 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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 ExploreLearning.com  ExploreLearning
A library of virtual manipulatives called "Gizmos", primarily for grades 312, in math and science. Math topics include the major strands of instruction according to national standards, as well as developmental math, college algebra and collegelevel
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 Exploring Hyperspace with the Geometric Product  Thomas S. Briggs
This paper presents an area of higherdimensional geometry to a general audience. It also highlights areas where new discoveries could be made. This exploration encounters double prisms, the double cylinder, prism cylinder, flat torus, spherical hypercylinder,
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 Expository Papers from the Geometry Center
Documents written at the Geometry Center that take advantage of hypertext to present information about mathematics or the Geometry Center in a style accessible to a wide audience. Engineering Education at the Geometry Center (Keynes, Wicklin); Outside
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 Extended Concurrencies of a Triangle  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
An exploration: take any triangle ABC. Construct equilateral triangles externally on each side and locate the center of each equilateral triangle. Label these centers A', B', and C' for the triangle centers opposite angles A, B, and C. Construct lines
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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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 Extracts from Thomas Hirst's diary  MacTutor Math History Archives
Quotations from Thomas Hirst's journals concerning the following mathematicians: Bertrand, Boole, Brioschi, Cayley, Chasles, Chebyshev, Cremona, De Morgan, Dirichlet, Gauss, Kovalevskaya, Liouville, Maxwell, Poinsot, and Steiner.
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 Fahrenheit to Celsius  Jim Loy
Ways to convert: two equations, two unknowns.
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 A Fair Deal For Housemates  Ivars Peterson (MathTrek)
Four friends move into a house and find they must choose among four rooms of different size and quality. Instead of sharing the rent equally, they decide to divide the total so that each person ends up satisfied with his or her combination of room and
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 The Fair Division Calculator  Francis Su
An interactive Java applet designed to help you determine how to divide among n people: a desirable object (such as a cake); an undesirable object (such as a set of chores); or a set of indivisible objects (rooms, desirable) with payments (rent, undesirable).
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 Fair Play and Dreidel  Ivars Peterson (MathLand)
For centuries, Jews have played the game of dreidel as part of the festivities associated with Hanukkah. Surprisingly, it turns out that this ancient game is also an unfair game. In 1976, Robert Feinerman of Herbert H. Lehman College (CUNY) in Bronx,
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 Fair Shares (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The birthday party is over, and one chunk of thickly frosted, richly decorated cake is uneaten. Your mother insists that you and your sister slice the cake into two equal pieces, so that she doesn't have to listen to you fight over which is bigger. What
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 The Fall and Rise of StandardsBased Education  Marzano, Kendall; Midcontinent Regional Educational Laboratory (McREL)
A National Association of State Boards of Education (NASBE) Issues in Brief. A brief historical overview that puts the standards movement in the context of recent education reform efforts and surveys some of the problems that have arisen in the development
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 FamilyEducation Network
Articles, discussion groups, professional advice, suggestions, and other resources for children of preschool and younger, elementary school, middle school, and high school and beyond. Resources topics include activities, health and safety, homework help,
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 Family Finance  Utah State University Family Finance
PowerPoint presentations for selfguided study: financial attitudes, values & goals; budgeting; creating your financial information binder; and how to budget your money. Other resources from the Utah State University Cooperative Extension agency include
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 The Family Photo and Counting on One Hand (Math Chat)  Frank Morgan; Christian Science Monitor
From Norman Goodwin: A photographer wants to line up the 11 members of the Goodwin family from shortest to tallest (left to right), starting with anyone, adding someone else on either side, and continuing by always adding someone next to those already
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 A Famous Infinite Series  Paul Trow
Explains how the 18th century mathematician Leonhard Euler found the infinite sum of the reciprocals of the square integers.
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 FanGraphs
Major and minor league baseball statistics and analysis, including graphs, splits, game logs, play logs, spray charts, plate discipline, PITCHf/x, strike zone heat maps, and more for every ballplayer and team.
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 Fashioning a World Brain  Ivars Peterson (MathLand)
When Peterson read about a revolutionary means of storing and distributing information, he couldn't help thinking about the current explosion of activity in electronic publishing, the Internet, and the World Wide Web. But the words were actually written
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 Feature Column: Monthly Essays on Mathematical Topics  American Mathematical Society (AMS)
Feature columns on new discoveries or interesting connections in mathematics, by David Austin, Bill Casselman, Joe Malkevitch, Tony Phillips, and Steven Weintraub.
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 Federal Statistical Office Germany
The statistics department of the German government. Press releases; socioeconomic data, with brief articles and key statistics; tables of recent economic figures; population data for other countries; the purchasing power of the deutschemark. Methodological
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 The Feeling of Power  Isaac Asimov
Science fiction that explores a time when only computers know how to multiply. "...seven times three is twentyone." "And how do you know that?" asked the congressman. "I just remember it. It's always twentyone on the computer. I've checked it any number
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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  MacTutor Math History Archives
Essay describing Fermat's theorem with links to mathematicians such as Sophie Germain, Legendre, Dirichlet, Shimura and Taniyama, etc., from its inception through Andrew Wiles' proof, with another web site and 17 references (books/articles).
