of July 8, 1999, reports that "according to the NRDC, the amount of ambient noise in the ocean may have increased by 10 decibels  in other words, 10fold  between 1950 and 1975." Is this correct?
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 Decimals and Logarithms in the Works? And a Dyer's Hand too?  Penn Leary
Shakespeare, Decimals and Logarithms: What did Shakespeare know about mathematics, particularly logarithms and the decimal system? And when did he know it? An article partly from Leary's book, The Second Cryptographic Shakespeare.
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 Decision Making Information  Model Education Systems Associates: MESA, Inc.
MESA specializes in the development, implementation and use of decision support systems and related quantitative information resources, especially quantitative tools for research, evaluation and policy analysis directed toward children and their living
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 Decision Tree for Optimization Software  Hans D. Mittelmann, P. Spellucci
Information on optimization software and optimization research, including links to a dictionary, tutorials, testcases, interfaces, and software.
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 Deep in the Jungles  Ivars Peterson (MathTrek)
Humans are predisposed to seeing order and meaning in a world that too often presents random choices and chaotic evidence. Random events sometimes get linked into a meaningful, though ultimately bogus, scenario... At the same time, the mathematics of
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 Defending the Roman Empire  Ivars Peterson (MathTrek)
Questions of military strategy can be handled mathematically. Charles S. ReVelle of Johns Hopkins University in Baltimore and Kenneth E. Rosing, recently retired from Erasmus University Rotterdam, describe their approach in the AugustSeptember American
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 The Definitive Four Fours Answer Key  David A. Wheeler
From 0 up to 40,000, whole number mathematical expressions that use only common mathematical symbols and exactly four 4s. Wheeler offers his solutions in three different formats: an abbreviated list of answers; a text file of results, mathematical expressions,
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 Deliberative Discourse Idealized and Realized: Accountable Talk in the Classroom and in Civic Life  Sarah Michaels, Catherine O’Connor, Lauren B. Resnick
An article in PDF format. Abstract: Classroom discussion practices that can lead to reasoned participation by all students are presented and described by the authors. Their research emphasizes the careful orchestration of talk and tasks in academic learning.
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 Dennis Stanton
Dennis Stanton is a professor at the University of Minnesota studying combinatorics and hypergeometric functions. Many of his papers are available online in PostScript and PDF formats. There are also exams and solutions from previous classes, and a complete
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 Density Functional Theory in Hydrodynamics
Density functional theory in hydrodynamics of a multicomponent multiphase
mixture. Density functional theory describes the multicomponent multiphase
mixture continuously without density jumps and interfacial surfaces.
Bulletin /Field of Application/
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 Department of Mathematics and Computer Science  North Carolina School of Science and Mathematics (NCSSM)
Learning materials for teachers and students include resources on algebra, advanced functions, and mathematical modeling; data sets used with the NCSSM textbook Contemporary Precalculus Through Applications; the AP Calculus Web Center; and Mathematics
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 Department of Science & Mathematics Education: Research and Development  Univ. of Melbourne, Australia
Read faculty research and learn about their projects and interests: children's understanding of statistical and probabilistic concepts; the negotiation of meaning in mathematics & science classrooms (The Classroom Project); the expression of algorithms
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 Dept. of Statistics  University of Illinois at UrbanaChampaign
Web pages generated by statistics courses; biographical sketches of faculty, staff, lab members, and graduate students; department newsletter. Graduate program admission requirements, degrees offered, courses, statistical consulting services, and The
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 Derivatives Page  Financial Pipeline
Derivatives are financial securities whose value is derived from another "underlying" financial security. Options, futures, swaps, swaptions, and structured notes are all examples of derivative securities. Derivatives can be used in hedging, protecting
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 Design, Analysis, Implementation, and Evaluation of Graph Drawing Algorithms  Petra Mutzel
Automatic Graph Drawing is a relatively new field in Computer Science. The task is to draw diagrams of objects and their relations in such a way that they are easy to read and understand. Applications are, e.g., animation of algorithms, data and flow
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 Design Ideas  Julie Coghill
A series of articles that discuss quilt design using proportion, asymmetry, and Pythagorean triples.
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 Designing a Sustainable Standardsbased Assessment System  Don Burger; Midcontinent Regional Educational Laboratory (McREL)
Designing and implementing a sustainable standardsbased system that consistently yields high student achievement involves more than setting and measuring academic goals. Changing to a standardsbased system provides an
opportunity to reexamine the
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 Designing Effective Professional Development: Lessons from the Eisenhower Program  U.S. Department of Education
The second report of the National Evaluation of the Eisenhower Professional Development Program, Part B (State and Local Activities), a multiyear evaluation being conducted by the American Institutes for Research (AIR) under a contract with the U.S.
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 Determinación Geométrica de los Números Primos y Perfectos  Omar E. Pol
Un breve ensayo en que "se describe la geometría que determina la distribución exacta de los números primos y también de los números perfectos. Se ilustra el texto con diagramas originales; se muestra el modelo principal
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 Detracking America's Schools: The Reform Without Cost?  Brewer, Rees, Argys; Phi Delta Kappan
The practice of grouping school students by level of ability, known as tracking, has long been used in American public schools. In recent years, opponents of tracking have argued that belowaverage students are hindered by being grouped together, while
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 Developing Algebraic Thinking  Suzanne Alejandre
Teacher lesson plan and student kinesthetic activities on the Traffic Jam activity and applet, as originally published in the inaugural (Fall, 2002) issue of ONMath, an electronic journal of the National Council of Teachers of Mathematics (NCTM).
