 Modes of Thinking  Cut the Knot!, Alexander Bogomolny
Mathematics is verbal for it's a language, and it is abstract for in its heart one finds proofs and axiomatizations. It is symbolic, rational, logical, and, nowadays, it is very digital. These are all indications that mathematics is firmly entrenched
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 Modular Arithmetic  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An essay on modular (or modulo) arithmetic, an unusually versatile tool discovered by K. F. Gauss (17771855) in 1801, with related links.
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 Modularity in Art  Slavik Jablan, Mathematical Institute, Belgrade
Jablan uses the word "modularity" to refer to the process of making art by repeating a simple block, tile, or motif to make a more complicated design, by symmetry/reflection and/or tessellation. This site includes a paper on such art and its math, linked
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 Molecular Information Theory and the Theory of Molecular Machines  Tom Schneider
Introduction to the use of information theory in studying molecular biology. The author is part of the Molecular Information Theory Group, a section of the Laboratory of Computational and Experimental Biology at the National Institutes of Health in Frederick,
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 Moment of Truth  Keith Devlin (Devlin's Angle)
"Just what do we mean by a 'proof'? It seems that mathematicians  and to avoid generating too many letters of complaint, let me hasten to rephrase that as 'we mathematicians'  are somewhat schizophrenic when it comes to answering this question. When
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 MoneyWise: Parents & Educators  Charles Schwab & Co., Inc.
Resources for teaching kids and teens money basics: articles; handson activities; life lessons; families & money surveys; questions and answers from Schwab's "Ask Carrie" service on everyday financial challenges; workshops, curricula, and more.
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 Monocosm: Introduction to Linear Xenology  Vladimir Trifonov; American Mathematical Society (AMS)
A ToposTheoretic Approach to the Foundations of Physics. The FourDimensionality Problem: Why does observable spacetime look fourdimensional? is related to the Compactification Problem. The Effective Metric Signature Problems: Why is the metric of signature
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 Monopoly Dollars and Sense  Ivars Peterson (MathLand)
The same rules underlie all of the varied editions of Monopoly, which feature themes ranging from golf to your favorite city. It's possible to describe the game in terms of a mathematical construction called a Markov chain, named for the Russian mathematician
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 Monthly Labor Review Online  Bureau of Labor Statistics
A journal from the Bureau of Labor Statistics that publishes both public and private research into the labor force, the economy, employment, occupational injuries and illnesses, wages, prices, etc. Abstracts of and excerpts from current articles may
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 The Monty Hall Trap  Jim Loy
What's the right answer? A simple description of the problem and whether to stay with your first choice, or switch.
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 More Complicated Than It Seems  Kate Nonesuch
In this review of the literature of approaches to adult numeracy instruction, Kate Nonesuch asks the question, "How can ABE math instructors apply research findings to their own teaching practice?" Through an extensive literature review and ongoing discussions
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 More than Just a Plane Game  Ivars Peterson (MathTrek)
When topologists started to explore the world of geometric forms in higher dimensions, they found that neither the intuition nor the vocabulary of ordinary geometry was sufficient to describe and classify the new forms they discovered. They introduced
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 More than Magic Squares  Ivars Peterson (MathLand)
Peterson writes about magic squares, quoting Benjamin Franklin's interest in them. In addition to giving a few examples, Peterson also mentions Victor E. Hill IV's musing about whether the discoverer of the magic square actually set out to find an example
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 Morley's Pursuit of Incidence  Cut the Knot!, Alexander Bogomolny
With all the geometric context of his theory (applets are provided for explorations), Morley's method is purely algebraic, founded on the theory of complex numbers. Curves are mappings x = f(t) from the unit circle. x = X + iY, where X and Y are the plane
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 Morley's Redux and More  Cut the Knot!, Alexander Bogomolny
In 1998 Alain Connes  a French Fields medalist  published a new proof of Morley's theorem (the three points of intersection of the adjacent trisectors of the angles of any triangle form an equilateral triangle).
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 Morphing Art (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
When you're riding along on your bike or in a car, you sometimes see the word "ONLY" painted on the roadway just before an intersection. The white letters look normal from where you're sitting. But if you were standing beside the "ONLY" instead of riding
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 Motion of Fluid Interfaces  J. A. Sethian
A paper and movie about a rising bubble. Imagine an air bubble rising in water, a thermal of hot air rising on a cold day, or smoke rising out of smokestack. In each case, the interface between the two fluids will change dramatically as the fluids move.
