 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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 Positive and negative Euler characteristic (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A symmetry pattern on the sphere always gives rise to a quotient orbifold with positive Euler characteristic. In fact, if the order of symmetry is k, then the Euler characteristic of the quotient orbifold is 2/k, since the Euler characteristic of the
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 The PostCALC Project  Duke University
The PostCALC Project is a branch of the Connected Curriculum Library that presents interactive, mathematicallybased modules designed for high school students who have finished a yearlong course in calculus. These modules, each appropriate for several
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 The postIMO97 web page  Olimpíada Matemática Argentina
Problems and results from the math olympics held in Argentina in July, 1997. Available in English and Spanish, with problems also in French, Russian, German, and a host of other languages.
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 Postulates and Theorems of Boolean Algebra  Julie Kenrow; Santa Clara University, Santa Clara, CA
Five postulates (identity, complement, commutative law, associative law, distributive law); and six theorems. Supplementary material for a course in electrical engineering (Logic Design).
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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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 POVRay  Persistence of Vision Raytracer Pty. Ltd
The Persistence of Vision RayTracer creates threedimensional, photorealistic images using a rendering technique called raytracing, which calculates an image of a scene by simulating the way rays of light travel in the real world. Download the latest
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 Powell's Books
Located in Portland, Oregon, USA; the largest independent bookseller in the United States, specializing in technical books and new, used, hardtofind, and antiquarian titles. An extensive subject and keyword list is available  search database of titles,
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 Power and Pedagogy: Transforming Education through Information Technology  Robbie McClintock
A book from the Institute for Learning Technologies (ILTweb), Teachers College, Columbia University. Chapters include: The Computer as a System; The Educator's Mission; The Span of Pedagogical Possibility; Making a New Educational System; and Education
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 Power Maths  A precalculus project  Sidney Schuman
A precalculus investigation designed to enable students to discover each calculus power rule independently (albeit in simplified form), and hence their inverse relationship. Students are required only to do simple arithmetic and some elementary algebra,
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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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 Powersim
A simulation software development company, offering consultant and support services for simulator design, construction, and use as well as the complementary software needed to build models and simulators. The site offers discussion groups, products, newsletters,
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 Powers of Ten  Eames Office
An "adventure in magnitudes" that depicts the relative scale of the universe in factors of ten, originally written and directed by Ray Charles Eames in 1968. Starting at a picnic by a Chicago lake, every ten seconds this nine minutelong documentary short
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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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 PQRST Puzzle Competition  Cihan Altay
PQRST is a quarterly online puzzle competition open to all, with competitions in January, April, July and October. Download the test as PDF, then solve and rate the puzzles within seven days. The PQRST site highlights top competitiors and puzzles receiving
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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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 The Precalculus Algebra TI83 Tutorial  Mark Turner
An online tutorial for using the TI83 graphing calculator to solve the
kinds of problems typically encountered in a college algebra or
precalculus algebra course. Stepbystep instructions with full key
sequences and animated screen images. Includes
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 PreCalculus  Trevor Roseborough
An introduction to calculus for the student who is about to learn the subject. It makes clear the connection between the integral and the derivative and suggests a more consistent notation before the student becomes hopelessly confused.
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 Precalculus Tutorial  John W. Bales
A tutorial for students enrolled in a precalculus, college algebra, or trigonometry course. Bates explains, "It does not, and cannot, replace the textbook or other class resources or assignments. At the instructor's discretion, all or part of this tutorial
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 The Precalculus Weblet  Dynamic Educational Materials
A partially online precalculus course with the following centers: Instruction (extending the instructional opportunities beyond the textbook; see Explore the Concepts and Starred Exercises), Reference (technology, glossary, history, sites that complement
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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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 A Preliminary Analysis of SATI Mathematics Data for IMP Schools in California  R. James Milgram
An analysis of the performance of Interactive Mathematics Program (IMP) students on the SATI mathematics examination, and a brief look at the supporting literature for IMP.
