 Presidential Election and the Length of the Shortest Piece (Math Chat)  Frank Morgan, MAA Online
Presidential election with 48% of the US popular vote does not come close to the extreme possibility, even with just two candidates, of winning with less than about 22% of the popular vote. See Math Chat of November 8, 1996. Answer to the Challenge: 1.
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 President's Column (MAA)  Ken Ross
MAA President Ken Ross wrote this column for Focus on the need to connect K12 and collegelevel reforms.
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 Pretty Functions  Ivars Peterson (MathTrek)
About graphing calculators, and the software Graphing Calculator, a computer program for quickly visualizing two and threedimensional mathematical objects. Graphs illustrate plotting a given function, then seeing what happens when you
modify the function
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 Prime Gaps  Ivars Peterson (MathLand)
A prime is a whole number (other than 1) that is evenly divisible only by itself and 1. That simple definition leads to following sequence of numbers: 2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, and so
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 Prime Listening  Ivars Peterson (MathTrek)
Mathematician Chris K. Caldwell of the University of Tennessee in Martin has developed a scheme for listening to sequences of primes  to hear both simple patterns and perplexing irregularities found among those numbers. "Multimedia allows the use of
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 Prime Numbers  MacTutor Math History Archives
Linked essay describing the work on primes from Pythagoras through Gauss, Legendre, Riemann, and Valee Poussin, with additional sections on still unsolved problems, the latest prime records, and other web sites, as well as 21 references (books/articles).
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 The Prime Pages  Chris Caldwell; Dept. of Mathematics & Computer Science, Univ. of Tennessee at Martin
An index of information on prime numbers. Definition; Articles and information on primes, including how to find and prove primality, and a wealth of historical information. Lists of primes and prime factorizations, including the first x primes and the
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 A Primer on Vorticity for Application in Supercells and Tornadoes  Charles A. Doswell III, Cooperative Institute for Mesoscale Meteorological Studies
"Vorticity is a 3dimensional vector.... associated with the spatial variation of the wind field." This tutorial for those interested in supercell thunderstorms and tornadoes contains four mathematical diversions exploring models of fluid dynamics and
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 Primes and Composites (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: Consider the sequence of integers 10n + 1: 11, 101, 1001, ... Are there infinitely many primes? Infinitely many composite numbers? Whenever n is odd, 10n + 1 is divisible by 11. Modulo 11, 10n + 1 = (1)n + 1 = 0 if n is odd,
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 A Prime Surprise  Ivars Peterson (MathTrek)
Many of the 100 or so people who had helped with the nineprime effort immediately signed up for the new quest and began checking numbers. To everyone's surprise, Manfred Toplic (the same!) set the new record, reporting on March 2 that he had found 10
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 Prime Talent  Ivars Peterson (MathTrek)
Whole numbers have all sorts of curious properties. Consider, for example, the integer 1998. It turns out that 1998 is equal to the sum of its digits plus the cubes of those digits (1 + 9 + 9 + 8 + 13 + 93 + 93 + 83). What's the largest number for which
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 Prime Theorem of the Century  Ivars Peterson (MathLand)
"Prime numbers have always fascinated mathematicians," Underwood Dudley of DePauw University in Indiana wrote in a 1978 textbook. "They appear among the integers seemingly at random, and yet not quite: There seems to be some order or pattern, just a little
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 Prime Treasure Hunt  Ivars Peterson (MathTrek)
The headline shouted, "Hacker accused of using U.S. West computers on math problem." The Associated Press news report, dated Sept. 15 [1998], went on to describe how computer consultant Aaron Blosser of Lakewood, Colo., had enlisted 2,585 computers at
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 Principia Cybernetica Web  Turchin, Joslyn, Heylighen, Bollen, eds.
Principia Cybernetica Project (PCP) is an international organization that tries to tackle ageold philosophical questions with the help of the most recent cybernetic theories and technologies. The Project's aim is the computersupported collaborative
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 Principia Mathematica  A.D.Irvine; Stanford Encyclopedia of Philosophy
The philosophy encyclopedia's entry on Principia Mathematica, the landmark work on mathematical logic and the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell. Next to Aristotle's Organon, it is the most influential book
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 Principles and Practice of Constraint Programming: Conferences  Department of Computing Science, Univ. of Alberta, B.C.
