- Modular Arithmetic Calculator - Paul Trow
The Modular Arithmetic Calculator performs arithmetic modulo m, and calculates square roots when m is prime.
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- Modular Arithmetic - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An essay on modular (or modulo) arithmetic, an unusually versatile tool discovered by K. F. Gauss (1777-1855) in 1801, with related links.
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- Monthly Themes - NRICH Maths, Univ. of Cambridge
Past problems from the NRICH Online Maths Club, archived by month. Each problem has a symbol indicating the stage, which tells you how little or how much mathematics you need to know to solve the problem but is no indication of its difficulty. The five
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- Move Over Fermat, Now It's Time for Beal's Problem - Keith Devlin (Devlin's Angle)
Beal's Problem is like Fermat's, but instead of focusing on equations with one exponent, n, there are three: m, n, and r. Thus, Beal's equation looks like this:
x^m + y^n = z^r. The idea is to look for whole number solutions to this equation where the
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- Mrs. Glosser's Math Goodies - Gisele Glosser
Interactive math lessons that work online and offline in a Web browser, and provide immediate feedback to students, with in addition Worksheets (on circumference and area; exponents; expressions and equations; integers; Ocean Math; order of operations;
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- MSTE Java - University of Illinois at Urbana-Champaign (UIUC)
Java-based activities submitted to MSTE, the Office for Mathematics, Science & Technology Education at UIUC. Topics include: best fit; box perimeter; Buffon's needle; CAD viewer; cereal box problem; chi-squared test analysis of random marbles; cliff
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- m@th IT
A "platform to promote, propagate, and mediate applied mathematics and computer sciences," with emphasis on cryptography, number theory, financial mathematics, logic and knowledge representation, and quantum computation. In particular, m@th IT offers
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- Mudd Math Fun Facts - Francis E. Su; Mathematics Dept., Harvey Mudd College
A site developed as a resource for professors wishing to enrich their courses with mathematical 'fun facts': more than 100 5-minute math tidbits that can be used at the beginning of class to get students interested in mathematics. They are best used in
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- The Music of the Primes - Marcus du Sautoy
An article on the Riemann Hypothesis, "the greatest unsolved problem of mathematics."
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- New York Journal of Mathematics (NYJM) - Mark Steinberger, Editor in Chief
Fully searchable research and university-level articles, such as "A Mathematical Theory of Origami Constructions and Numbers." With instructions for authors.
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- Noga Alon
Noga Alon researches combinatorics, graph theory, their applications to theoretical computer science, combinatorial geometry and number theory, and the relationship of combinatorial algorithms and circuit complexity. Some of his papers, along with a
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- Noncommutative Geometry, Trace Formulas and the Zeroes of the Riemann Zeta Function - Alain Connes
Lecture notes offering a general introduction to noncommutative geometry and a discussion of a fundamental example of noncommutative space related to the Riemann zeta function.
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- Nonlinear Dynamics (Mathematics Archives) - University of Tennessee, Knoxville (UTK)
Links to sites on nonlinear dynamics, chaos and turbulence studies, complex systems and visualization, continued fractions and chaos, dynamical systems and technology, dynamics and stability of systems, with indications of level and type of resource offered.
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- Nonstandard Analysis and the Hyperreals - Jordi Gutierrez Hermoso; Math Forum, Ask Dr. Math FAQ
An essay introducing the most basic ideas of nonstandard analysis and the hyperreal number system. Contents: A Very Brief History of Almost-Nothing and More-than-Everything; The Hyperreal Wish-List; Construction of the hyperreal numbers; Hyperreal arithmetic;
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- NOVA Online: Hunting the Hidden Dimension - Public Broadcasting System (PBS)
The PBS television series NOVA has produced a program about fractals, their impact on the world of mathematics, and the way they're shaping our understanding of nature. In addition to the program itself (in five chapters), the website offers a program
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- NOVA Online: The Proof - WGBH, Public Broadcasting System (PBS)
For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem - the idea that a certain simple equation had no solutions. This site includes an interview with Andrew Wiles (the man who spent seven
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- NSDL Middle School Portal: Math Pathway - NSDL; the Ohio State University
A middle school portal into NSDL's math resources, browsable by topic, or choose a pre-selected set of resources on given subjects.
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- NT Number Theory (Front for the Mathematics ArXiv) - Univ. of California, Davis
Number Theory preprints, from the U.C. Davis front end for the xxx.lanl.gov e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives. Search by keyword or browse by topic.
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- Number Bases - Math Forum, Ask Dr. Math FAQ
What is base 10? Binary? Hexadecimal? How can you convert from one base to another?
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- Number Dictionary - Gerardis Giannis, Tsibourakis Dimitris
Enter a number to see its characteristics, such as primality, Fibonacci numbers, factorization, sum of first primes, sum of two squares, triangular numbers, roots, perfect numbers, and more...
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- The Number Empire - Vitalii Vanovschi
Enter a positive integer up to 10^12, press the "Go!" button, and The Number Empire states -- in yes/no format -- whether you entered a prime number, a Bell number, a Catalan number, or a factorial. The same single click displays the integer written out
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- Number Gossip - Tanya Khovanova
Searchable database up to the number 10,000. Checks more than 40 fun predefined properties of numbers, and shows many original and unique properties of an input number. See also this math coach's math blog, lectures, and more from her home page.
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- Number Pi and Golden Section: the decimals occurrences are not random - Jean-Yves Boulay
An exploration of the occurrence of patterns of the digits in decimal representations of pi and the golden section.
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- Number Recreations - Shyam Sunder Gupta
Recreational aspects of number theory, prime numbers, and the like. Currently includes rare numbers, EPORNS (Equal Product Of Reversible Numbers), unique numbers, unlucky 13, fascinating squares, curious properties of 153, and amicable numbers (including
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- Number System - Prof. Nam Sun Wang; Univ. of Maryland, College Park, MD
A handout from a course on Computer Methods in Chemical Engineering, detailing bit and byte definitions, number system background, and conversions among bases: binary, octal, decimal, and hexadecimal systems.
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- Number-Theoretic Hacks - David Eppstein, Theory Group, ICS, UC Irvine
Simple number-theoretic algorithms. Egyptian Fractions - algorithms and references; C++ implementation of J. H. Conway's "nimber" arithmetic; C++ fast algorithm for computing 2-adic inverse; C program for rational approximation of real numbers; Interference
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- Number Theory - Alex López-Ortiz 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 all-rounders; 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 postsecondary-school education, was held July 1-14, 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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- 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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