- $1000 High School Calculus Student Award (Math Chat) - Frank Morgan, MAA Online
Solution to the challenge: Justin Smith calls 5939 a "right" prime because it remains prime after dropping any number of digits from the right: 5939, 593, 59, and 5 are all prime. How many right primes are there less than 1000? Is there a largest right
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- 65-m.p.h. Speed Limits, Large Primes, and Japanese Exams (Math Chat) - Frank Morgan; Christian Science Monitor
When a state increases a highway speed limit from 55 to 65 miles per hour, by what percent does the road capacity (in cars per hour) change?
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- Adventures in the MathZone - Ivars Peterson (MathTrek)
Ivars Peterson and his wife, Nancy Henderson, have written "a book that introduces children to a variety of ideas also of interest to today's mathematicians: knots, map coloring, Möbius strips and topology, prime numbers, chaos, fractals, and more. Our
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- Aesthetics of the Prime Sequence - Turpel Armand
A brief introduction to prime numbers, with a primality testing applet, a page on primes and music, primes and nucleotide bases, primes graphics, idiot savants and primes, primes-related software, related links, favorite books, and a special page of Lyapunov
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- Algebra.Help - John Traker
Algebra.help is an online resource designed to help people learn algebra. It offers lessons to teach or refresh old skills, calculators that show how to solve problems step-by-step, and interactive worksheets for testing skills. To be notified of updates
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- Andrew Granville
Andrew Granville researches number theory, combinatorics, and arithmetic geometry. His papers on these subjects are available for download in PostScript format. Granville also maintains a survey of results on the arithmetic properties of binomial coefficients.
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- Another Record Prime - Ivars Peterson (MathLand)
This time, it didn't take a supercomputer. The new record for the largest known prime number goes to someone using a Pentium-powered desktop machine. Joel Armengaud, a computer programmer working for Apsylog in Paris, made the discovery on Nov. 13 and
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- Arithmetic Properties of Binomial Coefficients (Organic Mathematics Proceedings) - Andrew Granville
Many great mathematicians of the nineteenth century considered problems involving binomial coefficients modulo a prime power (for instance Babbage, Cauchy, Cayley, Gauss, Hensel, Hermite, Kummer, Legendre, Lucas and Stickelberger). They discovered a variety
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- Articles on Mathematics - Subramaniyan Neelagandan
Articles in four formats: DVI, PDF, PS, and TEX Code. The Distribution of Prime Numbers & Integer Factorization; The Simplification of Fermat's Last Theorem; Exploration of Collatz's Conjecture.
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- Autograph (Mathematics) - Eastmond Publishing Ltd
Autograph is visualization software that operates in two modes: graphs, coordinates and bivariate data; and single-variable statistics and probability. Resources include graphs, statistics, screencam demos, Microsoft Word worksheets, PowerPoint presentations,
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- BigPrimes.net - BigPrimes.net
An archive of primes, plus information on each prime, and on prime numbers in general, number systems, types of numbers, and universal constants. The number cruncher will tell you facts about numbers you submit.
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- Calculators On-Line Center: Part II - Mathematics - Martindale's Reference Desk
Over 7,420 calculators for: Unit Conversion (Time, Distance, Length, Speed, Weight, etc.); Abacus; Basic Math; Complex Mathematics; Complex Math Education; Complex Math Calculators by Specialty: Algebra and Linear Algebra; Algorithms; Calculus; Central
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- CMP Software - Connected Mathematics Project, Michigan State University
Downloadable software designed to accompany CMP units. For the Factor Game winning strategies involve distinguishing between numbers with many factors and numbers with few factors; students analyze game strategies and are introduced to the definitions
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- Conceptual Mathematics - Karl F. Kuhn
Lesson outlines for teachers, math challenges, and philosophical discussions on how math helps us understand sports, fair taxation, gender difference, and more. The author's musings on mathematics as a game cover Pascal's Triangle, primes, the golden
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- Cubes of Perfection - Ivars Peterson (MathTrek)
...Six is the smallest perfect number. Twenty-eight comes next. Its proper divisors are 1, 2, 4, 7, and 14, and the sum of those divisors is 28. Incidentally, if the sum works out to be less than the number itself, the number is said to be defective
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- Curious Prime Numbers - Debra Sheets and Bill Tomlinson
The curiosity presented was discovered after trying to solve the following puzzle: There are 2 mathematicians S and P. S knows the sum of two numbers and P knows the product of those same two numbers. Assume that the numbers are integers greater than
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- Divisibility Rules - Math Forum, Ask Dr. Math FAQ
How can you tell whether a number is divisible by another number (leaving no remainder) without actually doing the division? Why do 'divisibility rules' work?
