 Chasing Arrows (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The reycling symbol looks like three bent arrows chasing each other around a triangular loop. You often find it printed on cardboard cartons, envelopes, greeting cards, packages, and trash containers. It's also an intriguing mathematical object. Imagine
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 Chinese Mathematics  MacTutor Math History Archives
Articles on mathematics in Chinese culture: An Overview of Chinese Mathematics; Nine Chapters on the Mathematical Art; The Ten Mathematical Classics; Chinese Numerals; and Chinese Problems. Also an alphabetical list of Chinese mathematicians, linked to
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 Chinese Remainder Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An explanation and proof, using modular arithmetic, of the Chinese Remainder Theorem, which concerns problems of the following type: There are certain things whose number is unknown. Repeatedly divided by 3, the remainder is 2; by 5 the remainder is 3;
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 Chinks in Digital Armor  Ivars Peterson  Science News Online
Tampering with a smart card can force it into making errors in the calculations used for encrypting data, potentially allowing the code to be broken.
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 Chris Fenwick's mathematics education (selforganised readingtolearn) research and teaching page  Chris Fenwick
Research material on mathematics education, from the perspective of a teacher of Alevel mathematics students.
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 Christianity and the Mathematical Sciences  the Heliocentric Hypothesis  MacTutor Math History Archives
Linked essay on Christianity's influence on the mathematical sciences. With references and other related web sites.
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 A Chronology of Mathematicians  MacTutor Math History Archives
A chronology of mathematicians between the dates stated, showing how the lives of
the mathematicians overlap: 700 BC700 AD; 7001650; 16251775; 17501850; 18251900; 18751957. Where either the birth or death of a mathematician is unknown (mostly for
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 A chronology of pi  MacTutor Math History Archives
Precomputer calculations of pi, from the Rhind papyrus through Ferguson (1946); computer calculations from Ferguson (1947) through Kanada, Takahashi (Sept 1999). With references and other related web sites.
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 Circles in the Sky  Ivars Peterson; Science News Online
Detecting the shape of the universe: evidence of a finite, multiply connected universe may show up in microwave data from future spacecraft.
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 Circles of Dissonance  Ivars Peterson (MathTrek)
Much of today's music rests upon ancient tradition going back thousands of years to the time of the Greek mathematician and mystic Pythagoras. The Pythagoreans observed that tones an octave apart are pleasing to the ear. In modern terms,
one can say
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 The Civilization of the Mayans  ThinkQuest 1997
Essentially a school paper in web format, covering, briefly, Mayan art, astronomy, ballgame, books and hieroglyphics, class system, and number system, with rated related Mayan links and references, and an abouttheauthors section.
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 Clash of the Chess Titans  Keith Devlin (Devlin's Angle)
Thoughts on the KasparovDeep Blue match of 3 May 1997. Throughout history, people have been building machines that can perform tasks better than humans. When Kasparov, referring to his upcoming match, talks about "an area that defines human beings,"
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 Classical Dynamics: Spinning Eggs — A Paradox Resolved  H. K. Moffatt and Y. Shimomura, Nature
"If a hardboiled egg is spun sufficiently rapidly on a table with its axis of symmetry horizontal, this axis will rise from the horizontal to the vertical. Conversely, if an oblate spheroid is spun sufficiently rapidly with its axis of symmetry vertical,
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 The Classical & Keynesian ADAS Model of the Canadian Economy  Elmer G. Wiens; Egwald Web Services Ltd.
Macroeconomics model of the Canadian economy considering both the aggregate supply and aggregate demand for products. Illustrated article with interactive supplemental page.
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 Classical Thermodynamics, Heat Transfer  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to classical thermodynamics, heat transfer: the study of the flow of heat through matter, including phase
change and combustion. Historically, the source of Fourier series. History; applications and
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 Climate Dynamics, Chaos and Quantum Mechanics  Dr. A. Mary Selvam
A theory of everything for chaos, quantum mechanics, and gravity, applicable to macroscale weather patterns and subatomic dynamics as well as turbulent fluid flows. Contents focus on nonlinear dynamics and chaos (fractal geometry), iteration, a cell
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 The Clique Algorithm  Ashay Dharwadker
A polynomialtime algorithm for finding maximal cliques in a graph with new bounds on Ramsey numbers.
