 The Ideal Voting System (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: What is the shortest line segment fencing off prescribed area 0 < A < 1 in a unit square? (What about the leastarea piece of plane dividing off prescribed volume 0 < V < 1 in a unit cube? What about a 4D cube?) ...assume
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 Identical Calendars for 2000 (Math Chat)  Frank Morgan, MAA Online
For programming into the VCR on January 1st for correct day and date, what years in the 1900s have the same calendar as the year 2000? An identical calendar must, like 2000, be a leap year starting on a Saturday. Leap years occur every four years, and
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 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
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 Ido Efrat
A mathematics professor at Ben Gurion University of the Negev in Israel. Site includes the syllabi for current courses and a list of Efrat's publications in abstract algebra, especially group theory. Some articles may be downloaded in PDF or DVI format.
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 IFS (Iterated Function Systems) for 2D and 3D Visualization  Craig M. Wittenbrink
Using fractal interpolation to graphically represent two and threedimensional scalar data: download article in PDF or PostScript format, and view related images.
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 If You Build It, Will They Come? Participant Involvement in Digital Libraries  Giersch, Klotz, McMartin, Muramatsu, Renninger, Shumar, and Weimar
A paper concerning a workshop involving representatives from several digital libraries with user participation. The workshop explored the ways users participate in digital libraries, and methods of studying these participants' interactions.
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 Illinois Mathematics Association of Community Colleges (IMACC)
A searchable site that offers online versions of AMATYC publications, including "Crossroads in Mathematics: AMATYC Standards," "The AMATYC position on Adjunct Faculty," and local publications, including "Illinois Mathematics and Computer Science Articulation
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 The Illustrative Mathematics Project
Providing guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience with the Common Core State Standards, and by publishing other tools
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 Image Coding Using Fractals  Signal and Image Processing Group, University of Bath
Graphs show how image compression using fractals compares to other methods. Also includes comparison pictures and a list of articles on fractal compression, some of which may be downloaded in gzipped PostScript format.
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 Image Coding Using Wavelets  Signal and Image Processing Group, University of Bath
Read the article "What makes a good orthonormal wavelet for image compression?" Download other wavelet articles in PDF or PostScript format. Visit the Wavelet Warehouse, a repository of wavelet filters (biorthogonal and orthonormal) to download and
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 Image Compression  from DCT to Wavelets: A Review  Subhasis Saha
An article published in ACM Crossroads, the student magazine of the Association for Computing Machinery, about how recent growth in dataintensive multimediabased Web applications has not only sustained the need for more efficient ways to encode signals
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 Images Created by Man & Chaos  Alan Beck
Some personal observations on fractal art and artists. "...the fractal artist does not create but explores, does not manufacture but discovers. Instead of being repelled by computers, such adventurers revel in them, as European mariners of old rejoiced
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 Immersed in Klein Bottles  Ivars Peterson (MathTrek)
"Need a zerovolume bottle? Searching for a onesided surface? Want the ultimate in nonorientability?" The intriguing subject of these cryptic entreaties is a bizarre mathematical object known as a Klein bottle, discovered in 1882 by German mathematician
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 The impact of dynamic geometry software on learning  Bryan Dye; MathsNet
A paper that aims to measure the impact of use of dynamic geometry software on learning via the Internet; to compare various software packages, for example: Geometer's sketchpad, Cinderella, and CabriGeometre; and to measure the impact of "home learning"
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 The Impact of the Math Forum's Problem(s) of the Week on Students' Mathematical Thinking  K. Ann Renninger, Laura Farra, and Claire FeldmanRiordan
Article in PDF format. Presented at the International Conference of the Learning Sciences 2000.
