 Pick's Theorem  Cut the Knot!, Alexander Bogomolny
A description with proof of Pick's theorem, including links to further pages including exercises with an applet for the geoboard, Farey Series, and SternBrocot Tree. An interactive column for MAA Online that uses a Java applet to simulate a puzzle or
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 Place Value  Cut the Knot!, Alexander Bogomolny
Dictionary definitions of place value and what they lack; the emphasis on place value in the NCTM Standards; its importance in understanding our numeration system; how it arises from one of several possible representations of grouping in the counting
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 Planetcalc  Anton Egoshin
More than a hundred free calculators on math topics ranging from area of a triangle by its coordinates to total squares (the number of squares in given rectangles). Categories of others include date and time, health, computers, engineering, finance, navigation,
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 Plouffe's Inverter  Simon Plouffe
A database of more than 84,800,000 mathematical constants like Pi, Sqrt(2), Catalan and Euler's gamma. Enter a number, search or browse, and the programs will find what the number is made of. From the author of the Encyclopedia of Integer Sequences (with
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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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 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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 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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 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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 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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 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 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 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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 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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 ProblemoftheWeek  David Poole; Department of Mathematics, Trent University, Canada
Most of these problems can be done using only high school mathematics and logical reasoning. Eight problems with solutions and one without, from the fall of 1997, at Trent University, Canada. An email contact is listed, for those outside the university
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 Problem of the Week  Dr. Annalisa Crannell; Franklin & Marshall College
Puzzles to solve in number theory, geometry, probability, cryptography, and the like. See problems from 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, and 1997.
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 Problem of the Week  Elgin Johnston, Department of Mathematics, Iowa State University of Science and Technology
Download PDFs of challenging problems in number theory, abstract algebra, graph theory, and other topics every Monday. Intended for undergraduate students enrolled at Iowa State University: "Solvers of each week's problem will be listed on the Problem
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 Problem of the Week  Pavel Belik, Augsburg College
Weekly challenges, posted for undergraduates at Augsburg College, that run the gamut from number theory to geometry and beyond.
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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 Island  Samuel A. Rebelsky
Challenging openended word problems on the topics of games, such as Blockade, Finger Multiplication, and The Word Pyramid; puzzles such as Error Correction, Error Detection, The Fake Coin, Friday the 13th, and Leap Birthdays; and problems based on figures,
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 Project Euler  Colin Hughes
Browse hundreds of challenging problems that require mathematical insights as well as computer and programming skills to solve. Popular puzzles include "Add all the natural numbers below one thousand that are multiples of 3 or 5," "By considering the
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 Project Welcome (Web Educator's Library Collection of Mathematical Explorations)  MAA (Mathematical Association of America)
Interactive mathematical programs in a newly developed, Javabased interface.
Download online or offline versions of the player. Twenty lessons, with summaries, include "Best Linear Fit," "Limits of Functions," "Piecewise Functions," "Nonlinear Equations,"
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 PROMYS: The Program in Mathematics for Young Scientists  Boston University Department of Mathematics and Statistics
PROMYS encourages ambitious high school students to explore the creative world of mathematics. Each summer, approximately 60 high school students from around the country gather on the campus of Boston University for six weeks of rigorous mathematical
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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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 Proofs in Mathematics  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A discussion of the value of proofs in the classroom, followed by a collection of proofs classified as either simple or charming. Simple proofs: Number of vowels in a Lewis Carroll game; Pigeonhole Principle; Number of X's and O's; Coloring points in
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 Publications of François Morain
Links to papers on elliptic curves: Primality proving; Complex multiplication; Pseudoprimes; Elliptic curves over finite fields; Discrete logarithm over algebraic curves; Character sums; Miscellaneous. Also in French.
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 Pure Maths, Impure Thoughts  David A. Santos, Community College of Philadelphia
Includes lecture notes in elementary algebra, linear algebra, number
theory, probability, a problem seminar, plus review material in
precalculus and multivariable calculus. Selections available en castellano.
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 The Puzzle TOAD  Tom Bohman, Oleg Pikhurko, Alan Frieze, and Danny Sleator, School of Computer Science, Carnegie Mellon University
Send the authors your solutions to their challenging graph theory, number theory, geometry, discrete mathematics, logic, and other puzzles. Revisit periodically to see the latest question, and download PDFs of solutions of past problems.
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 Pythagorean Triples  H.B. Meyer
A Javascript calculator for pythagorean triples. In English and German.
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 Pythagorean Triples  Math Forum, Ask Dr. Math FAQ
What is a Pythagorean triple? What do Pythagorean triples have to do with Fermat's Last Theorem?
