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 Appealing Numbers - Ivars Peterson (MathTrek) A short history of amicable numbers - pairs in which each number is the sum of the proper divisors of the other. The smallest such pair is 220 and 284. The number 220 is evenly divisible by 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which add up to ...more>> Arbelos Internet Math Society - Bert Liberi and William F. Widulski, Westchester Communtiy College A mathematics society dedicated to the pursuit of elegance in problem-solving. Every month, solve challenging problems that require "more imagination than memorization." Also, access old problems and solutions; and study a list of heuristics of problem-solving, ...more>> Arithmagic - Ivars Peterson (MathTrek) Arthur T. Benjamin eschews the usual trappings of the magician's trade. Calling himself a mathemagician, he astonishes audiences with amazing feats of mental arithmetic. Behind the scenes, he reveals how you, too, can look like a genius without really ...more>> A Bibliography of Bernoulli Numbers - Karl Dilcher A bibliography of Bernoulli numbers by Karl Dilcher and Ilja Sh. Slavutskii. The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They are particularly important in number theory, especially in connection ...more>> BrainBashers - Kevin N. Stone A collection of logic, language and math puzzles, in a choice of easy/medium/hard. Rate the puzzles; show their answers. Logic puzzles include Einstein's Puzzle. Play games of strategy, such as "Four in a Row" (also known as "Connect Four") or games based ...more>> CalculationRankings - Youri Lieberton Arithmetic problems to solve or number sequences to complete as a stopwatch counts down. Play the games to compare high scores against other speedy problem solvers; take the timed tests to see correct answers after submission. ...more>> Carl Offner's Home Page - University of Massachusetts, Boston Expository papers by Offner on mathematics and computer science (levels: advanced undergraduate to 1st-year graduate student): Repetitions of Words and the Thue-Morse Sequence; Finite Fields and Pseudo-Random Number Generation; Some Early Analytic Number ...more>> Coffee Hour Problem of the Week - Matthew McMullen Classic and "found" problems, as well as original challenges, in number theory, logical reasoning, statistics, calculus, geometry, and algebra. McMullen has posted PDFs of the PoWs, as well as their solutions, since 2007. ...more>> A compendium of NP optimization problems - Crescenzi & Kann A continuously updated catalog of approximability results for NP optimization problems. Because no NP-complete problem can be solved in polynomial time (unless P=NP), many approximability results (both positive and negative) of NP-hard optimization problems ...more>> Computing Science: A Question of Numbers - Brian Hayes; American Science An article about the ISC (Inverse Symbolic Calculator) and numbers. "In my daydream, Neil Sloane and Simon Plouffe are contestants on "Jeopardy," the TV game show. Sloane picks the category "Integer Sequences" for \$400, and Alex Trebek reads the answer: ...more>> 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 ...more>> David Sumner's Home Page - David Sumner Study guides, exams, quizzes, problem sets, exam review materials, utilities, programs and simulations, syllabi, and other materials for courses such as calculus, sequences and series, graph theory, number theory and cryptography, and probability. The ...more>> Digits, Squares, and Cycles - Ivars Peterson (MathTrek) Fascinating patterns lurk among the digits of whole numbers. Pick a positive integer, such as 57. Square each of the digits, then add the squares together: 5^2 + 7^2 = 25 + 49 = 74. Do the same thing with the digits of 74: 7^2 + 4^2 = 49 + 16 = 65. Keep ...more>> Edutest: Online Assessment Resource Assessment testing based on nationally recognized standards in Math and Language Arts for grades 2-8. Scoring is instant and both parents and teachers can review the tests and the correct answers with their students. The site has some information for ...more>> Encyclopedia of Combinatorial Structures - Virginie Collette; INRIA A site designed to be similar to Sloane's Encyclopedia of Integer Sequences but with an emphasis on sequences that arise in the context of decomposable combinatorial structures. Like the EIS, the database is searchable by the first terms in the sequence, ...more>> Enumeration of the Binary Trees (Catalan Numbers) - Ivan Galkin For each number of nodes, n, there is a certain number of possible binary tree configurations. These numbers form a