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 Motion under Curvature  J. A. Sethian
A paper and movie of a curvature collapse. A famous theorem in differential geometry, proved less than ten years ago, says that any simple closed curve moving under its curvature collapses nicely to a circle and then disappears. That is, no matter how
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 MOTIVATE  Univ. of Cambridge, UK
MOTIVATE is a project incorporating a series of videoconferences, run by the Millennium Mathematics Project at Cambridge. The objectives of MOTIVATE are: to enrich the mathematical experience of school students, to broaden their mathematical horizons,
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 Move Over Fermat, Now It's Time for Beal's Problem  Keith Devlin (Devlin's Angle)
Beal's Problem is like Fermat's, but instead of focusing on equations with one exponent, n, there are three: m, n, and r. Thus, Beal's equation looks like this:
xm + yn = zr. The idea is to look for whole number solutions to this equation where the solution
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 MSEB Classics  Mathematical Sciences Education Board, National Research Council
Reports issued between 1990 and 1995, from the MSEB: Mathematical Preparation of the Technical Work Force: Report of a Workshop; What Should I Look for in a Mathematics Classroom?; Achieving Quality in Undergraduate Mathematics (see also Looking for Gauss...or
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 MSRI Journal  Ivars Peterson (MathTrek)
The new journalistinresidence program at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California represents one effort to improve communication of mathematics. Peterson will spend the summer of 1999 there.
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 MSRI Reflections  Ivars Peterson (MathTrek)
Thoughts about and a description of Berkeley, California's Mathematical Sciences Research Institute, an important center of the mathematical world.
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 Multicultural Pavilion, University of Virginia  Paul Gorski
Sites for educators interested in multicultural issues. Resources for teachers, including reviews of children's music, multicultural activities, online archives, and links to multicultural websites; papers, book reviews, and published materials; statistical
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 Multidimensional Analysis  George W. Hart
A brief introduction to Multidimensional Analysis, a generalization of linear algebra that incorporates ideas from dimensional analysis. The central idea is that vectors and matrices as used in science and engineering can be thought of as having elements
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 Multimedia Catalogue  Biography Index  Institute and Museum of the History of Science of Florence, Italy
Biographical texts of personalities connected in some way to Galileo. Each text is accompanied by still or animated images or by filmed sequences. Included are Archimedes, Aristotle, Bernoulli, Brahe, Copernicus, the Galilei family, Kepler, Milton, Ptolemy,
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 Multimedia Documents  The Geometry Center
Conference proceedings; research papers that use hypertext to present information in a nonlinear fashion, many including movies or interactive pictures; expository papers that use hypertext to present information about mathematics or the Geometry Center
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 Multirate Signal Processing Group  Univ. of Wisconsin  Madison
Members' research, software developed by the group, references; people, publications, other links.
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 Multiresolution Signal Processing Group  University of Minnesota
The group's research consists of developing and applying multiscale signal processing techniques and wavelets in the design of high quality interactive audio, image and video multimedia databases and coders, optimal data acquisition schemes for radar,
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 Multivariate polynomial interpolation  Shayne Waldron
A summary of some ongoing investigations into the error in multivariate interpolation. This page is organised to more generally serve those interested in multivariate polynomial interpolation (error formulae and computations). Work on differencing, multipoint
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 Murder and the Economist  Ivars Peterson (MathTrek)
The prominent role of economic principles is certainly evident in all the mysteries of Marshall Jevons. It doesn't take long for protagonist Henry Spearman to begin invoking economic theory in Murder at the Margin, which started the series off in 1978.
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 The Mutilated Checkerboard in Set Theory  John McCarthy
An 8 by 8 checkerboard with two diagonally opposite squares removed cannot be covered by dominoes each of which covers two rectilinearly adjacent squares. This site presents a set theory description of the proposition and an informal proof that the covering
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 My Reckonings  Ron Doerfler
Doerfler's book Dead Reckonings: Calculating without Instruments "describes techniques of computation and approximation that can be used to rapidly and mentally calculate mathematical quantities." Other sections of the site discuss sundials; astrolabes
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 Mystic Chaos: A Preliminary Report  Ivars Peterson (MathLand)
Billed as a fantasy adventure game, Chaos involves solving a mystery  or rather, a large number of little puzzles that supposedly add up to something bigger  starting from scratch. You have to figure out what the mystery is and how you as the player
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 Myths in Math  Charles E. Mannix and Ken Ross
An article about myths concerning the mathematics job market.
