 NumberTheoretic Hacks  David Eppstein, Theory Group, ICS, UC Irvine
Simple numbertheoretic algorithms. Egyptian Fractions  algorithms and references; C++ implementation of J. H. Conway's "nimber" arithmetic; C++ fast algorithm for computing 2adic inverse; C program for rational approximation of real numbers; Interference
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 Number Theory  Alex LópezOrtiz and the Sci.Math FAQ Team
Links to information on: Fermat's Last Theorem (History of Fermat's Last Theorem; What is the current status of FLT?; Related Conjectures; Did Fermat prove this theorem?), and Prime Numbers.
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 Number Theory Calculator  Bardesane: Giuseppe Merlino
A blog with free math programs for Windows: prime numbers, twin prime pairs, Goldbach conjecture, Collatz conjecture, Fibonacci numbers, N = x^2 + y^2, modpow (A^B mod. C), primality test, prime factors, divisors number and sum, Pascal's triangle, nextprime,
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 Number Theory Centres  Keith Matthews, Dept of Math, University of Queensland, Brisbane, Australia
An alphabetical list of links to international number theory groups and research centres.
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 Number theory  Dario Alpern
A collection of calculators, tables, and articles about number theory, with an applet that is able to factor large numbers and a quadratic diophantine equation solver.
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 Number Theory Foundation
A foundation for collecting donations from supporters of number theory and disbursing them to encourage research. Supporters have directed available funds towards activities in computational and combinatorial number theory, and also towards general number
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 Number Theory: Historical things  Keith Matthews, Dept. of Math, University of Queensland, Brisbane, Australia
Biographies of past number theorists and various items of historical interest, including prizes, photos, and mathematical family trees.
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 Number Theory List  Yahoo Groups
Archives of a mailing list devoted to discussions of the serious mathematical study of the additive and multiplicative properties of positive integers including powers of integers, squares, cubes, triangular, factorial, fibonacci, composite, prime, perfect,
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 Number Theory Web  Keith Matthews, Dept of Math, University of Queensland, Brisbane, Australia
A collection of links to online information of interest to number theorists everywhere, including number theorists' home pages and departmental listings.
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 Number World  David Geistert
Key in any positive integer less than 10^15 and press the "Look up" button for properties about it: factorization, divisors, cross sum, equivalence in multiple bases, and more. Number World's math tools include an equation solver, an equation system solver,
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 Numeracy Hour Activities  Ambleside Primary School on the Web
Games designed by or with children, and interactive teaching programs to download. Games and activities include Amblegraph (create simple bar charts online); Online Calculator; Analogue Clock (a time teaching tool); Table Trees (multiplication tables);
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 Numerical Problems (Algorithm Design Manual)  Steven S. Skiena
A chapter from the Algorithm Design Manual, by Steven S. Skiena. Specific algorithms: Solving Linear Equations; Bandwidth Reduction; Matrix Multiplication; Determinants and Permanents; Constrained and Unconstrained Optimization; Linear Programming; Random
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 Numericana.com  Gérard P. Michon
The online companion of Numericana, this site contains excerpts from Michon's book, including the entire glossary of scientific terms. Browse an index with pithy summaries, browse by popularity, or search nearly two hundred of his "final answers" of readers'
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 Numericon  School of Mathematical Sciences, University of Technology, Sydney, Australia (UTS)
Mostly elementary presentations of: Numbers we've all heard of; Perfect numbers; Facts about prime numbers; Australian cricket's 25 leading allrounders; Pythagorean triples; Pi in the sky; 73939133; and Fermat's Last Theorem.
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 The Official Scoring Site of the International Mathematical Olympiad 2001  Wolfram Research
The IMO 2001 competition, for students under the age of 20 who have had no postsecondaryschool education, was held July 114, 2001, in Washington, DC, USA. Each country represented is allowed up to six participants. This site records scores and supplies
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 Olimpíada Brasileira de Matemática  Sociedade Brasileira de Matemática (SBM)
The Olimpíada Brasileira de Matemática (OBM) is a competition open to all students enrolled in Brazil's fundamental or middle studies. Browse or download archived exam problems and solutions dating back to 1997. Read news about olympiads, or the journal
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 Oliver Knill
Research, teaching, and media by this preceptor in Harvard's math department. Knill began in dynamical systems, tackling first ergodic and spectral theoretical questions, then probability theory and elementary number theory. This led to his "passion for
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 Once in a Millennium (Math Chat)  Frank Morgan, MAA Online
Challenge: The year 2000 can be represented as the sum of consecutive integers:
2000 = 398 + 399 + 400 + 401 + 402. The year 2001 can be represented as the sum of consecutive integers: 2001 = 1000 + 1001. In fact, every year in the millennium from 2000
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 OnePage Proof of Fermat: Critique (Math Chat)  Frank Morgan, MAA Online
Critique the following short proof of Fermat's Last Theorem sent in by
reader Rob Connelly. (In perhaps the biggest mathematics news of the century, Andrew Wiles recently came up with a very long and complicated proof of this 350year old problem.) Answer:
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 OnLine Encyclopedia of Integer Sequences  The OEIS Foundation Inc.