sequence of integers with respect to n. A useful way to describe an integer sequence is to construct a generating function... ...more>> Essay Ideas - Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia For a course on Using Computers in Mathematics Instruction. Friday the 13th (show there are at most three and at least one Friday the 13th in each year, consider when two consecutive months can be have Friday the 13th); Gingerbread Man (a Microsoft Excel ...more>> 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 ...more>> Experiments with the 3n+1 Sequence - Alfred Wasserman An online program tests numbers for convergence under the 3n + 1 sequence. Also available in German. ...more>> Four Numerical Triangles in Nexus - Len Smiley Three well-known combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that ...more>> Friedman Numbers - Erich Friedman A Friedman number is a number that can be written in some non-trivial way using its digits, the operations + - * / ^ and concatenation of digits. For example, 25 and 126 are Friedman numbers, since 25 = 5^2, and 126 = 6 * 21. Page includes a list of all ...more>> From Lewis Carroll to Archimedes - Cut the Knot!, Alexander Bogomolny On March 29, 1879, Vanity Fair began offering its subscribers a new weekly puzzle invented by Lewis Carroll... on March 17, 1953 Frank Gray, a research scientist at Bell Labs, filed patent no. 2632058, for the Gray code encoding the vacuum tube. An n-digit ...more>> Future School Developer of educational software, online tutoring, and home schooling courses. Video tutorials. Sample lessons and ordering information available. ...more>> General Mathematics, N-Z (Funk & Wagnalls Multimedia Encyclopedia) - Lycos Zone: Mathematics Short articles on basic mathematics, including biographical information about mathematicians, from John Napier to Zeno of Elea. ...more>> Generating Functions - Interactive Mathematics Miscellany and Problems, Alexander Bogomolny The definition and properties of generating functions with several examples, including variants of coin change, fast algorithm for computing Banzhaf and Shapley-Shubik power indices, covering the chessboard with tromino and more. Many examples are illustrated ...more>> Hands-on Math: Activities for the Elementary Classroom - Janine Parker Lesson plans for children in grades one through six about topology, number patterns, and geometry. Handouts for each lesson may be downloaded in PostScript form or as GIF files, and a zipped DOS program to display Platonic solids, Archimedean solids, ...more>> Home Run Numbers - Ivars Peterson (MathTrek) The integers 61 and 62 have been very much in the news this summer. On the major-league baseball front, Mark McGwire hit his 62nd home run on Sept. 8, and Sammy Sosa matched that total on Sept. 13, surpassing the record of 61 home runs in a season held ...more>> Identities for Linear Recurring Sequences - Kevin Brown There are several methods for computing the Nth term (mod M) of a linear recurring sequence of order d in log_2(N) steps, but most such methods require d^2 full multiplications (mod M) per step. The algorithm described below requires only d(d+1)/2 ...more>> 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. ...more>> IXL Learning IXL provides free online practice, organized by grade levels K-8 and aligned to state standards. Choose one math skill from among the hundreds offered, and submit your answer. Respond incorrectly, and click on the "explanation" button to learn more; get ...more>> Journal of Integer Sequences - Jeffrey O. Shallit, editor-in-chief This is an electronic journal devoted to papers dealing with integer sequences and related topics. All papers are available as html documents. ...more>> Juggling by Design - Ivars Peterson (MathTrek) The earliest known depiction of juggling is on the wall of an Egyptian tomb nearly 4,000 years old. The painting shows a woman keeping three balls aloft. It's only in the last decade or so, however, that juggling has become the subject of serious mathematical ...more>> Juggling by Number (MatheMUSEments!) - Ivars Peterson (Math Muse for Kids) Mathematicians have invented a way to write down juggling patterns as sets of numbers. They look at the order in which balls are tossed into the air and then caught. Each toss or catch happens on a particular beat, as if the juggler were keeping time ...more>> K-12 Math Problems, Puzzles, Tips & Tricks - Math Forum Links to calculation tips (Beat the Calculator, Divisibility Rules, Multiplication Tips), Math Problem sets, and math number and line puzzles. ...more>> Keith Numbers - Mike Keith A Keith number is