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 CLN: Community Learning Network
Designed to help K12 teachers integrate technology into their classrooms. Includes over 225 menu pages with more than 4,200 annotated links to educational WWW sites, as well as over 100 WWW resources of their own.
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 Clusters and Decagons  Ivars Peterson  Science News Online
A novel pattern made up of overlapping, 10sided tiles may serve as a model of how atoms arrange themselves into a quasicrystalline structure.
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 Clutch Hitting  Elan Fuld
Download the PDF of a study examining whether clutch (or choke) hitters exist in professional baseball. Using playbyplay data, Fuld found substantial evidence that clutch hitters exist in Major League Baseball, when sacrifice flies are considered as
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 CME Project  Center for Mathematics Education, Education Development Center, Inc. (EDC)
The CME Project is a fouryear, NSFfunded, comprehensive high school mathematics program that is problembased, studentcentered, and organized around the familiar themes of Algebra 1, Geometry, Algebra 2, and Precalculus. The CME Project sets as its
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 CODEE Learning Assets Library  Consortium for Ordinary Differential Equations Experiments (CODEE)
Electronic versions of the 19921997 CODEE newsletters, which published pedagogical articles, lesson plans, computer experiments, and software reviews related to ODEs. The Consortium for Ordinary Differential Equations Experiments (CODEE) seeks to disseminate,
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 "The Code War"  Beyond Discovery  Dana Mackenzie et al.; National Academy of Sciences
An online science article from the Beyond Discovery series that explores the trail of developments in the branch of mathematics known as number theory that led to modernday encryption techniques. Contents include: Early Ciphers; The Enigma Challenge;
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 Cognition Learning and Development Lab  Nicole McNeil, University of Notre Dame
The Cognition Learning and Development (CLAD) Lab studies how children think, learn, and solve math problems, in pursuit of the mechanisms involved in the development of quantitative reasoning, symbolic understanding, and problem solving. What basic cognitive
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 Cognitive Apprenticeship (Learning and Mathematics)  Collins, et al.; Math Forum
In a chapter entitled "Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics," in the 1989 book Knowing, learning, and instruction: Essays in honor of Robert Glaser, Allan Collins, of BBN Laboratories, and John Seely Brown
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 Coins, Art, and Math in North Bay  Ivars Peterson (MathTrek)
North Bay's Nipissing University hosted the annual meeting of the Ontario
Association for Mathematics Education, which attracted about 650 math teachers. As one of the featured speakers, I presented a talk on randomness. My examples included slot machines,
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 Collaborative Learning  Mathematics Education at The Math Forum
A collection of links to collaborative and cooperative learning resources on the Web, including articles, discussions, and teaching techniques that emphasize collaboration.
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 The Collage Theorem  Cut the Knot!, Alexander Bogomolny
To find an IFS whose attractor is "close to" or "looks like" a given set, one must endeavor to find a set of transformations  contraction mappings on a suitable set within which the given set lies  such that the union, or collage, of the images of the
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 The Collapsing Compass  Godfried Toussaint
There has been considerable interest during the past 2300 years in comparing different models of geometric computation in terms of their computing power. One of the most wellknown results is the proof in 1672 due to Mohr that all constructions that can
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 CollegeLevel Standards and Guidelines  Mathematics Education at the Math Forum
The Math Forum's suggested sites on standards in college math education, including links to standards on the Web, sessions at conferences, and reports.
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 College Preparatory Mathematics (CPM): Change From Within  Smart Catalog
Description of a high school mathematics curriculum that replaces the current, standard collegepreparatory math program with a rich problembased, integrated curriculum.
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 Coloring Penrose Tiles  Ivars Peterson (MathTrek)
One set of Penrose tilings consists of a pair of diamondshaped figuresone fat and one skinny. Attempts to color such Penrose diamond tilings led some people to conjecture that three colors suffice. Now, mathematicians Tom Sibley of Saint John's University
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 Combinatorics  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to combinatorics, loosely the science of counting, studying families of sets (usually finite) with certain characteristic arrangements of their elements or subsets, and asking what combinations are possible,
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 Combinatorics (MathPages)  Kevin Brown
About 40 "informal notes" by Kevin Brown on combinatorics: Dedekind's problem, cumulative permutation sequences, the factorial number system, Hardy and Ramanujan on partitions, solving magic squares, collecting k complete sets of coupons, and many more.
