 Pell's equation
 MacTutor Math History Archives
Linked essay on the indeterminate quadratic equation. With references and other related web sites.
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 Perfect, Amicable and Sociable Numbers  David Moews
Definitions, descriptions, and discussions of perfect, amicable, and sociable numbers; aliquot sequences, related problems, and other definitions of divisibility, with a short bibliography.
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 Perfect Numbers  MacTutor Math History Archives
Linked essay describing the work on perfect numbers from Pythagoras through Euclid, Nicomachus, the Arabs, Cataldi, Descartes, Mersenne, Fermat, Euler, Barlow, Catalan, Cole, and others; with other web sites and 20 references (books/articles).
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 Perfect Problems  Vasek Chvátal
Unsolved problems on perfect graphs, a collection for people with at least a basic knowledge of the subject. Contents include: Perfection of special classes of Berge graphs; Recognition of special classes of Berge graphs; Decompositions of perfect graphs;
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 Peter Doyle  Mathematics, Univ. of California at San Diego
Advanced tutorials, proofs and papers, mostly statistics, probability, geometry, and graph theory, but with examples from other mathematics areas as well. Don't miss Dr. Doyle's Flip Flops.
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 Photos by Paul Halmos  Mathematical Association of America (MAA)
Snapshots taken by Paul R. Halmos of notable contemporaries, academics, and other intellectuals of the 20th century. Search or browse the tagged collection of pictures, each of which includes a brief note about the subjects photographed in Halmos' own
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 Phyllotaxis  Pau Atela, Chris Golé; Smith College
An interactive site for the mathematical study of plant pattern formation. Sections of the site include: Introduction to Phyllotaxis (classification, Fibonacci/golden angle, microscope, mathematical model, and lattices); history; glossary; references;
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 PianoMath Home Page: Improving Math Skills through Music  Peter Taussig, E. Paul Goldenberg
Essays and activities on links between music and mathematics. PianoMath is
a crossdisciplinary curriculum of musical classroom activities relating to
arithmetic, geometry, graphing, logic foundation, and prealgebra. It is
now being tested at an elementary
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 Pi Through the Ages  MacTutor Math History Archives
A history of pi: the Rhind papyrus (Egypt), Ptolemy, Tsu Ch'ung Chi, al'Khwarizmi, Al'Kashi, Viet, Romanus, Van Ceulen, Gregory, Shanks, Lambert, Euler, Buffon, and many more, with other Web sites and 30 references (books/articles).
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 pLab: Random Number Generation  Peter Hellekalek; Mathematics Dept., University of Salzburg
Results and links on this fundamental topic in stochastic simulation. RNGs are deterministic algorithms that produce numbers with certain distribution properties. Roughly speaking, these numbers should behave similar to realizations of independent, identically
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 Planetqhe (Probabilistic Learning Activities Network)  David Kay Harris
Outoftheordinary probability problems. The site focuses on using methods of probability to solve counterintuitive problems and deepen students' understanding and competence in the domain. Sections include: a brief history and rationale of the site;
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 Poetry and Mathematics  JoAnne Growney
Poems by the Bloomsburg University mathematics professor: "All Day," "The Blacksmith," "Fly," "Conditionals," "The Prince of Algebra," "Geometry Class," "My Dance is Mathematics," "The Witch," as well as several square poems, in which the number of syllables
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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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 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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 The President's Educational Technology Initiative
This site promotes President Clinton's initiative, begun in 1996, to bring computers to every student in the United States. The site includes quotations and bibliography on the benefits of information technology, information on the administration's accomplishments
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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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 Probability Theory: the Logic of Science  E. T. Jaynes, Dept. of Physics, Washington Univ., St. Louis, MO
Chapters (entirely in PostScript files) include: Principles and Elementary Applications; Advanced Applications; Appendices; and References. The long table of contents is on the Web. The LaTeX source is available for download (gz).
