 Kepler's Sphere Packing Problem Solved  Keith Devlin (Devlin's Angle)
Mathematician Thomas Hales of the University of Michigan announced in 1998 that — after six years effort — he had proved that a guess Kepler made back in 1611 was correct. The problem asks what is the most efficient way to pack equalsized
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 Key Aspects of Knowing and Learning the Concept of Function  Annie and John Selden; Mathematical Association of America
Marilyn Carlson and Michael Oehrtman discuss "what is involved in knowing and learning the function concept," including "the reasoning abilities involved in understanding and using functions and the dynamic conceptualizations needed for understanding
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 Key Issues for the Mathematics Community  The Math Forum
Links to Web resources addressing key issues, compiled in the following categories: Key Questions; Key Problems and Opportunities; Equity and Access (Minorities and Mathematics; Women and Mathematics; Resources for People with Disabilities; NonEnglish
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 Keynesian ISLM Model of the Canadian Economy  Elmer G. Wiens; Egwald Web Services Ltd.
Macroeconomics model of the Canadian Economy based on the Keynesian ISLM
model. Illustrated article with interactive supplemental page.
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 Key Problems and Opportunities  Key Issues in Mathematics at The Math Forum
Third International Mathematics and Science Study (TIMSS); National Science Foundation in Peril; The Necessity of Setting Research Priorities.
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 Key Questions  Key Issues in Mathematics at the Math Forum
Links to Web resources addressing questions such as: Why should the public support mathematics? Why is a research mathematics program necessary for graduate science programs? Why are we wellsuited to teach mathematics to scientists and engineers? Why
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 Keyword search of AI publications  College of Computing, Georgia Tech University
To search, simply enter a query and press the 'search' button. If you enter two or more words, any document that contains ANY of the words will be found.
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 Kinetic Theory  Stepan A. Amossov
A site devoted to mathematical problems of kinetic theory and its applications in physics, chemistry and economics, with some papers, information about forthcoming seminars and conferences, and links to other resources in related fields. Best in Internet
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 The King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry  Siobhan Roberts
As a companion to The King of Infinite Space, a biography of Donald Coxeter, this website provides photographs, archives, papers, video footage, links and other resources, allowing readers to further explore Donald Coxeter’s infinite passion for geometry.
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 Knot Magic Not Magic
(MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
Sometimes what looks like an impressive knot isn't a knot at all. Magicians and escape artists are experts at tying phony knots. Though magicians like knots that can fool people, mathematicians are mostly interested in real knots, especially knots that
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 Knotted Walks  Ivars Peterson (MathTrek)
Given that it normally takes some effort to create a knot, the spontaneous formation of knots in ropes and strings can appear rather puzzling. Having no obvious explanation of the effect, frustrated users can't help but acknowledge this knotting phenomenon
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 Knowing, doing, and teaching multiplication (Learning and Mathematics)  Magdalene Lampert; Math Forum
In this 1986 article Magdalene Lampert, of the Institute for Research on Teaching at Michigan State University, advocates incorporating students' intuitive knowledge about mathematics into classroom lessons. Like Richard Lesh, she encourages putting new
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 Kriging Description  Fortner Software
The site describes kriging, a sophisticated method of determining the best estimate for each point in a target matrix, based on statistical principles. Kriging is named after a South African engineer, D. G. Krige, who first developed the method. The article
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 KTheory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to Ktheory, a blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic
information about
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 Kumar Jeev's Research  Kumar Jeev
Articles in PDF format, PowerPoint presentations, C++ code, and abstracts. Includes "Symbolic Stochastic Systems and the Matrix Tree Theorem," with JeanLouis Lassez, in which an alternative proof for the Matrix Tree Chain theorem, proven by Tom Leighton
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 The Ladies' Diary  Ivars Peterson (MathLand)
The Ladies' Diary: or, Woman's Almanack was published annually, starting in 1704. Printed in London, it featured the usual stuff of almanacs: calendar material, phases of the moon, sunrise and sunset times, important dates (eclipses, holidays, school
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 L'Algebrista  Michele Cerulli
Software designed to introduce pupils to theoretical thinking and symbolic manipulation. The site includes publications and a description of the software. In English and Italian.