Links to previous and future conferences concerned with all aspects of computing with constraints including: algorithms, applications, environments, languages, models, systems. Contributions are welcome from any discipline concerned with constraints,
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 PRISM (Parallel Research on Invariant Subspace Methods)
A project the goal of which is to develop infrastructure and algorithms for the parallel solution of eigenvalue problems. PRISM is currently investigating a complete eigensolver based on the Invariant Subspace Decomposition Algorithm
for dense symmetric
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 Prisoners of Time  U.S. Dept. of Education
Report of the National Education Commission on Time and Learning, April 1994, established as an independent advisory body to study the relation between time and learning in American schools. "The degree to which today's American school is controlled by
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 Prized Geometric Logic  Ivars Peterson (MathTrek)
Computer programs can handle all sorts of data [such as] a set of discrete
elements, such as temperatures. Some elements of a set may be larger in value than others, or they may exhibit some other relationship that allows you to rank them or put them
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 Prize offered for solving number conundrum  Ivars Peterson  Science News Online
A proof of a conjecture related to Fermat's last theorem would earn $50,000.
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 Prizes and Perils of Popularizing  Keith Devlin
A series of vignettes abouut some of the leading popularizers of mathematics. Sections include: Casti's Tale; Devlin's Tale; Stewart's Tale; Paulos's Tale; Dunham's Tale; and Why Do We Do It? Previously published in Focus.
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 Probability Abstract Service  University of Washington, Seattle, WA
Latest abstracts, with some preprints and information about authors; all abstract titles (old and new titles and authors, a large file); old abstracts; submission and subscription information; and related WWW servers.
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 Probability and Statistics (MathPages)  Kevin Brown
More than 40 "informal notes" by Kevin Brown on probability and statistics: evaluating probabilities of Boolean events, area under the bell curve, N items distributed in M bins, dice rolling a given sum, a better lottery, meetings and birthdays, on random
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 Probability Theory and Stochastic Processes  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to probability theory: enumerative combinatorial analysis when applied to finite sets; thus the techniques and results resemble those of discrete mathematics. The theory comes into its own when considering
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 The Probability Web  Bob Dobrow; Department of Mathematics and Computer Science, Carleton College
A collection of pages to serve people with interests in probability theory and its applications. Information is presented under the following headings: Probability links, Abstracts, Listservers, Newsgroups, People, Jobs, Journals, Software, Books, Booksellers,
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 Problem at the Art Gallery  Ivars Peterson (MathLand)
The Crystal Art Gallery was being readied for its grand opening, and I had to figure out how many guards were needed to make sure that every wall of paintings was under scrutiny. I was also ordered to keep costs as low as possible. The trouble was that
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 The Problem of Knot Classification  Charilaos Aneziris
Contents: Denoting Regular Knot projections; When is a notation drawable?; Equal Drawability; Identifying Equivalent Knot Projections; Ordering Knot Notations; Connected Sums; Comparing Regular Knot Projections; NF=14 Results; Calculating the Alexander
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 Problem of the Week Articles  the Math Forum @ Drexel
These three published articles give context to using the Math Forum's Problems of the Week with students: Writing to Develop Understanding: The Math Forum @ Drexel's PoWs; Problems of the Week Engage Students with Special Needs; and The Impact of the
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 Problem Solving in Mathematics  Jim Wilson; Univ. of Georgia
Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links
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 Problem Solving  It Has to Begin with Noticing and Wondering  Hogan, Marie; and Alejandre, Suzanne
Middle school teacher Marie Hogan observed as the Forum's Director of Professional Development modeled a full cycle of the Problems of the Week (PoWs) in Hogan's West Covina (CA) classroom. This coauthored article about their experience around the PoW
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 Problem Solving with Heron's Formula  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
A paper on the development and demonstration of Heron's formula for the area of a triangle given the lengths of its three sides. Problems and explorations are included for using Heron's formula.
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 Professional Development in a Technological Age: New Definitions, Old Challenges, New Resources  Cathy Miles Grant
This paper looks broadly at the field of professional development and the underlying principles that guide current approaches. The paper suggests specific issues that come with the process of supporting teachers in technology use, and concludes with a
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 Professor Badih Ghusayni
Ghusayni, who teaches in the Department of Mathematics at Lebanese University, serves as Managing Editor of the International Journal of Mathematics and Computer Science. Purchase and download his books and journal articles on complex and harmonic analysis,
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 Professor L N Trefethen, Numerical Analysis  Balliol College, Oxford University, UK
Links to books and recent papers by the head of the Numerical Analysis Group at Oxford University. Books include: Spectral Methods in Matlab, Finite Difference and Spectral Methods, Numerical Linear Algebra, and Spectra and Pseudospectra.