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- Divisibility Rules to 50 and Beyond - Stephen D.T. Froggatt; Math Forum, Ask Dr. Math FAQ
A quick way of testing primality of larger numbers: the idea of deleting the last digit and adding or subtracting a multiple of the digit from the remaining number can be generalized to test for divisibility by prime numbers up to 50 and beyond.
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- Dream Frequency .com
CGI web applications to calculate the factors of a number, calculate the prime numbers below a number, test a number for primality, calculate a word's position in the alphabetically sorted list, convert hex to ASCII, or convert temperature from celsius
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- Eighth Grade (AAA Math) - John Banfill
Interactive math exercises, lessons, and games covering basic arithmetic concepts and methods, for eighth grade.
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- Entropia.com
The Global Internet Community for Science and Mathematics Distributed Research Computing, Entropia.com is a community dedicated to performing real research on a massive scale using ordinary home and office computers connected through the Internet. Entropia.org's
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- Eratosthenes' Sieve (Algebra Interactive!) - Arjeh M. Cohen, Hans Cuypers, Hans Sterk
An applet from the first chapter of the HTML-based book Algebra Interactive!, an introduction to abstract algebra providing an algorithmic approach to algebraic structures ranging from the elementary structures of the integers, polynomial rings in one
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- Eratosthenes' Sieve with JavaScript - H. B. Meyer
An interactive animation with JavaScript of the sieve of Eratosthenes, showsing how the prime numbers <= 400 can be "sieved."
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- Excel Math - AnsMar Publishers, Inc.
Excel Math is a mathematics curriculum for Kindergarten through Sixth grade students. Students are repeatedly given practice in the use of the concepts, following their introduction, so that they retain them and develop a solid foundation on which to
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- Expression Calculator - D. Block, Vestris, Inc.
A calculator for Windows 95/98/NT that does 2D plots and financial functions, constants, operators, logical functions, dozens of common functions, primes and hyperbolic functions, students and Gauss integrals, Fresnel, elliptic integrals, trigonometric
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- The Factor Game (i-Math Investigations) - Illuminations; National Council of Teachers of Mathematics (NCTM)
An online, interactive, multimedia math investigation. The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through
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- Factoring and Primes (High School Math) - Homeworkhelp.com, Inc.
The words "Product" "Factor," "Factoring," and "Prime"; How do I factor a natural number?; How do I know if a number is divisible by 2, 3, 4, 5, 9, 10, or 11?; How do I know whether a number is prime (i.e. can't be factored any further)?; Table of 1000
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- Factoring Large Numbers (CEC) - Tim Olson, Meadow Valley Middle School, Panaca, Nevada
A grade 7 lesson plan: Have students choose a large even number, say 642. How could you tell what numbers that are all prime would go into this number? Let the students discover how many times they can divide out a group of small numbers. Then introduce
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- Factorization using the Elliptic Curve Method - Dario Alejandro Alpern
A Java applet that factors numbers up to 1000 digits long, outputting their number of divisors, sum of divisors, Euler's totient, Moebius number, and sum of squares. Also accepts numerical expressions.
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- Factors of 1000 numbers starting from googolplex - Dario Alejandro Alpern
Known prime factors of numbers in the range 10^(10^100) to 10^(10^100)+999.
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- Favorite Math Problems - Greg Weidman
Examples of Diophantine equation problems, with hints and solutions: 1000 Lockers, 5^999.999 mod 7; PQ knows; Rational 5's; Prime Around.
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- Finding Prime Factors - Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about finding prime factors, along with divisibility rules for some prime numbers.
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- The First 10,000 Primes - Chris Caldwell; Dept. of Mathematics & Computer Science, Univ. of Tennessee at Martin
The first 10,000 prime numbers, in a table.