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 Language and Mathematics (Learning and Mathematics)  Cocking, Chipman; Math Forum
In their 1989 paper, "Conceptual Issues Related to Mathematics Achievement of Language Minority Children," Cocking and Chipman examine the mathematical ability of language minority  particularly bilingual  students, attempting to identify linguistic
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 La Quinta Operación Matemática (The Fifth Arithmetical Operation)  Domingo Gómez Morín
Simple arithmetic methods (no derivatives, no decimals, no cartesian system) for solving roots that also include the most advanced algorithms (Newton, Halley, Bernoulli)of analytic geometry and infinitesimal analysis. For Morin's more recent numerical
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 L'arbre de Delaunay  JD. Boissonnat et al.
L'arbre de Delaunay est une structure randomisé permettant de mettre à jour la triangulation de Delaunay. Cette structure permet de traiter des requètes de localisation. Delaunay triangulation code for Delaunay meshing in 2 and 3 dimensions
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 Launchings  David Bressoud
This monthly column, sponsored by the Mathematical Association of America (MAA), originally aimed "to publicize and expand upon the CUPM Curriculum Guide 2004 and its two companions: the Curriculum Foundations Project, and the CUPM Illustrative Resources."
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 Laurent Habsieger
A research associate at Laboratoire Algorithmique Arithmétique Expérimentale, Laurent Habsieger studies analytic number theory, coding theory, and combinatorics. Some articles on these topics are available for download in PostScript format.
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 Lava Lamp Randomness  Ivars Peterson (MathTrek)
Researchers have come up with a novel application of the mesmerizing movements of the lava lamp's globules. They use them as the starting point for generating a sequence of random numbers. Called lavarand, the randomnumber generator is the tongueincheek
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 The Law of Small Errors  Keith Devlin (Devlin's Angle)
As the number of words in a manuscript tends to infinity, the probability of a
significant error making it into the final version approaches 1. As with any selfrespecting infinite sequence in an undergraduate calculus class, "approaching infinity" here
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 Laws of Thought  Keith Devlin (Devlin's Angle)
"What Zeno of Citium actually did was found the Stoic school of logic. Though modern mathematical logic is popularly credited as having its beginnings in the syllogistic logic of Aristotle, most of the fundamental notions of contemporary propositional
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 LD Online, the interactive guide to learning disabilities for parents, teachers, and children
A vast array of information on topics within the area of learning disabilities, LD InDepth offers articles, research findings, and useful forums, including an area specifically devoted to dyscalculia, or learning disorders in math. See also 10 Tips
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 Learning and Teaching Ordinary Differential Equations  Annie and John Selden; Mathematical Association of America
Research "illuminating aspects of learning and teaching ordinary differential equations (ODEs) that can inform ongoing curricular innovations": "Making Connections between Representations"; "Numerical Approximations and Graphical Predictions"; "Proofs
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 Learning and Teaching Ordinary Differential Equations  Chris Rasmussen and Karen Whitehead; Mathematical Association of America
"Advances in technology, together with an increased interest in dynamical systems, are influencing the nature of many first courses in ordinary differential equations (ODEs). In addition, there is an increased emphasis on nonlinear differential equations,
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 The Learning Community  Stanley, Sarah; Allee, Angie; Mills, Connie; and Flanagan, Melissa
Dedicated to giving parents "... the information and resources they need to raise their children lovingly, supportively, and successfully." Since 1993, the nonprofit Learning Community has helped schools and families work together on behalf of children.
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 Learning Disabilities Online  Audiblox
Provides a selection of articles on learning disabilities. Learn about
the symptoms, possible causes, and ways to prevent learning disorders. Audiblox sells products designed to correct learning disabilities.
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 Learning Fractions (Learning and Mathematics)  Nancy K. Mack; Math Forum
In this 1990 article, Nancy K. Mack of the University of Pittsburgh considers how informal knowledge (such as dividing a pizza) can be used to enhance formal knowledge (such as one's understanding of fractions). Informal knowledge in this context means
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 Learning & Mathematics Discussion Sessions  Math Forum
Newsgroup discussions inspired by recent work on how students learn mathematics among mathematicians, teachers of mathematics, and students of educational psychology that occurred on the Math Forum's newsgroup geometry.precollege. Much of the work around
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 Learning Point Associates
Learning Point is a diversified, nonprofit consulting organization with clients of all sizes across the country, from state education agencies and singleschool districts to private foundations and forprofit corporations. It began as the North Central
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 Learning Strategies Database: ContentSpecific Learning Strategies for Mathematics  Center for Advancement of Learning, Muskingum College, New Concord, Ohio
Database of background information, purposes and advantages of various strategies, and descriptions of specific strategies themselves. Includes general tips and suggestions, information organization, substitution and memory strategies.