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 PrenticeHall Publishing Company  Pearson Education
A leading publisher of college course materials. For education, see Merrill Education (in particular Educational Psychology and Special Education), or Prentice Hall School, browse math titles by course, or search the PrenticeHall catalog.
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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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 Prependix A: Math Notation On KCT
 Karl Hahn
Math notation over the Web: symbol conventions used by Karl Hahn for his Calculus Tutor Notes.
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 Preprints  Yale Mathematics Department
Download files via FTP. Single documents and papers with only a few simple diagrams are stored as ASCII TeX files. An index lists titles and authors of papers.
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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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 Preuve Proof Prueba
A newsletter in French, Spanish, and English, the theme of which is teaching and learning mathematical proofs. Includes an extensive bibliography consisting of books, chapters in books, journal articles, and theses.
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 Pricing and Hedging of Derivative Securities  Lars Tyge Nielsen
A book that introduces the theory of pricing and hedging of derivative securities in continuous time graduate and advanced undergraduate students and for researchers in both academia and the financial industry. Includes background in stochastic process
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 Primality Testing  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about primality testing, from "How does the Sieve of Eratosthenes work?" to "Is there an algorithm to determine whether a very large number is prime?"
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 Prime Curios!  G. L. Honaker, Jr., Chris K. Caldwell
A collection of curiosities, wonders and trivia related to prime numbers. Look up a number (up to 10^21+) and find what connections it has to the primes. The database has over 3400 curios corresponding to more than 1960 different numbers. The number of
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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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 primegen  D. J. Bernstein
Download primegen, a small, fast library to generate prime numbers in order. Using the Sieve of Atkin instead of the traditional Sieve of Eratosthenes, it generates the 50847534 primes up to 1000000000 in just 8 seconds on a Pentium II350; it prints
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 The Prime Glossary  Chris Caldwell; Dept. of Mathematics & Computer Science, Univ. of Tennessee at Martin
A guide to the terminology of prime numbers, and links to other pages with fuller definitions and information, written on two levels: for schoolteachers and students to define the basic words of elementary prime number theory and list the unusual or curious
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 Prime Hunter Game  Benny Lam, Gameducate.com
Hunt for prime numbers (or the largest prime factor in a composite number) from a board with a random layout of digits. Free download, or shareware version available. For Windows.
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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 Number Generator  Mark Chamness
This Java applet quickly generates a long list of prime numbers. When you pause or stop the list, you can scroll through the numbers.
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 Prime Number Listening Guide  Chris Caldwell; Dept. of Mathematics & Computer Science, Univ. of Tennessee at Martin
A guide to an online program that you can use to create your own "primal sounds" if you can play midi files. Caldwell introduces a few ways to hear the primes and use them to hear both the simple patterns (there are some) and the perplexing irregularities
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 Prime Number List  James Brennan
A page with a script that generates a list of prime numbers. Once started, it will run until you click 'Stop' or your computer runs out of memory. A second page writes the list to a new Web page suitable for printing.
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 The Prime Number Maze  William Paulsen; Arkansas State University, Jonesboro, AK
Navigate mazes of binary numbers determined by the distribution of the prime numbers. Try mazes at Beginner (binary notations and prime numbers), Intermediate (500 rooms), Advanced (5000 rooms), Super Advanced (6 times larger than the advanced), or Ultimate
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 Prime Numbers  Alex LópezOrtiz and the Sci.Math FAQ Team
Links to information on: Largest known Mersenne prime; Largest known prime; Largest known twin primes; Largest Fermat number with known factorization; Algorithms to factor integer numbers; Primality Testing; List of record numbers; What is the current
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 Prime Numbers and Factoring  Ray Ontko
A collection of links related to prime numbers and factoring of very large numbers, including FAQs from RSA Labs.
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 Prime Numbers and Factors  Machinery's Handbook 25
Tables give factoring information on numbers from 9600 to 21600. Reprinted from Machinery's Handbook, 25th Edition ("The Bible of the Mechanical Industries"). Prime numbers in the tables are indicated by the letter P. If a number is not prime, the table
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