 The Carpets Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An intuitively obvious fact that the area of a carpet is equal to the area
of the floor beneath admits several reformulations and nontrivial
consequences, some of which are discussed and dynamically illustrated at
the site.
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 Carroll's Paradox  Math Academy Online/Platonic Realms
An online encyclopedia article on Lewis Carroll's paradox, in Charles Dodgson's Alice in Wonderland.
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 The Case Against Block Scheduling  Jeff Lindsay
An analysis and opinions. Sections include: Nature of the Problem, reviews of case studies (including Bateson's Canadian studies), Advantages of Block Scheduling, Suggestions for Improved Use of Time, Comments From Around the Country, Questions to Ask
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 Catalog of Isohedral Tilings by Symmetric Polygonal Tiles  Doris Schattschneider
A collection of Sketchpad and JavaSketchpad files supplementing the article
"One Corona is Enough for the Euclidean Plane" by mathematicians Doris
Schattschneider and Nikolai Dolbilin. Tilings of the Euclidean plane by a single polygon are considered,
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 A Catalog of Random Bits  Ivars Peterson (MathLand)
Researchers use random numbers for tackling a wide range of problems, from modeling molecular behavior and sampling opinion to solving certain equations and testing the efficiency of algorithms. Such numbers also play crucial roles in a wide variety of
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 Categorical Geometry  Zhaohua Luo
See a brief tour of categorical geometry, which studies the geometric properties of unitary categories. The categorical approach to algebraic geometry was initiated by Yves Diers in his pioneer book Categories of Commutative Algebras (Oxford University
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 Category Theory  JeanPierre Marquis
An entry in the Stanford Encyclopedia of Philosophy covers category theory's definitions, history, and philosophical significance. Also includes a bibliography.
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 Cattle of the Sun  Ivars Peterson (MathTrek)
The story goes that Archimedes of Syracuse (287212 B.C.) was annoyed with Apollonius of Perga (262190 B.C.), who had criticized Archimedes' work on the multiplication of large numbers. For revenge, Archimedes devised a fiendish computational problem
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 Cavities of chaos  Ivars Peterson  Science News Online
Sorting out quantum chaos in the microwave lab: The rectangle and the (rounded) stadium have long served as geometric playing fields for theorists studying differences between regular and chaotic motion. They can readily calculate sample trajectories
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 CC (Concord Consortium) Library: Papers  Robert F. Tinker
From Robert F. Tinker, Director of the Educational Technology Lab of the Concord Consortium, a nonprofit, research and development organization dedicated to furthering the technology revolution worldwide through innovations in hardware, software, learning
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 Cédric Villani
For mathematicians, the 2010 Fields Medalist offers his publications, lecture notes for students, errata sheets, and his research into collisional kinetic theory (Boltzmann type), collisionless kinetic theory (Vlasov type), and optimal transport. "For
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 Cellular Automata Miscellanea  José Manuel Gómez Soto
Cellular automata theses, reports of summer research, working papers, lectures, and articles, some in Spanish, many by Harold V. McIntosh. Also, download the CAM/PC exerciser CAMEX and a program collection of NXLCAU, the Linear Cellular Automata for NeXTSTEP.
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 Census and Statistics Department, Hong Kong Special Administrative Region  Hong Kong SAR Government Information Centre
The statistics collection department of the Hong Kong Government. Key geographic, climate, population, and socioeconomic data, press releases, other publications, and an overview of the department. Frequently requested timeseries are available online
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 Census Challenges (Math Chat)  Frank Morgan; Christian Science Monitor
Gordon Squire notes that planners for the 2000 U.S. Census wonder what to do about missing certain groups of people such as many homeless in New York. Suggestions include statistical random sampling. What approach would you suggest?
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 Census Sampling Confusion  Ivars Peterson  Science News Online
To obtain a more accurate enumeration in the year 2000, the Census Bureau has proposed integrating the results of conventional counting techniques with the results of a large sample survey of the population, but others want to use the straight count (direct
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 Center for Cognitive Technology  Richard E. Clark, Director
Conducting and analyzing interdisciplinary research on the role of new technology in the development of advanced expertise and performance motivation. See, in particular, the publications "Teaching general problemsolving skills is not a substitute for,
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 The Center for Game Science
Makers of free online fraction games such as Treefrog Treasure, Refraction, and Creature Capture. The Center for Game Science also offers its research publications on science, technology, engineering, and math (STEM) games for scientific discovery; for
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 Center for Improving Learning of Fractions  University of Delaware School of Education
A research and development center aimed at understanding difficulties students have with fractions. Center publications include "Improving AtRisk Learners' Understanding of Fractions," published in the Journal of Educational Psychology; "Developmental
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 Center for Nonlinear Dynamics (CNLD)  University of Texas at Austin
Research in the Center for Nonlinear Dynamics concerns complex dynamics, chaos, and pattern formation in systems driven far from thermodynamic equilibrium. Experimental, numerical, and theoretical studies have revealed chaotic behavior and complex spatial
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 Center for the Development of Teaching (CDT)  Education Development Center, Inc. (EDC)
A research and development center whose goal is to learn how teachers' practice can be transformed to support students' construction of knowledge. Currently focusing on mathematics and science teaching, the Center carries out research and action projects
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 Central Office of Statistics, Malta
The COS collects statistics for the Maltese government. List of publications, tables of key data, and press releases.