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 Learning to Think Mathematically: Problem Solving, Metacognition, and SenseMaking In Mathematics [PDF file]  Alan H. Schoenfeld, University of California, Berkeley
A chapter in D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics. "The goals of this chapter are (a) to outline and substantiate a broad conceptualization of what it
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 The Legacy of the Reverend Bayes  Keith Devlin (Devlin's Angle)
How do you use inconclusive evidence to assess the probability that a certain event will occur? One method that has become increasingly popular in recent years depends on a mathematical theorem proved by an 18th Century English Presbyterian minister by
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 Leibniz's 333yearold problem solved  Vladimir Sotirov
Arithmetizations of the traditional syllogistic. The first Leibniz trial to arithmetize the Aristotelian syllogistic explored divisibility of integers; it was unsuccessful. The second one used pairs of coprime numbers and was successful, as Slupecki
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 Leonardo, Water, and Math  Ivars Peterson (MathLand)
Leonardo da Vinci had a special interest in water, both practical and theoretical. Between the years 1506 and 1510, as he shuttled between projects in Milan and Florence, Leonardo jotted down his thoughts in a scientific notebook. His intention was to
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 L'Equipe de Logique Mathématique
 Université DenisDiderot, Paris, France
In English and French. Mathematical Logic Team. People, seminars, preprints, links to other logic sites in France.
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 Lesson Study: A PCMI Experience  Tony Anderson, Jennifer Kumi Burkett, Gail Burrill, Joyce Frost, Jerry Gribble, Jill Ryerson, and Celeste Williams
An article written by the Japanese Lesson Study group from the 2003 Park City Mathematics Institute (PCMI) about their experience developing the lesson, "Studying Dimensionality Through a StairStep Fractal." With an explanation of the Japanese lesson
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 Lesson Study in Japan  U.S. Science Education  Education Department, Mills College
Research into Japanese "lesson study," a process in which teachers cooperatively develop and critique new lessons. The site focuses on possible applications and challenges of lesson study to U.S. science and math education. Read related articles and
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 Level Set Methods Applied to Microchip Manufacturing  J. A. Sethian
A paper and movies on microchip manufacturing. Part of the process of manufacturing a computer chip consists of digging holes in silicon wafers and coating them with materials. At various stages, level set methods can be used to track the evolution of
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 Lev Semenovich Vygotsky Centennial Project  A.J. Lock, Dept. of Psychology, Massey University, New Zealand
A 1996 site cataloguing resources on Lev Semenovich Vygotsky (18961934), marking the centenary of Vygotsky's birth by setting up the equivalent of a Web conference on his opus. The site invites people to submit a piece of around 1000 words as comments
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 Lewis Carroll's Logic Game  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Discussion of an invention of Lewis Carroll's that competes with Venn diagrams for solving logical problems. Topics include the bilateral and trilateral diagrams, syllogisms, two Java applets, sample soriteses, and Carroll's Game of Logic.
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 Library of Math  David A. Smith
Definitions, comments, examples, propositions, and proofs on Business Algebra, Business Calculus, Calculus I, Calculus III, Euclidean Geometry, Financial Mathematics, Group Theory, and Trigonometry. The Library of Math website was designed to be a "browserquiet"
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 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.
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 Life in the Frequency Domain  J. Paul Giolma
A paper that complements standard college textbooks' coverage of time and frequency domain analysis. Includes sections entitled The Continuous Fourier Transform; A View of the Transform; The Inverse Transform; The Impulse Function; Convolution; Fourier
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 Life  Jim Loy
A short explanation of the rules for John Conway's Game of Life.
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 Limited English Proficiency Students and Mathematics  Kristen Lockwood; Math Forum
An annotated bibliography of resources for mathematics teachers and others interested in how language may affect the thought, achievement and assessment of students of limited English proficiency, as well as these students' access to knowledge and education.
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 The Limits of Mathematics  Ivars Peterson (MathTrek)
In Godel's realm, no matter what the system of axioms or rules is, there will always be some assertion that can be neither proved nor invalidated within the system. Indeed, mathematics is full of conjectures assertions awaiting proof with no assurance
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