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 Implementing Curriculum, Instruction and Assessment Standards in Mathematics (NCREL)  Cathy Cook; Pathways to School Improvement
From Critical issues in mathematics. National educational standards are being developed in nearly all subject areas. The National Council of Teachers of Mathematics has recently developed standards for mathematics; its Curriculum and Evaluation Standards
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 Implications Rules  Alan Selby
Implication Rules: two puzzles that show the difference between one and twoway implication rules. Mastering the difference is a simple, first step, in rule and patternbased thought, needed to precisely read rules, definitions and statements in all
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 Impossible World  Vlad Alexeev
About impossible figures in art. These figures can be painted on paper but cannot be represented in space. There are many artworks by M.C. Escher, Jos de Mey, Sandro del Prete and many other artists. Also, you can view animations and read articles about
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 Impressions from ICME9  Cut the Knot!, Alexander Bogomolny
Statistics on attendance (by country) at the International Congress on Mathematics Education held in Tokyo, Japan in August, and impressions of talks on the state of mathematics education in the year 2000. According to Mogens Niss (Denmark) who gave the
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 InCharge Education Foundation  InCharge Education Foundation, Inc.
The nonprofit InCharge Education Foundation promotes financial wellness by offering data, information, research, and education on the behaviors and issues facing average individuals and families on consumer credit, money management, and financial wellbeing
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 The Incredible Pi Code  Ivars Peterson (MathTrek)
Researchers have expended a great deal of effort computing as many of the digits of pi as computer technology and mathematical methods allow. Last year, Yasumasa Kanada of the University of Tokyo calculated pi to 206,158,430,000 decimal digits. A high
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 The Independent Set Algorithm  Ashay Dharwadker
A polynomialtime algorithm for finding maximal independent sets in a graph with new bounds on Ramsey numbers.
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 Index Using Mathematics Subject Classification (MSC)  Dave Rusin; The Mathematical Atlas
The index pages at this site are organized according to the Mathematics Subject Classification (MSC) scheme. (This is the scheme developed by the American Mathematical Society and Zentralblatt für Mathematik.) General headings include Foundations;
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 Indian numerals  MacTutor Math History Archives
Linked essay on the method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value), which emerged in India. With references and other related web sites.
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 The Indian Sulbasutras  MacTutor Math History Archives
Linked essay on the Sulbasutras, appendices to the Vedas that contain all that is known of Vedic mathematics, and give rules for constructing altars. (The Vedic people entered India about 1500 BC from the region that today is Iran. The word Vedic describes
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 Individual Differences and the United States Education System  Douglas Trelfa
An overview of ability grouping and tracking in the United States, from The Educational System in the United States: Case Study Findings, March 1999. A discussion of the diversity of beliefs found regarding the question of how to deal effectively and
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 The Inertia Tensor and After Dinner Tricks  Steve Drasco
In PDF format, a paper introducing momentum, angular momentum, the inertia tensor, and principle axes and stable/unstable rotations.
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 Infinity  MacTutor Math History Archives
Linked essay on the mathematical, philosophical, and religious aspects of infinity. With references and other related web sites.
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 Infinity: You Can't Get There From Here!  B. Sidney Smith; Math Academy Online/Platonic Realms
A "minitext" offering a concise introduction to the concept of infinity. Includes historical background, Cantor's set theory, and an introductory discussion of cardinality, as well as suggested reading.
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 Information and Communication, Circuits  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to information and communication, circuits, which includes questions of particular interest to algebraists, especially coding theory (related to linear algebra and finite groups) and encryption (related
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 Information Mechanics Group  Massachusetts Institute of Technology
A research group for the physics of computation. Resources for CAM8, a computer and operating system designed for work with cellular automata, and various papers, which are available for download in PostScript format .
