 Planes of Budapest  Ivars Peterson (MathTrek)
Nearly every Sunday during the winter of 1933 in Budapest, a small group of students would meet somewhere in the city at a park or cafe to discuss mathematics. The gathering typically included Paul Erdös (19131996), György (George) Szekeres,
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 Planet Math
Designed to be a central repository for mathematical knowledge on the web, with a pedagogical slant. All content is usercontributed, either to the Encyclopedia or to the reviewed listings of papers, books, and lecture notes. Polls, discussions, and feedback
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 Plato: Acceptance of Astronomy as a Science  Michael Tirabassi
Translations from Plato's Dialogues (Loeb edition): The Myth of Er (a multihemispere model of the sky  Republic, X, 616B617). The True Astronomer Must be the Wisest of Men (Epinomis 990a); Pursue Astronomy as you Would Geometry (Republic 530b); Realise
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 Platonic Solids  Paul Bourke
Definitions, formulas, and illustrations of the threedimensional regular polyhedra: tetrahedron, octahedron, hexahedron (cube), icosahedron, dodecahedron, including the solids as drawn in Kepler's Mysterium Cosmographicum, and as represented in stone
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 Plato's Molecule  Ivars Peterson (MathTrek)
In his dialogue Timaeus, the Greek philosopher Plato (427347 B.C.) carefully laid out his reasoning for ascribing certain geometric shapes to the minuscule particles that constituted the four elements of matter. In his view, these elements  fire, air,
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 Playing with RuthAaron Pairs  Ivars Peterson (MathLand)
On April 8, 1974, Henry (Hank) Aaron hit his 715th major league home run, surpassing the previous mark of 714 career home runs long held by baseball great Babe Ruth. Understandably, the event received considerable coverage in newspapers and magazines
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 Plus Magazine  Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Plus (formerly PASSMaths) is a triannual online magazine for older pupils and the general public. It publishes articles explaining the diverse applications of mathematics used in solving problems in physics, chemistry, biology, engineering, and economics.
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 Poe's Secret  Ivars Peterson (MathTrek)
Writer Edgar Allan Poe (18091849) is famous for his short stories of the mysterious and the macabre. His popular tale "The GoldBug," published in 1843, is often cited as one of the best works of fiction that turn upon a secret message. Poe had a longstanding
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 Polynomials, Rational Functions  Dave Rusin; The Mathematical Atlas
A page reserved for the analytic study of polynomial functions studied in calculus classes. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; selected topics; other web sites with this
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 Polytopes and Polyhedra  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to geometric objects made from straight pieces: polygons, polyhedra, and generalizations. Applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables;
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 Population Index 19861998  Office of Population Research, Princeton University
The primary reference tool to the world's population literature, presenting an annotated bibliography of recently published books, journal articles, working papers, and other material on population topics. It covers all fields of interest to demographers,
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 The Position of the Sun  Dave Rusin; The Mathematical Atlas
A computer program to calculate the position of the sun, with an article describing the calculation of the apparent sun position in local coordinates for an earth observer: notation; solution; removing the effect of one variable and simplifying the solution;
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 Potential Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to potential theory, the mathematical treatment of the potentialenergy functions used in physics to study gravitation and electromagnetism. If some electrically charged particles are distributed in
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 The Power of Innovative Scheduling  Robert Lynn Canady; Educational Leadership Journal
A November 1995 article. "Alternative schedules may not add hours to the school day, but they can vastly improve the quality of the time students spend at school." Issues facing all schools; scheduling tips for elementary, middle and high schools; references.
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 The Power of One  Robert Matthews, The New Scientist
Benford's law demands that around 30 per cent of the numbers in a given data set will start with a 1, 18 per cent with a 2, right down to just 4.6 per cent starting with a 9. This essay provides a mathematical history behind the counterintuitive law,
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 Powers of 5 and Traveling to the North Pole (Math Chat)  Frank Morgan; Christian Science Monitor
What is the remainder when you divide 5^999,000 by 7?
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 Powersums, Fermat, Waring; Quotes, History...  Nico F. Benschop
Links to papers on the ideas of Fermat, Waring, Goldbach, Cantor, Hensel, HasseMinkowski, and Selmer, and the following mathematical concepts: semigroups, sequential logic synthesis, cubic roots, and state machines and their sequential closure. With
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 Practical Foundations of Mathematics  Paul Taylor
The full text (online, in HTML) of the book (some diagrams may be missing), published by Cambridge University Press in March, 1999 as number 59 in their series Cambridge Studies in Advanced Mathematics. Practical Foundations collects the methods of construction
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 A Practical Guide to Wavelet Analysis  Christopher Torrence and Gilbert P. Compo
Read an introduction to wavelet analysis and Monte Carlo methods, or download it in PDF or PostScript format. Use an interactive wavelet plotting form to investigate sample time series or your own data. Download wavelet software in Fortran, IDL, or
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 The Practice of Logical Frameworks (1996)  Frank Pfenning
A survey article discussing the history of work on logical frameworks and their current open problems. Deductive systems, given via axioms and rules of inference, are a common conceptual tool in mathematical logic and computer science. They are used to
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 Practice Online! The Electronic Complement to INTERFACES (POL)  Institute for Operations Reseach and the Management Sciences (INFORMS)
A practiceoriented electronic information service of INFORMS, jointly sponsored by INTERFACES and the INFORMS Roundtable. Forum, submission guidelines, supplemental materials online, tables of contents and abstracts, Edelman abstracts, practiceoriented
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 Precollege science and math 'lack focus'  Janet Raloff  Science News Online
A National Science Foundation report finds no one at the helm of U.S. science and math education, with the result that students are exposed to smatterings of topics that vary regionally and encourage little indepth learning. The analysis, released in
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 Preconditioned Eigensolvers  Andrew Knyazev; Dept. of Mathematics, Univ. of Colorado at Denver
Investigations into matrixfree iterative methods for partial eigenvalue
problems that take advantage of using preconditioners to accelerate convergence. Papers, an interactive discussion, a bibliography, related conferences, and links to software.
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 Preparing for University Calculus  Mathematics and Statistics Committee of the Atlantic Provinces Council on the Sciences (APICS)
Answers frequently asked questions about university level calculus courses, such as "What math will I need in university?" and "What is calculus?" Also download the booklet, which offers sample questions and hints of the sort often found on calculus placement
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 Preparing Teachers of Mathematics: Asking the Right Questions  Lynn Arthur Steen; St. Olaf College
Lynn Steen writes that the problems of teacher preparation arise from multiple sources and require correspondingly different solutions. About mathematics teachers, prospective mathematics teachers, and curriculum issues.
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 Preservice Teachers' Conceptions of Mathematics and How to Teach It  Annie and John Selden; Mathematical Association of America
"The way teachers explain mathematics depends, to a large extent, on the conceptual grasp they acquire in their college classes. In addition, they often teach as they were taught, modeling themselves after their college mathematics teachers as much as
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 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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