an n-digit integer N with the following property: If a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed, with the first n terms being the decimal digits of the number N, then N ...more>> Keith's Think Zone - Keith Enevoldsen Fun math miscellany about number sets, n-dimensional hyperspheres and hyperballs, big numbers, areas and volumes, angles — the revolution, shortcut arithmetic, and more. See, in particular, the brain teasers "deadly disease puzzler" and "the world's ...more>> Lehmer's Conjecture - Michael Mossinghoff; Dept. of Mathematical Sciences, Appalachian State Univ. A summary of what is known today about Lehmer's Conjecture, including descriptions of algorithms, histories of searches performed, and various lists of polynomials with small measure. References and a thesis available for downloading. ...more>> Le site des maths à petites doses - Saint-Martin Arnaud Supplementary information and explanations of various mathematical topics, often illustrated with figures and JavaScript, as well as some sample problems and multiple-choice quizzes. In French. ...more>> Letter/Number Puzzles - Math Forum, Ask Dr. Math Common Question A selection of answers to questions about cryptograms, alphametrics, letter sequences, and other letter/number puzzles, such as SEND + MORE = MONEY. ...more>> License Codes - Ivars Peterson (MathTrek) Some states use complicated schemes for establishing driver's license identification numbers. The numbers may include check digits to detect errors or fraud, or they may encode such personal data as the month and date of birth, year of birth, and sex. ...more>> LSL Math Traits - Gary T. Leavens A guide to an archive of mathematical traits written in the Larch Shared Language (LSL), constituting a small LSL handbook. The traits do not duplicate the traits in Guttag and Horning's book, but add to them. Real numbers; Polynomial Functions and Polynomials; ...more>> Marc Chamberland A mathematician at Grinnell College interested in differential equations and dynamical systems. Resources for the 3x + 1 problem and the Jacobian Conjecture include papers to download in PostScript format and information and proceedings for related conferences. ...more>> Maris-McGwire-Sosa Numbers (Or: Mathematics Plays Baseball, Again) - Mike Keith An article in the spirit of Playing with Ruth-Aaron Pairs by Ivars Peterson, wherein in honor of the 62nd season home run hit by Mark McGwire on 8 Sept 1998 and Sammy Sosa on 13 Sept 1998, which eclipsed the long-held record of 61 by Roger Maris, Keith ...more>> Mastering Mastermind - Ivars Peterson (MathTrek) "Games offer wonderful playing fields for developing mathematical problem-solving skills. For Mathew Mitchell of the School of Education at the University of San Francisco, the preferred training ground is a classic game called Mastermind. "Students young ...more>> The Mathematical Works of Rajesh Ram - Rajesh Ram A collection of formulas and identities: Fibonacci, Pell, square and triangular numbers, and sums of cubes and other powers, with an identity related to Ramanujan's Number. ...more>> The Mathman - Don Cohen Materials for sale for K-12 students, teachers and parents; pre-calculus. Materials include Get Ready for Calculus (Calculus By and For Young People book, CD-ROM, worksheet book, videotapes and map) and Changing Shapes with Matrices. Patterns, visualization, ...more>> Medieval Harmony - Ivars Peterson (MathTrek) Harmonic numbers. The history of mathematics contains many gems of mathematical reasoning and thought. At a Mathematical Sciences Research Institute meeting last October, number theorist Hendrik W. Lenstra Jr. of the University of California at Berkeley ...more>> A Nameless Number - Len Smiley Triangle-free polygon dissections are a variant of the dissection questions of Catalan, Schroeder, and others: In a convex (n+2)-gon with n+2 labeled nodes, what is a(n), the number of ways of drawing non-intersecting diagonals so that no triangles are ...more>> Names for Numbers - Ivars Peterson (MathTrek) Once someone discovers an interesting pattern or type of behavior, those particular numbers are likely to earn a collective name. So we have perfect numbers, amicable numbers, lucky numbers, Mersenne numbers, Fermat numbers, Fibonacci numbers, Keith numbers, ...more>> Neil J. A. Sloane Neil Sloane's research ranges far and wide and includes coding theory, sphere packing, lattices and quadratic forms, packing lines, and planes, spherical codes and designs, quantizing, geometry, combinatorics, the design of experiments, integer sequences, ...more>>
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