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 Central Service for Statistics and Economic Studies (STATEC)  Luxembourg
The agency for official statistics for the country of Luxembourg. Description of the agency and tables, graphs, and brief articles about key social and economic data available in English and German. More information may be found in the French version
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 Central Statistical Bureau of Latvia  Republic of Latvia
The statistics collection department of the government of Latvia. Key socioeconomic figures, press releases, list of publications, legal basis and history of the bureau. A version of the site is also available in Latvian.
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 Centre for Innovation in Mathematics Teaching  University of Plymouth
A focus for research and curriculum development in mathematics teaching and learning with the unifying aim of enhancing mathematical progress in schools and colleges. The site includes: The Mathematics Enhancement Programme; Resources: worksheets in HTML
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 The Challenge of Detracking: Finding the Balance between Excellence and Equity  Lockwood, Cleveland; UEWeb
Download this PDF for an introduction to and background of tracking; terminology, issues, and data showing prevalence and impact; and bibliography.
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 Chance Encounters at ICME9  Cut the Knot!, Alexander Bogomolny
From the International International Congress on Mathematics Education held in Tokyo in August, 2000, impressions that came from personal, often unplanned, meetings with such mathematicians as N. P. Dolbilin (who outlined the history and the current state
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 CHANCE  J. Laurie Snell, Mathematics Dept., Dartmouth College
Materials designed to help teach a "Chance" course or a more standard introductory probability or statistics course. A Chance course is a case study quantitative literacy course designed to make students more informed and critical readers of current news
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 Chance of Bank Balance $0.00 (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: My colleague Dick De Veaux reports that upon returning from a threeweek trip, he found his checking account balance at exactly $0.00. Without further information, how would you estimate the probability of such an event?
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 Changes of Mathematical State  Ivars Peterson  Science News Online
A discussion of constraintsatisfaction problems, more specifically the logic puzzle in theoretical computer science known as the satisfiability (SAT) problem (e.g. working out a seating plan), the current state of research on computational "phase transitions,"
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 Channeling quantum information efficiently  Ivars Peterson  Science News Online
By carefully choosing how a message is encoded and decoded, it's possible to approach the theoretical maximum for transmitting information via photons or other quantum particles.
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 Chaos and the Solar System  Paul Trow
An essay on the historical development of chaos theory, especially as it relates to the solar system.
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 Chaos at Maryland  The Chaos Group, the University of Maryland at College Park
Research in chaotic dynamics: the theory of dimensions, fractal basin boundaries, chaotic scattering, controlling chaos, and more. Read research papers, link to Daniel P. Lathrop's Nonlinear Dynamics Lab and the Pattern Formation Laboratory, learn about
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 Chaos, Fractals, and Arcadia  Robert L. Devaney; Dept. of Mathematics, Boston University
An animated description of some of the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia. Introduction; Thomasina's Geometry of Irregular Forms; The Chaos Game; The Sierpinski Hexagon; Thomasina's Fern; Valentine's Grouse; Summary
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 The Chaos Hypertextbook: Mathematics in the Age of the Computer  Glenn Elert
Formerly titled "Chaos, Fractals, Dimension": an illustrated paper submitted for the author's M.S. in secondary science education from Columbia. Contains chapters on: Mathematical Experiments (Iteration and Orbits, Orbit and Bifurcation Diagrams, Universality);
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 Chaos in the Classroom  Robert L. Devaney; Dept. of Mathematics, Boston University
One of the most interesting applications of technology in the mathematics classroom is the fact that it allows teachers to bring many new and exciting topics into the curriculum. In particular, technology lets teachers bring some topics of contemporary
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 Chaos vs. Determinism  Harold Brochmann
Recursive vs. Newtonian Functions  two ways of calculating the value of an investment; The Real World  how do things work in reality? (planetary orbits); The Logistic Function  a study of population growth and extinction.
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 Characteristics of Gifted Children: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on characteristics of gifted children: perfectionism, sensitivity, social skills and emotional skills, underachievement, and visualspatial learning.
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 Charles Babbage Institute of Computer History (CBI)  University of Minnesota
CBI is a research center at the University of Minnesota dedicated to promoting the study and preservation of the history of information processing. As part of its mission, CBI maintains an archival collection available for use by the public that includes
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 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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