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 Fermat's Little Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A description with proof involving modular arithmetic, and related links.
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 A Few Aspects of Cryptology  David Hamer
Read about cipher machines such as Enigma, Geheimschreiber, NEMA, SIGABA and others; visit the gallery showrooms of the Crypto Simulation Group (CSG), a group of historians and researchers in the field of cryptology; download sample simulators and published
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 Fibonacci at Random  Ivars Peterson  Science News Online
In a book completed in 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes
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 Fibonacci Numbers and the Pascal Triangle  Radoslav Jovanovic
Brief articles about Pascal's triangle, Fibonacci numbers, Lucas numbers, and the golden section, including the relations between Fibonacci numbers and Pascal's triangle, and Fibonacci numbers and the golden section. In English, German, or Serbian.
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 Fibonacci's Chinese Calendar  Ivars Peterson (MathTrek)
In a book completed in 1202, mathematician Leonardo of Pisa (Fibonacci) posed the problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second
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 Field Extensions  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to field extensions. Mathematicians once spent time on a subject call the "Theory of equations," which was full of algorithms and the theory of polynomials and their roots. Nowadays this is the subject
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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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 Field Theory and Polynomials  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to field theory and polynomials. Field theory looks at sets, such as the real number line, on which all the usual arithmetic properties hold, including, now, those of division. The study of multiple
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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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 Financial Noise  Ivars Peterson (MathTrek)
The conventional view of stock markets and their behavior is that the price of a stock reflects all the information available on that stock. In this model, any variations in price would correspond to the arrival of new information. Some of that information
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 Finding Common Ground in K12 Mathematics Education  Mathematical Association of America
"Starting point" documents, designed to advance the discourse about how to improve K12 mathematics teaching and learning, that emerged from MAAconvened pilot meetings between mathematicians and mathematics educators thought to be strongly aligned with
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 Finding the Center of a Circular Starting Line in an Ancient Greek Stadium  Rorres, Romano; SIAM Review
A 1997 essay by Chris Rorres and David Gilman Romano, which presents and compares two methods for finding the center and radius of a circular starting line of a racetrack in an ancient Greek stadium. Graphs and tables are included. Introduction, ThreePoints
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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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 First Digits  Ivars Peterson (MathTrek)
Take a look at a newspaper page listing stock market prices. You might think that each of the numbers from 1 to 9 would occur equally often among the first digits of all the listed prices. Instead, however, you're very likely to find that numbers starting
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 The Five Percent Solution  Keith Devlin (Devlin's Angle)
"Mathematical disciplines such as statistics, optimization theory, probability theory, queuing theory, control theory, game theory, and operations research are all used routinely in making difficult choices in public policy, health, business, manufacturing,
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 Five Strategies for Integrating the Internet into the Curriculum  American Library Association (ALA)
An essay organized into Strategy One: Use technology to teach information literacy; Strategy Two: Go on a webquest; Strategy Three: Teach students to use computer applications; Strategy Four: Join a telecollaborative project; and Strategy Five: Look at
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 FiveThirtyEight  Nate Silver, Editor in Chief
Quantitative features, interactives, and "datalabs" on politics, economics, sports, and other topics by Silver, Carl Bialik, and others. Science posts have included "How Statisticians Could Help Find That Missing Plane," "Toilet Seat Covers: To Use or
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 Fixed Point Theory on the Web  M. A. Khamsi
Fixed Point Theory and Applications sites; Mailing List; Conferences: previous and forthcoming; books on fixed point theory; other interesting sites on the Web; bibliography database; abstracts; papers on fixed point theory; general information.
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 Flight of the Bumblebee  Ivars Peterson (MathLand)
How did proving that a bumblebee can't fly originate? Who started the story? It apparently first surfaced in Germany in the 1930s, and the story was about a prominent Swiss aerodynamicist. One evening, the researcher happened to be talking to a biologist
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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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 Fluid Mechanics  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to fluid mechanics, which studies air, water, and other fluids in motion: compression, turbulence, diffusion, wave propagation, and so on. Mathematically this includes study of solutions of differential
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 Focus on Student Practice  Suzanne Alejandre
Article about how students worked on the Problem of the Week (PoW) "Wooden Legs" in a way that developed the Common Core State Standards (CCSS) Mathematical Practice of "making sense of problems and persevering in solving them." This article, originally
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 Fold Everything  National Geographic Society
See how paperfolding inspires the design of aircraft, stent grafts, and the packaging and transportation of telescope lenses in this overview of the history and future of origami. With downloadable instructions for folding a peacock, as well as an online
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 Folding Maps  Ivars Peterson (MathTrek)
Erik D. Demaine of the computer science department at the University of Waterloo
in Ontario and his coworkers have developed an efficient method for recognizing when a creased sheet is foldable into a flat package (results are reported in an unpublished
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 Following Benford's Law, or Looking Out for No.1  Malcolm W. Browne; The New York Times Company
An article from the New York Times on the Web: Dr. Theodore P. Hill asks his mathematics students at the Georgia Institute of Technology to go home and either flip a coin 200 times and record the results, or merely pretend to flip a coin and fake 200
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