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 The Development of Group Theory  MacTutor Math History Archives
Linked essay describing the rise and progress of group theory from the 18th through the 19th centuries, with references (books/articles).
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 Dice and Valentine's Day Symmetries (Math Chat)  Frank Morgan; Christian Science Monitor
A dice challenge from S. H. Logue: The six faces of four dice have these numbers on them: A 1 1 5 5 5 5 B 4 4 4 4 4 4 C 3 3 3 3 7 7 D 2 2 2 6 6 6. You and your opponent each choose one die to use throughout the game. Each round you both roll, and the
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 Dien dàn Toán hoc.net
A math site in Vietnamese.
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 Difference and Functional Equations  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to functional equations, those in which a function is sought which is to satisfy certain relations among its values at all points. For example, we may look for functions satisfying f(x*y)=f(x)+f(y) and
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 Differential Geometry  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to differential geometry, the language of modern physics and an area of mathematical delight. Typically, one considers sets which are manifolds (that is, locally resemble Euclidean space) and which come
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 Different Ways to Represent Numbers  Chad Lake
Online paper that discusses and illustrates counting in bases other than 10; converting to decimal; the Snake Algorithm (the algorithm, summary of binarytodecimal Snake Algorithm, decimaltobinary Snake, extending the Snake to other bases, and summary
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 Digital Manipulatives: New Toys to Think With  Resnick, Martin, Berg, Borovoy, Colella, Kramer, Silverman; MIT Media Laboratory
Manipulative materials such as Cuisenaire Rods and Pattern Blocks enable children to explore mathematical and scientific concepts such as number and shape through direct manipulation of physical objects. Resnick et al. have developed a new generation
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 Digital Mathematical Performance  Gadanidis, George; Borba, Marcelo; Hughes, Janette; et al.
Watch video, liveacted dramatic storyboards, and animations of how people "perform" mathematics: Flatland, "Help Me, Fermi," Should Parallel Lines Never Meet," "The Pleasure of Making 10" (linear equations), "The Waiter" (the missing dollar problem),
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 Digits, Squares, and Cycles  Ivars Peterson (MathTrek)
Fascinating patterns lurk among the digits of whole numbers. Pick a positive integer, such as 57. Square each of the digits, then add the squares together: 5^2 + 7^2 = 25 + 49 = 74. Do the same thing with the digits of 74: 7^2 + 4^2 = 49 + 16 = 65. Keep
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 Diophantine geometry in characteristic p: a survey  José Felipe Voloch
An article that appeared in Arithmetic Geometry, F. Catanese, ed., Symposia Mathematica XXXVII, Cambridge Univ. Press, 1997, pp. 260278. Introduction; Curves; Abelian varieties and their subvarieties; Diophantine Approximation in characteristic p; Omitted
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 Dipping math scores heat up debate over math teaching...  Bridget Murray, American Psychological Association (APA) Monitor
... psychologists differ over the merits of teaching children 'whole math'. An APA newsletter article that outlines the debate over the effectiveness of whole math, a demonstrative approach where manipulatives help children understand math concepts. "Some
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 Discoveries & Breakthroughs Inside Mathematics  American Mathematical Society (AMS)
Read articles and watch video news segments about the latest discoveries and applications of mathematics: "Do the Math Dance," "Mathematician Calms the Skies with Turbulence Detection Algorithm," "Become a Smarter Shopper," "The Science Behind Movie Magic,"
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 Discovering Geometry Newsletter  Key Curriculum Press
A free biannual publication providing information and teaching techniques for The Geometer's Sketchpad software package, the Discovering Geometry Newsletter is a resource for those interested in geometry and technology education. Download PDFs of past
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 Discover Magazine  The Walt Disney Company
The monthly magazine of science and technology. Covers space, biology, health, medicine, AIDS, computers, new technology, the environment, astronomy, ancient life, archeology, evolution, physics, mathematics, ecology, and more. Available online: selected
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 Discrete Fourier Series Transform  Eric Brasseur
A brief introduction to the discrete Fourier transform and its application to signal sampling. Also available in French.
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 Discussiones Mathematicae  Borowiecki; Technical University of Zielona Góra, Poland
Four journals: Differential Inclusions, Control and Optimization; General Algebra and Applications; Graph Theory; and Probability and Statistics. Information for each journal includes a general description, subscription information, list of editors,
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 Disorder in the Deck  Ivars Peterson (MathTrek)
About 30 years ago, tournament bridge players started using computershuffled rather than handshuffled decks. Almost immediately, there was an outcry protesting the apparently wild fluctuations in the distribution of cards of different suits in computerdealt
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 Distributed Maple  Wolfgang Schreiner; RISCLinz, Johannes Kepler Universität Linz
A system for writing parallel programs in the computer algebra system Maple, so that different computers in a network can perform parts of the same computation. The program may be downloaded here in .tar or .zip form. The manual, a README file, and papers
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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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 Dividing The Plane  Jim Loy
A line divides the plane into two pieces (regions). Draw another line. The plane is now divided into three or four regions. It is three regions if the lines are parallel, four if they intersect. A third line divides the plane into seven regions. Find
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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 with Roman Numerals  Jim Loy
Roman numeral division can be very easy or fairly difficult, depending on the two numbers. An example of division by pieces, and a general method using repeated subtraction.
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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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 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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 Dominique Foata
Dominique Foata is a mathematician specializing in combinatorics. Abstracts of his papers are available online, and they may be downloaded in .dvi, PostScript, or TeX formats. The site also contains a summary and errata for the textbook Calcul des Probabilités,
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