 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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 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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 Linear and Multilinear Algebra; Matrix Theory (Finite and Infinite)  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to linear and multilinear algebra and matrix theory. As presented to engineers and as the subject of much numerical analysis, this subject is Matrix Theory. To an algebraist or geometer, it is the theory
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 Linear & Nonlinear Programming Publications, Preprints, & FAQs  Technical University of Braunschweig
PostScript files and some abstracts. Many articles in German.
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 Lines, Circles and Beyond  Cut the Knot!, Alexander Bogomolny
Third in a series of columns that draw on Frank Morley's fundamental paper On the Metric Geometry of the Plane nLine. Bogomolny's initial intention was to expose the simplicity of and the motivation behind Morley's original proof of his famous theorem.
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 Linguistic Geometry (LG)  Boris Stilman; Dept. of Computer Science & Engineering, Univ. of ColoradoDenver
Solving search problems of high dimension. Since 1991, Professor Stilman has been developing a new area in Artificial Intelligence, Linguistic Geometry, based on the investigation into sophisticated human heuristics resulting in highly selective searches,
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 Lin McMullin
Resources for AP Calculus teachers, information and articles on computer algebra systems (CAS), and other materials. Conference presentations include "Teaching Limits So That Students Will Understand Limits." See, in particular, the guide to the AP Calculus
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 L'Institut des Hautes Études Scientifiques  IHÉS
L'Institut des Hautes Études Scientifiques de BuressurYvette (France) est un institut de recherche avancée en mathématiques et physique théorique avec une ouverture vers l'épistémologie et l'histoire des sciences. Il offre à des savants d'envergure
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 Lizard Game (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The rocky Coast Range of California is the setting for an unusual game played by a brightly colored sideblotched lizard. Each male of the species has one of three throat colors, and each color of lizard has a different mating behavior. The lizards play
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 Locating, Using, and Integrating InternetBased Mathematics Materials (NCREL)  Gilbert Valdez; Pathways to School Improvement
Goals, options for action, criticism, and implementation pitfalls; informative video and sound clips; organizations, agencies, and websites that work toward providing schools with better Internet and mathematics materials access. From the North Central
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 Loci  Mathematical Association of America (MAA)
Loci is a peerreviewed journal publishing articles, modules, applets, and reviews continuously as they are ready to be posted. Loci takes advantage of the World Wide Web as a publication medium for materials containing dynamic, fullcolor graphics;
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 Lockhart's Lament  Keith Devlin (Devlin's Angle)
Keith Devlin writes in his March, 2008, column: "This month's column is devoted to an article called A Mathematician's Lament, written by Paul Lockhart in 2002. Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York. His article has
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 Logical Art and the Art of Logic  Guenter AlbrechtBuehler
An illustrated essay about pentominoes, flat shapes formed from five (Gr.pente = five) unit squares. Also a DOS program for pentomino solutions (6x10) and galleries of pentomino creations.
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 Logic and Philosophy of Logic (Philosophy Resources on the Internet)  EpistemeLinks.com
Encyclopedia articles and related Web sites.
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 Logic Circuit Minimization Using Karnaugh Map Lookup Tables  John Eric Franklin
Four variable truth tables drawn in a four by four grid is called a
Karnaugh map to an electrical engineer. Karnaugh maps were developed in
the 1950's and help to produce sumofproduct equations (AND,OR). I have
added the XOR operator (exclusiveor)
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 Logic (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on mathematical logic, covering axioms, deduction, fallacy, Kurt Gödel, and mathematical induction.
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 The Logo Foundation
A nonprofit educational organization devoted to informing people about Logo and supporting them in their use of Logobased software and learning environments. The site includes links for workshops and seminars; books and videos; Logo software (at discount
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 The Long Island Consortium for Interconnected Learning (LICIL)
The Long Island Consortium for Interconnected Learning in Quantitative Disciplines is a comprehensive, interdisciplinary project aimed at improving how faculty teach and how students learn in mathematically based subjects. It combines change in modes
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 Longitude and the Académie Royale  MacTutor Math History Archives
Linked essay describing longitude from Eratosthenes' mapping efforts through the 1681 Académie Royale expedition, with 8 references (books/articles).
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 Losing Each Mile But Winning the Marathon (Math Chat)  Frank Morgan, MAA Online
Joan was entered to run a special 26.5mile marathon, and she hoped to average under nine minutes per mile over the total distance. She had a number of friends measure her time over various mile segments of the course, and for each possible mile that
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