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 NADE Math SPIN  National Association for Developmental Education's Special Professional Interest Network for those interested in teaching mathematics
A professional organization for developmental math professionals to interact and share with each other. The site features links to best practices in developmental mathematics, newsletters, email discussion group, and conferences. Also available from
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 Names for Numbers  Ivars Peterson (MathTrek)
Once someone discovers an interesting pattern or type of behavior, those particular numbers are likely to earn a collective name. So we have perfect numbers, amicable numbers, lucky numbers, Mersenne numbers, Fermat numbers, Fibonacci numbers, Keith numbers,
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 Napoleon's Theorem  Cut the Knot!, Alexander Bogomolny
On the sides of a triangle construct equilateral triangles (outer or inner Napoleon triangles). Napoleon's theorem states that the centers of the three outer Napoleon triangles form another equilateral triangle. The statement also holds for the three
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 NASA Technical Report Server (NTRS)  National Aeronautics and Space Administration
Keyword search of the following databases: Ames Research Center; Astronomy & Astrophysics (ADS); Dryden Flight Research Center; Glenn Research Center; Goddard Institute for Space Studies; Goddard Space Flight Center; ICASE; Jet Propulsion Laboratory;
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 National Association for the Education of Young Children
The nation's largest organization of early childhood professionals and others dedicated to improving the quality of early childhood education programs for children from birth through age eight. Online resources include: articles for parents and teachers;
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 National Center for Health Statistics (NCHS)  Centers for Disease Control and Prevention
The source for information about health and vital statistics in the United States. View tables of important statistics online or download data sets and reports (often in PDF format.)
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 National Center for Research on Teacher Learning (NCRTL)  National Center for Research on Teacher Learning (NCRTL)
Based in the College of Education at Michigan State University, NCRTL conducts research in teacher education. Brochures and publications (special reports, craft papers, research reports, technical series, issue papers, conference series, and video packages)
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 National Center for Technology Planning (NCTP)  Dr. Larry S. Anderson, Founder/Director
A clearinghouse for the exchange of many types of information related to technology planning: school district technology plans available for downloading via a computer network; technology planning aids (checklists, brochures, sample planning forms, PR
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 National Center to Improve Practice (NCIP)  Education Development Center, Inc. (EDC)
The National Center to Improve Practice in Special Education Through Technology, Media and Materials promotes the effective use of technology to enhance educational outcomes for students with sensory, cognitive, physical and social/emotional disabilities.
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 National Centre for Excellence in Mathematics and Science Teaching and Learning  University of Limerick
Ireland's NCEMSTL researches, coordinates, supports, develops and implements programmes to enhance Irish science and mathematics teaching and learning at all levels. Read Centre publications and reports; learn about its courses and other events. Register
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 The National Centre for Excellence in the Teaching of Mathematics  Tribal Education Ltd.
The UK's National Centre for Excellence in the Teaching of Mathematics (NCETM) aims to meet the professional aspirations and needs of all teachers of mathematics and realise the potential of learners through a sustainable national infrastructure for mathematicsspecific
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 The National Clearinghouse for English Language Acquisition (NCELA)
Online library and bibliographic database; technical, language education, and classroom materials links; conferences and meetings calendar; discussion group; Newsline (weekly bulletin); and state resource listings. Read classroom centered practices for
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 National Commission on Mathematics and Science Teaching for the 21st Century  U.S. Department of Education
A Glenn Commission plan to ensure that every American student receives excellent instruction in math and science  instruction critical to maintaining the U.S. edge in the competitive global economy. The report sets three goals: to establish an ongoing
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 National Council for Accreditation of Teacher Education (NCATE)
The professional accrediting organization for schools, colleges, and departments of education in the United States. See what institutions say about NCATE, and read testimony to the Senate Committee on Labor and Human Resources about NCATE's message and
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 National Institute of Standards and Technology (NIST)  U.S. Department of Commerce
Working with industry to develop and apply technology, measurement, and standards. Links to a site guide; Measurement and Standards Laboratories; Advanced Technology Program; Manufacturing Extension Partnership; Baldridge Quality Program. Events, publications,
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