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 InfoWeb's Teachers Gateway  North Carolina Department of Public Instruction (DPI)
New and important information for teachers; educational research  links to studies, papers and reports about how children learn, effective teaching, etc.; instructional resources on and off the Web; education news; law and policy; award programs; education
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 innumeracy.com  Steve Head
A site devoted to the nature of chance and critical thinking, a result of a search of various sites that may be of use to others whose desire is to develop a more critical mind. Some articles are posted to the Probability and Critical Thinking pages;
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 InSITE: The Information Network of SITE  Society for Information Technology and Teacher Education
A clearinghouse for textbased and multimedia materials related to the integration of technology into teacher education, including staff development, exploring how educators from various content areas and at various locations can collaborate over the
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 The Institute for Figuring  Margaret and Christine Wertheim, CoDirectors
"If mathematics is a language of pattern, its structures may be seen as the verses of a formal, yet fantastical poetics. Across the globe people have delighted in the harmonies of this language and the patterns discovered therein. These are the songs
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 The Institute for Nonlinear Science  University of California, San Diego
A research group whose topics include chaotic lasers, granular dynamics, and fractal image compression. Some related articles are available for download in PostScript or PDF formats.
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 Institute for Scientific Computation  Texas A&M University
The Institute for Scientific Computation (ISC) conducts and coordinates multidisciplinary research into data management, mathematical modeling, numerical solutions, and visualization. Read about ISC research and the Computational Sciences Certification
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 Institute for Special Education  University of Fribourg/Switzerland
A variety of research projects in English, German, and French, including Training of cognitive strategies  a computer programme for learningdisabled children; Publications (quarterly journal, books in German).
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 Institute of Mathematical Geography (IMaGe)  Sandra Lach Arlinghaus
Archives of SOLSTICE: An Electronic Journal of Geography and Mathematics. Chapters, notes, and book reviews dating from 1986, in variously jpg, pdf, html, or simple text formats. Sample articles include "Extension of Barr's Problem to the Set of Platonic
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 Institute of Mathematical Statistics  Elyse Gustafson, Executive Director
The Institute of Mathematical Statistics (IMS) is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. IMS' main technical journals are the Annals of Statistics,
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 The Institute of Mathematics and its Applications (IMA)
The professional and learned society for qualified and practising mathematicians, based in the UK and with thousands of members worldwide. IMA aims to promote mathematics and its applications in all sectors: industry, commerce, education, the public sector
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 Institut National de la Statistique et des Etudes Economiques (INSEE)  France
Statistics about France. L'INSEE rassemble, traite, analyse et diffuse les données statistiques relatives à l'économie et à la société. Faits et chiffres; produits et services; inventaire communal; liens vers
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 Instituto Brasileiro de Geografia e Estatística (IBGE)
The Brazilian agency that collects statistical and geographic information. "Brazil in Brief," short articles with graphs and/or data tables for key socioeconomic topics; the "Minimum National Social Data Set," a set of information following United Nations
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 Instituto Nacional de Estadística e Informática (INEI)  Perú
El Instituto coordina las actividades estadísticas e informáticas oficiales del Perú. Notas de Prensa; Capacitación (Escuela Nacional de Estadística e Informática y Capacitación a Distancia con cursos para el Censo);
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 Instituto Nacional de Estadística, Geografía e Informática (INEGI)  Mexico
The government agency that provides statistical and geographic information for the country of Mexico. Introduction to Mexico; tables, articles, and maps of geographic, population, and economic information; structure and modernization of the department.
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 Instituto Nacional de Estatística (INE)  República de Bolivia
El Instituto tiene las funciones de: estudiar, compilar y difundir la información estadística de Bolivia. Introducciones de Bolivia y INE; Resumen Estadístico de Bolivia; Informacíion Estadística y Geográfica;
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 Instructional Resources  Microsoft Corporation
Microsoft's instructional resources are divided into lesson plans (math), howto articles, and tutorials. You may search each section's resources by age group, Microsoft product, theme or learning area. See also the Design Gallery Live.
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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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 Integral Equations  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to integral equations, which seek functions that satisfy relationships with their integrals. For example, the value of a function at each time may be related to its average value over all preceding time.
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 Integral Transforms, Operational Calculus  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to integral transforms, which include the Fourier transform as well as the transforms of Laplace, Radon, and others, convolution operators, and operational calculi. History; applications and related
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