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 Pythagoreisches Tripelprogramm  Heinz Becker
A Java applet that reads a and gives integer solutions of a^2+b^2 = c^2. In German and English.
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 Pythagoräische Tripel (Pythagorean Triplets)  H. B. Meyer
A calculator for Pythagorean triplets, making visible the oneto one correspondence between triplets and certain pairs of relatively prime numbers, and an interesting correspondence with certain sequences of letters A, B, or C. (Javascript is required.)
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 The Quadray Papers  Kirby Urner, 4D Solutions
An Introduction to Quadrays. The game of quadrays starts with a regular tetrahedron and four rays pointing from its center to the four corners; these or any ray built from these rays are labelled 4tuples  i.e. four numbers separated by commas and enclosed
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 Quandaries and Queries (Math Central)  Dept. of Mathematics and Statistics, University of Regina, Saskatchewan, Canada
A math Question and Answer area for K12 students and teachers, with searchable archives of past questions and answers.
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 Query Interface to the Contents of the Mathematics Archives  University of Tennessee, Knoxville (UTK)
Search software, abstracts and reviews; teaching materials, etc. by keyword.
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 Rama Math Help  Marty Schultz
Pages to help people solve the alien number machines in the Sierra game Rama, with a lesson in base 8 and 16 (and 10) and base conversions, useful for others, too. Includes a review of base 10 and an overview of bases 8 and 16. There is also a link to
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 The Ramanujan Journal  Frank Garvan
This journal publishes research articles in the areas of mathematics influenced by Srinivasa Ramanujan, specifically number theory. Potential topics include the circle method and asymptotic formulae, diophantine analysis including irrationality and transcendence,
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 The Rational Mean  Domingo Gomez Morin
Blog by a Venezuelan engineer. See, in particular, Morin's arithmonic mean and other original methods for approximating the roots of algebraic equations.
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 The Real Y2K Problem (Math Chat)  Frank Morgan, MAA Online
Solution to the challenge: Every year in the millennium from 2000 to 2999 can be represented as the sum of consecutive integers, except one year. Which year cannot be represented as the sum of consecutive integers? New challenge: Where do you think you
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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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 Recommended Mathematics Literature  International Mathematics Olympiad (IMO)
A page of readings recommended by the International Mathematics Olympiad in association with Amazon.com Books. Major sections include: Problem Solving; Collections of Mathematical (Competition) Problems; Anthologies and Surveys; Number Theory; Analysis;
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 Recreational Mathematics Topics  Steven Dutch; University of Wisconsin  Green Bay
Contents: Symmetry, Crystals, Polyhedra and Tilings: an extensive, illustrated collection including reflectional and rotational symmetry; repeating patterns in two and three dimensions; building crystal forms with unit cells; regular, Archimedean, radial,
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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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 The Return of Zeta  Ivars Peterson (MathTrek)
The Riemann hypothesis is widely considered the outstanding unsolved problem in mathematics. Generations of mathematicians have been lured into hunting for a proof of this celebrated conundrum. All have so far failed. Lately, however, a cautious optimism
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 Riemann Zeta Function and Hydrogen Spectrum  Ivan Iliev
Analytic and numerical evidence, as well as conjectures and ideas, that connect the Riemann zeta function with energyrelated concepts. Iliev's manuscript derives a Zeta Rule for the definition of the hydrogen spectrum, presents a modification of the
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 RngPack  Paul Houle
A pseudorandom number generator package for Java. Pseudorandom means that the "random" numbers are generated by a deterministic mathematical process, not by a fundamentally random physical process such as radioactive decay or Johnson noise. RngPack contains
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 Rolf's Calculator  Rolf Howarth
A fully featured JavaScript scientific calculator that includes trig functions and logarithms, factorials, 12 levels of parentheses, logs to base 2, bitwise logical operators, hex, octal, binary and ascii display.
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 The Roman Press, Inc.  Steven Roman
Home page of a California mathematics professor, including research articles, books and textbooks, and software.
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 Russian Peasant Multiplication  Math Forum, Ask Dr. Math FAQ
What is Russian peasant multiplication? How do I use it? Why does it work? How is the Russian peasant algorithm connected to binary numbers?
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 RuthAaron Pairs and an Algorithm  Joe K. Crump
A page on RuthAaron numbers and a novel algorithm capable of generating
very large ones (200+ digits).
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 Scientific Applications of Linux  HerngJeng Jou and Kachina Technologies, Inc.
SAL (Scientific Applications on Linux) is a collection of information and links to software for scientists and engineers. Math categories include computer algebra systems, arrayoriented and linear algebra systems, statistics, and number theory. Numerical
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