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 The Combinatorics Net and Annals Of Combinatorics  Bill Chen
Links to combinatorics articles, groups, conference reports, seminars, journals, books, typesetting and graph drawing, software, preprints, open problems, research announcements, news and stories, and related sites. The Annals of Combinatorics publishes
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 Combustion Chaos  Univ. of Houston, Univ. of Texas at San Antonio
An interdisciplinary research group studying the dynamics of pattern formation in burner stabilized premixed flames. Includes graphics, movies, and Java simulations of different patterns, explanations of models and experiments, and list of related publications;
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 Comedy Tonight, Math Style!  Ivars Peterson (MathLand)
Edward Burger and Colin Adams aren't yet as well known as such famous comedy teams as Laurel and Hardy... but they are not only performers but also math professors at Williams College in Williamstown, Mass. They bring antic energy, slapstick humor, and
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 Comments on Mathematics and Education  E. Lee Lady, University of Hawaii
Notes on the teaching and learning of math. What Is Mathematics? What Makes Mathematics So Hard? My Attitude Towards Teaching. Universities and Learning. Also email comments from readers, on: Teaching Maths in the public schools; Giving Students Power
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 Common Core Online  Darren Burris
Articles on Common Core State Standards (CCSS) mathematics, dating back to December, 2011, as "scooped," or digitally curated, by a Boston, MA, teacher.
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 Communication and Information, including Encryption  Dave Rusin; The Mathematical Atlas
See the Report of the Working Group on Cryptology and Coding Theory National
Science Foundation, April 1718, 1997. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites
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 Commutative Rings and Algebras  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to ring theory. Commutative rings are sets like the set of integers, allowing addition and (commutative)
multiplication. Of particular interest are several classes of rings of interest in number theory,
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 COMPASS: Curricular Options in Mathematics Programs for All Secondary Students  Linda A. Roach
COMPASS provides information and assistance with the implementation of five comprehensive curriculum projects that support the Standards set forth by the National Council of Teachers of Mathematics (NCTM): Application Reform in Secondary Education (ARISE);
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 A compendium of NP optimization problems  Crescenzi & Kann
A continuously updated catalog of approximability results for NP optimization problems. Because no NPcomplete problem can be solved in polynomial time (unless P=NP), many approximability results (both positive and negative) of NPhard optimization problems
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 Completing Latin Squares  Ivars Peterson (MathTrek)
Using only the numbers 1, 2, 3, and 4, arrange four sets of these numbers into a fourbyfour array so that no column or row contains the same two numbers. The result is known as a Latin square... in Latin squares of order 4, each row (and each column)
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 Complexity Online  University of New South Wales
A scientific information network about complex systems, structures and processes that involve nonlinearity. Topics in complexity include artificial life, cellular automata, chaos, evolutionary computation, fractals, genetic algorithms, neural networks
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 Complex Numbers  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A series of articles on the algebraic structure of complex numbers and their application to solving various problems in algebra and geometry. Several of the discussed features, for example, real and complex products, are drawn from very recent literature
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 A comprehension tool for mathematics?: the Math Forum @ Drexel's Online Mentoring Guide  Renninger, Ray, Luft, and Newton
Two studies of the Math Forum's Online Mentoring Guide (OMG) address whether and how online comprehension tools might support mathematics learning. In Study 1, the culture of the preservice teachers' (PTs') mathematics classroom and their work with the
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 Computational Geometry  arXiv.org ePrint archive
The computational geometry section of the Computing Research Repository (CoRR), moderated by Joseph O'Rourke. Recent papers.
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 Computational Geometry  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to computational geometry, intended for topics whose geometric aspects are fairly straightforward, but for which the main questions involve efficient, accurate computation. A number of geometric questions
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 Computational Geometry  Joseph O'Rourke
Computational Geometry is concerned with designing algorithms and computer programs to perform geometric computations. A need for such computations arises in many fields: computer graphics, robotics, pattern recognition, geography, manufacturing, etc.
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