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 Professor Salah Mecheri  Salah Mecheri
Home page of a mathematical analysis professor in Saudi Arabia. Includes publications, references, research statements, primarily focused on operator theory.
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 Professor Warwick Sawyer  Mark Alder
Articles by the author of Mathematician's Delight: "Things and Unthings  An approach to negative numbers," "The Contribution of Music to Mathematical Discovery," "Some Thoughts on Education and Mathematics," "Saturday Morning Mathematics in Cambridge,"
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 Profile (John H. Conway): Not Just Fun and Games  Mark Alpert, Scientific American
A short biography of the Englishborn Princeton University mathematician and a discussion of some of his major mathematical contributions. ...over the past three decades Conway has made some of his greatest contributions to mathematical theory by analyzing
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 Program Information Guide Service (NCBE)  The National Clearinghouse for English Language Acquisition and Language (NCELA)
Short monographs that provide schoolbased personnel with information on innovative practices for working with linguistically and culturally diverse students: bilingual and ESL, language minority, immigrants, etc. The National Clearinghouse for English
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 A Progression of Primes  Ivars Peterson (MathTrek)
Searches for patterns among prime numbers  whole numbers exactly divisible only by themselves and one  have long served as stiff tests of the ingenuity and perseverance of mathematicians. In recent years, the use of computers has brought a steady stream
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 Project 2061: Science Literacy for a Changing Future  American Association for the Advancement of Science (AAAS)
A longterm initiative to reform K12 education nationwide so that all highschool graduates will be literate in science. The project is creating a coordinated set of reform tools and services—books, CDROMS, online resources, and workshops. This site
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 ProjectBased Learning (Learning and Mathematics)  Blumenfeld, Soloway, Marx, Krajcik, Guzdial, & Palincsar; Math Forum
In this 1996 article, "Motivating projectbased learning: Sustaining the doing, supporting the learning," Blumenfeld and her colleagues at the University of Michigan describe projectbased learning and the benefits of using longterm projects as part
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 Project Hermite  Shayne Waldron
Because bounding the error in Hermite interpolation in terms of the derivative which kills the interpolating space is of interest in numerical analysis and in the analysis of ordinary differential equations, there is an extensive literature on the subject.
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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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 Projet PRISME  INRIA, Sophia Antipolis
Les activités du projet PRISME sont centrées sur la géométrie algorithmique et ses applications, et sur les aspects géométriques de la robotique. Les études sont motivées par les nombreux domaines
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 Promoting Engagement and Supporting Leadership Development:
Online Teacher Professional Development at the Math Forum  Wesley Shumar, Jason Silverman, & Troy P. Regis, Drexel University
PDFformat article. Abstract: Teacher professional development (TPD) in its current state is typically episodic, fragmented, and often not rewarding over the long haul. There is need for a more substantial and extensive core set of TPD experiences that
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 Proof  Jim Loy
Brief descriptions of different types of proof, both mathematical and not.
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 Proof, Mathematical (Encarta Encyclopedia 2000)  Microsoft Encarta Online
An argument that is used to show the truth of a mathematical assertion. In modern mathematics, a proof begins with one or more statements called premises and demonstrates, using the rules of logic, that if the premises are true then a particular conclusion
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 A Proof of the Full ShimuraTaniyamaWeil Conjecture  Henri Darmon
Download an article in PDFformat on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
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 A Proof of the Pythagorean Theorem by Liu Hui (third century A.D.)  Donald B. Wagner
Web version of an article which appeared in Historia mathematica, 1985, 12, pp. 713. Includes Chinese characters, which were not in the published version. Some statements here are no longer up to date, but the article has not been significantly modified.
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 Proofs Without Words  Cut the Knot!, Alexander Bogomolny
Martin Gardner wrote, "There is no more effective aid in understanding certain algebraic identities than a good diagram. One should, of course, know how to manipulate algebraic symbols to obtain proofs, but in many cases a dull proof can be supplemented
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