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- FTL
An online magazine with articles about space, science, and science fiction. Features include a series of humorous articles by Ian Stewart, with topics ranging from lattice polyhedra (and conceptual art) to Diophantine equations (and camels).
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- Fun With Mathematics! - Harry J. Smith
Mathematical recreations, curiosities, and software, from computing pi, tesseracts, and data encryption to golygons and quaternions - and much more.
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- Fun With Numbers - Sage Weil
Integers and Real Numbers. 250,000 digits of the square root of nine; the first 28,915 odd primes; the first even prime - the whole thing; 50,000 Random Numbers; the First 999 Factorials; Fractional approximations of pi; Powers of 2; 1.2 million digits
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- Gaussian Primes - Jim Loy
This is an introduction to Gaussian primes, complex numbers with integers for real and imaginary parts that are divisible by themselves and 1, but no other complex numbers with integer coefficients. This shows calculations of the first few Gaussian primes.
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- Goldbach's Prime Pairs - Ivars Peterson (MathTrek)
Prime numbers serve as building blocks in the mathematics of whole numbers. Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove. The Goldbach
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- Great Computations - Ivars Peterson - Science News Online
Owners of home computers have joined researchers in cracking problems and crunching data, searching for signs of intelligent extraterrestrial life, running large models of the world's climate, and carrying on a worldwide effort to identify record-breaking
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- Guessing the Prime Number Theorem and Treacherous Logic (Math Chat) - Frank Morgan, MAA Online
The Prime Number theorem says that the probability P(x) that a large integer x is prime is about 1/log x. At about age 16 Gauss apparently conjectured this estimate after studying tables of primes. Greg Martin suggested to me a heuristic way to approach
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- HAKMEM - Beeler, Gosper, Schroeppel; Artificial Intelligence Laboratory, MIT
A list of math and computer-related problems, unsolved in 1972 when the list originated, compiled "with the hope that a record of the random things people do around here can save some duplication of effort - except for fun." Topics include: Geometry,
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- Home Page of John B. Cosgrave - John B. Cosgrave
The author of A Prime For The Millennium, in which is outlined his discovery of what he calls a 'millennium' prime, (a prime number with exactly 2000 digits), also provides links to a Fermat number record and the possiblity of a 6th Fermat prime. Prof.
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- Icon Odds and Ends - Dept. of Computer Science, Univ. of Arizona
Icon is a high-level, general-purpose programming language with a large repertoire of features for processing data structures and character strings; an imperative, procedural language with a syntax reminiscent of C and Pascal, but with semantics at a
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- Ideas, Concepts, and Definitions (MegaMath) - Nancy Casey; Los Alamos National Laboratory
A glossary and reference page to help students learn more about mathematics and find out what some of the special words mean. Topics: Doing What Mathematicians Do; Truth and Proof; Mathematical Objects and Their Properties; Modeling and Abstraction; Algorithms;
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- Infinite Primes - Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about whether there is an infinite number of primes, and the frequency of their distribution.
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- Integer Sequences and Arrays - Clark Kimberling; Dept. of Mathematics, Univ. of Evansville, Evansville, IN
Certain seemingly simple sequences of integers baffle the best mathematicians. Other sequences, less baffling, exhibit patterns - or absence of patterns - whose appeal shines beyond whatever applications these sequence might find outside mathematics.
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- Introduction to Number Theory - X.-D. Jia; Southwest Texas State College
Lecture notes (1996): Factorization of Integers; Congruences; Quadratic Residues; Continued Fractions.
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- Investigating Patterns: Number Patterns Fun with Curves & Topology - Jill Britton
Annotated list of links within various number pattern, curve, and topology topics. Linked items feature activities for students. Topics include: prime numbers/magic squares, clock or modular arithmetic, the golden ratio, Fibonacci numbers, binary numbers/Pascal's
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- Javascript School Math Toolkit - Jeff LeMieux
JavaScript Pythagorean solver, proportion problem solver, percent proportion problem solver, chord to circumference calculator, denominator to repeating decimal checker, subtraction worksheet generator, addition worksheet generator, multiplication worksheet
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- Joe's Number Theory Web - Joe K. Crump
Methods for factoring large numbers, exploration of 2^n mod n, equal sums of like powers, tridigital squares, balanced bases, and Weiferich primes.
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