- 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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- One-Page 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 350-year old problem.) Answer:
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- On-Line 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, n-secting 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, one-semester 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 18-century 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 Non-Euclidean
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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, Springer-Verlag
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 Stern-Brocot 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 post-IMO97 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, hard-to-find, 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, Hasse-Minkowski, 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 II-350; 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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- Problem-of-the-Week - 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 open-ended 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, Java-based 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 Shimura-Taniyama-Weil Conjecture - Henri Darmon
Download an article in PDF-format 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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