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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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 Pythagoras' Theorem in Babylonian Mathematics  MacTutor Math History Archives
Linked essay examining four Babylonian tablets that all have some connection with the Pythagorean theorem. With references and other related web sites.
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 Quadratic, Cubic, and Quartic Equations  MacTutor Math History Archives
Linked article describing the progress made on these equations from the Babylonians through Leibniz in 1673, with another Web site and 12 references.
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 The Quantum Age Begins  MacTutor Math History Archives
Linked essay describing the beginnings of quantum theory, from Kirchoff's blackbody radiation work in 1859 to Bohr, Einstein, and von Neumann in the 1930's, with 33 references (books/articles).
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 Quantum Lie Algebras  Gustav Delius
A comprehensive, continuously updated bibliography of literature on Quantum Lie Algebras. Mathematica notebooks containing calculations and animations of quantum root systems are included.
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 QuasiTiler (Gallery of Interactive Geometry)  Eugenio Durand; The Geometry Center
Generate Penrose tilings or design your own nonperiodic tilings of the plane with this interactive application. In the process, you can select and visualize plane crosssections of a lattice in anywhere from 3 up to 13 dimensions. Geometry of Quasicrystals
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 Random Walk on the Speiser Graph of a Riemann Surface [PDF]  Peter G. Doyle
A paper that appeared in the Bulletin of the American Mathematical society, which considers the problem of determining the conformal type of a covering surface of the Riemann sphere with punctures. To such a surface there corresponds a Speiser graph of
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 Readings and Poetry Selections for Mathematics in Poetry  JoAnne Growney, Bloomsburg Univ., Bloomsburg, PA; The Math Forum
Annotated bibliography for the contributed paper session, "The Scholarship of Humanistic Mathematics," AMSMAA Joint Meetings, Orlando, Florida, 1996.
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 Reciprocity Laws  Franz Lemmermeyer
Reciprocity Laws. From Euler to Eisenstein has just appeared in SpringerVerlag Heidelberg. It is an updated version of Chapters 1  11 as they used to be available at this site; the table of contents with ps and pdf files of Chapter 11 (corrected version)
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 Recreational Mathematics  MAA Online
From the Mathematical Association of America's Basic Library List  a bibliography of articles (in print, not on the Web) on Recreational Mathematics: Games and Puzzles; Puzzle Collections; Contests and Problems; Martin Gardner; Miscellany.
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 Research in Math Education  Mathematics Education at The Math Forum
Research into the learning and teaching of mathematics: methods; K12 and college undergraduate education (articles, conference sessions); bibliographies; centers; studies; special interest groups; organizations and journals.
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 Research  Peter Alfeld; University of Utah
Researchrelated materials: An interactive applet that lets you explore the BernsteinBézier form of a bivariate polynomial; recent papers, complete bibliography, recent talks, computer graphics (illustrating various mathematical concepts: US Global Positioning
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 Resource Bibliography: Children's Trade Books in Math  Beth G. Newhouse, Department of Mathematics & Statictics, Arizona State University
A selected bibliography of books for kids that teach and reinforce math concepts, organized by topic: counting and number, number operations, large numbers, money, geometry, algebra, miscellaneous topics. Originally compiled by Dorothy Giroux and Denise
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 Resource Material  Spencer, Chan; Univ. of Toronto Mathematics Network
A collection of resource material for use in classes or extracurricular activities in high schools: answers, explanations, and expositions of some common but deep math questions. In the process of answering three basic questions, this area delves into
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 Resource Room (Math Central)  University of Regina, Regina, Saskatchewan, Canada
French version: Centre de ressources. A service of Math Central that allows mathematics educators to share resources having to do with math teaching. Submissions are stored in a database that can be browsed by educational level and curriculum strand,
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 Resources for Teachers of Developmental Mathematics (MAA)  Mathematical Association of America
A page assembled by the ad hoc Subcommittee on Developmental Mathematics, with the beginnings of an annotated bibliography of articles related to developmental mathematics, including articles on the adult learner of mathematics and experimental programs
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 Resources for the Teaching of Complex Analysis  Paul Fishback
The page includes: sample F(z) for Windows files (downloadable: for each example, an F(z) file is listed along with an MS WORD document describing the F(z) file and its creation in greater detail; a TI86 program that approximates contour integrals using
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 The Return of Odysseus and the Elements of Euclid  Andrew Wiesner; Classics Dept., Colorado College
The author's 1994 honors thesis, which attempts to shed new light on the origins of Greek mathematics.