Before publishing that new sequence you have just found, you might want to check here to see if it's already been discovered. Directions for how to look up a sequence in the table, abbreviations used, sending in a new sequence; how to look up a reference
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 On the 3x + 1 Problem  Eric Roosendaal
Numerical data and some conjectures on this problem, also known as the Collatz problem or the Syracuse problem. All numbers up to 29,300 * 10^12 (~ 26 * 2^50) have been checked for convergence.
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 OpenMathText.org  David A. Santos, Alain Schremmer
OpenMathText.org is a depository of free, downloadable texts and is primarily dedicated to the specification, development, and dissemination of free, editable and downloadable mathematical texts aimed, mainly, at "just plain folk." OMTo invites registrants
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 Open Problem Garden  Matt DeVos and Robert Šámal
A collection of unsolved problems  mainly, graph theory, combinatorics, and number theory. A wiki for each open problem includes relevant bibliographical citations, importance rating, and recommendation for undergraduates. Navigate by math subject,
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 Open Problems for Undergraduates (DIMACS)  Robert Hochberg, Center for Discrete Mathematics and Theoretical Computer Science, Rutgers Univ.
A collection of open problems in Discrete Mathematics in the areas of Graph Theory; Combinatorial Geometry; Geometry/Number theory; and Venn Diagrams, currently being researched by members of the DIMACS community. These problems are easily stated, require
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 Organic Mathematics Workshop: The Proceedings  Borwein, Borwein, Corless, Jörgenson, Sinclair, eds.
Proceedings of a 1996 workshop held at Simon Fraser University, Vancouver, Canada. Speakers (top experimental and computational mathematicians); their articles, with equations, code, photos, videos, and annotations; and related resources and links. Invited
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 Organisation des nombres premiers  Mustapha Chouar
Une répartition des nombres premiers qui utilse la fonction 1+4+2 avec une représentation graphique de l'addition des carrés et une spirale.
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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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 Overview of "Mathematician's Secret Room"  Hisanori Mishima
Challenges to unsolved problems in Number Theory, some translated into English from the Japanese.
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 Page of Conversion (Convert It)  Ramsviks, Adler
Enter a number and press the tab key to convert among bases, tempreatures, and measures and weight.
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 Papers on the History of Mathematics  Gregory Cherlin, Rutgers University
A random selection of term papers submitted in undergraduate, onesemester courses on the history of mathematics. Topics include zero, Fermat, Euler, Newton, Euclid's proof of the Pythagorean Theorem, Fibonacci, Vieta, conic sections, mathematics at Princeton
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 Pascal's Triangle from Top to Bottom  Matthew Hubbard and Tom Roby
A comprehensive resource for the study of Pascal's Triangle. The section "Applications" addresses questions such as "What types of questions are answered by the binomial coefficients?" and "What number greater than 1 shows up most often in Pascal's Triangle?"
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 Pass Calculus  Le Site PassCalculus.com
Calculus question solution service. Solutions offered via email, phone, or fax; quotes are free; payment by credit card. Sample solutions and FAQ online.
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 Paul Erdos: An Infinity of Problems  Ivars Peterson (MathLand)
Paul Erdos died of a heart attack on Sept. 20 [1996] at the age of 83. Considered by many as one of the great mathematicians of this century and certainly one of the most prolific ever, he will be missed. For more than 50 years, Erdos wandered the globe
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 Penn State University Mathematics Department
Course home pages and instructional material; seminars, colloquia, and conferences; and subject area pages for Penn State research centers, with preprints and links to other resources on the Web: Algebra and Number Theory; Dynamical Systems; Mathematical
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 A Perfect Collaboration  Ivars Peterson (MathLand)
Euclid and Euler seem an unlikely pairing. One was the most prominent mathematician of antiquity, best known for his treatise on geometry, the Elements. The other was the most prolific mathematician in history, the man whom his 18century contemporaries
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 Perfect Numbers  Math Forum, Ask Dr. Math FAQ
What is a perfect number? How many are there? How can you calculate a perfect number from a Mersenne prime?
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 Perplexus  flooble
A large archive of mathematically inclined puzzles and problems displayed by category. Includes logic, number theory, geometry, probability and other problems. All are rated by difficulty and quality and discussed in depth by visitors. Most with solutions.
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 Peter Ash's Thoughts on Math and Education  Peter Ash
Musings on doing and teaching mathematics, book reviews, and math problems both elementary and advanced from the creator of Cambridge Math Learning. Blog posts, which date back to August of 2007, include "Very Proper Fractions"; "Physical Models for NonEuclidean
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 Phi's Fascinating Figures  Ron Knott
More properties of the number Phi, its multiples and powers, continued fractions, formulae, and numerical relations between Phi and its powers.
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 Physics Forums
Discussions emphasize physics, but "PF" also includes an entire directory on mathematics: General Math; Calculus & Analysis; Differential Equations; Linear & Abstract Algebra; Topology & Geometry; Set Theory, Logic, Probability, and Statistics;
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 Pi: A Source Book  J. Borwein, SpringerVerlag
A complete history of pi, with resources for teachers for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three classes: a selection of the mathematical
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 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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 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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