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 The Rise of Calculus  MacTutor Math History Archives
Linked essay describing the history of Calculus from the Greeks through Newton and Leibniz, with 28 references (books/articles).
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 Rivendell Educational Archive  Leigh Denault
An educational archive of materials in botany, history, math, science, drama, literature, philosophy, and art. Math resources include mathematician biographies, a fractal image gallery, and a bibliography.
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 The Role of Calculators in Math Education  Heidi Pomerantz, Bert Waits for USI/CPMSA
This PDF article outlines the benefits of calculator use in mathematics classrooms from kindergarten through the university level, describing how calculators, when used appropriately, can be a tool for learning mathematics. The document has six sections:
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 Search the MacTutor History Archive  University of St. Andrews, Scotland
Search all or any combination of topics: Biographies; References; Quotations; History Topics; Bibliography; Famous Curves; Societies. With search suggestions.
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 Selected Recent Publications  George W. Hart
Areas of Hart's research and pointers to further information, including a bibliography of his publications. Links to pages on: Multidimensional Analysis; Nonintrusive Appliance Load Monitoring; Telecommunications Network Management; Viterbi Algorithm
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 Semigroup Theory  Jim Renshaw
A directory of Semigroup Theorists, bibliographic database, and conferences in Group and Semigroup Theory. With a link to a package for doing commutative diagrams, by Paul Taylor.
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 ShowMe Center
A National Science Foundation project supporting implementation of standardsbased middle grades mathematics curricula. The site features a calendar listing professional development opportunities; information about five different math curricula (Connected
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 Simultaneous Perturbation Method for Optimization  James C. Spall
A site devoted to a powerful method for optimization of processes dependent on more than one variable. The method pertains to "stochastic optimization," that is, optimization in the presence of random variation (such as measurement noise). The site provides
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 Soap Bubbles  Ron Hipschman; The Exploratorium
Why does a bubble form a sphere? Why not a cube, tetrahedron, or other geometrical figure? This site from San Francisco's Exploratorium provides information on the shape of bubbles and what happens when bubbles meet, with formulas for longlife bubble
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 Society for Chaos Theory in Psychology & Life Sciences
An association of researchers and practitioners interested in applying dynamical systems, chaos, and complexity theory to psychology and the life sciences. Joining the society; contents and submission information for the journal Nonlinear Dynamics, Psychology,
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 Some Problems in Matroid Theory  Thomas Zaslavsky
Sources of problems compiled by Zaslavsky, and problems he's found interesting: Bonin's Projective Bound; Maximum rFlat; Covering And Packing by Flats. For general sources of information on matroid theory, see Matroid Miscellany.
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 Special Functions  D. Lozier; Applied and Computational Math Division, NIST
This area of numerical computation has the property that input to its software is of small dimension, so highaccuracy reference software that produces test data with guaranteed error bounds is feasible. Library developers need illustrations of anomalous
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 Special Relativity  MacTutor Math History Archives
Linked essay describing the history of special relativity from Newton's laws through Lorentz and Einstein, with 12 references (books/articles).
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 Squaring the Circle  MacTutor Math History Archives
Linked essay covering the problem of squaring the circle in the form which we think of it today, which originated in Greek mathematics: given a circle, construct geometrically a square equal in area to the given circle. This article discusses the history
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 Srinivasa Ramanujan  Sociedad Andaluza de Educación Matemática THALES
Biografía de Ramanujan: Presentación; Formación; Trabajo; En Cambridge; Su obra; Bibliografía; Otras páginas de interés
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