 The handling of geometry definitions in school textbooks  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
Some historical background and a discussion of the value of students constructing their own understanding of mathematical proofs; misconceptions that arise from readymade definitions; and the advantage of a constructivist approach, which allows pupils
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 Hankies, Snarks, and Triangles  Ivars Peterson (MathLand)
Both Alice's Adventures in Wonderland and Through the LookingGlass and What Alice Found There contain many examples of Dodgson's passion for mathematical games, puzzles, logic paradoxes, riddles, and all sorts of word play. Indeed, his fascination with
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 Hard Questions About Practice  Richard F. Elmore
"Educators need to look closely at the organizational and instructional practices that affect the learning of students and adults in schools." From Educational Leadership, May 2002, Vol 59 No 8, pp 2225.
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 Harold Reiter's Home Page  Harold Reiter, Department of Mathematics, University of North Carolina at Charlotte
Freely downloadable puzzles and problems from the founder of teachers circles and math clubs in Charlotte and Mecklenburg, longtime writer of MathCOUNTS questions, and member of the ETS/College Board CLEP (CollegeLevel Examination Program) Precalculus
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 Harry Bohan's Web Site
Site contains personal info (education, jobs, list of publications), hyperstudio stacks of K8 math programs (some available for download here, all available by sending the required number of HD disks to Harry Bohan), an extensive page on teaching multiplication,
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 The Hartman Fractal Hypotenuse Hypothesis  John "Dobe Doinat" Hartman
Proving the maximum fractal dimension of an infinitely squiggly staircase replacing a normal hypotenuse in a square or rectangle.
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 Harvard Sports Analysis Collective
Dedicated to the quantitative analysis of sports strategy and management, this Harvard student organization focuses on the intersection of sports, sports business, statistics, and problem solving. Original analysis and research into sports analytics authored
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 A Head for Numbers  Robert Kunzig, Discover Magazine
An article exploring the connections between our brains and numbers: what injuries to the brain have taught us about people's ability to calculate.
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 Hearty Munching on Cardioids  Cut the Knot!, Alexander Bogomolny
A cardioid curve (roughly resembling a kidney bean) is the locus of points traced by a point on a moving circle that rolls without slipping on the outside of a circle of equal radius (explore the illustrative applets). An interactive column for MAA Online
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 Helena A. Verrill  Department of Mathematics, Louisiana State University
Notes, links, handouts, and other materials from the courses that Verrill teaches, such as Solving Discrete Problems, Calculus, Elliptic Curves, and Modular Forms. She also provides a Java applet for a wallpaper drawing program and stepbystep illustrations
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 Helmer Aslaksen
A mathematics professor at the National University of Singapore. Research involves abstract algebra, including the trigonometry of symmetric spaces, and calculations for the Chinese, Islamic, and Indian calculators. Papers about these topics may be
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 Helmut Prodinger
Helmut Prodinger researches analysis of algorithms, combinatorics, tree enumeration, and number theory. Many of his papers on these subjects are available online in PostScript, .dvi, and/ or TeX form.
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 Henry Segerman's webpages  Henry Segerman
Mathematical and typographical art "of various kinds and dimensions." See, in particular, Segerman's 3D printed sculpture, book covers and posters, diamond Go, ambigrams, autologlyphs, autological words, Escher's Printgallery, and mathart tshirts available
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 Herbert Wilf
Herbert Wilf is a combinatorialist. The entire text of his books generatingfunctionology, A = B, and Algorithms and Complexity may be downloaded in PDF format, as may his "East Side, West Side" lecture notes on combinatorial objects and Maple programming.
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 Hermann Grassmann and the Prehistory of Universal Algebra  Desmond FearnleySander
A definition of universal algebra, with a sketch of its prehistory. "...abstract algebras are divided by a very simple scheme into selfcontained `species'. Within each species a perfect duality is found between families of formal laws and the families
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 Hiding in DNA  Ivars Peterson (MathTrek)
Spies might have to start boning up on molecular biology to pass along and decipher secret messages. During World War II, German spies used microdots to hide information in plain view. Consisting of a greatly reduced photograph of a typed page, a microdot
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 Hiding in Lattices  Ivars Peterson  Science News Online
An improved mathematical strategy for encrypting data: the mathematics of lattices offers an alternative basis for a publickey cryptosystem. A lattice is a regular array of points, each one specified by a set of coordinates. Two coordinates would designate
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 Hilbert Space Methods for Partial Differential Equations  R. E. Showalter
Chapters from a monograph on partial differential equations, in dvi and pdf formats, to download: Elements of Hilbert Space; Distributions and Sobolev Spaces; Boundary Value Problems; First Order Evolution Equations; Implicit Evolution Equations; Second
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 Hilbert's Tenth Problem  Russian Academy of Sciences
A page to promote research connected with the negative solution of Hilbert's Tenth Problem and developed techniques, which have applications in the theory of algorithms, algebra, number theory, model theory, proof theory and in theoretical computer science.
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 The history of cartography
 MacTutor Math History Archives
Linked essay on how map making has played an important role in the development of mathematics.
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 History of Compactness  Manya Raman
Download a paper that discusses the development of the concept of compactness, one of the most important and useful notions in advanced mathematics and a sort of gatekeeper topic to higherlevel mathematics. By presenting an historical treatment of this
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 History of Mathematics  David R. Wilkins, Trinity College, Dublin
A directory of Web sites and pages around the world relating to the history of mathematics. Also biographies of some seventeenth and eighteenth century mathematicians, taken from A short account of the history of mathematics (4th edition, 1908) by W.
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 History of Mathematics (MathPages)  Kevin Brown
About 40 "informal notes" by Kevin Brown on math history: Zeno and the paradox of motion, Archimedes and the square root of 3, Mayan numeration, Hipparchus on compound statements, Planck's analysis of Kaufmann's experiment, the ten means of Ancient Greece,
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 A history of the Burnside problem  MacTutor Math History Archives
Linked essay on the development of the questions: Is a finitely generated periodic group necessarily finite? Is a finitely generated periodic group of bounded exponent necessarily finite?
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 A history of time: 20th century time
 MacTutor Math History Archives
Linked essay on the dramatic changes in ideas about time in the 20th century.
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 A history of time: Classical time
 MacTutor Math History Archives
Linked essay on the central role time has played in mathematics from its very beginnings.
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 The history of voting
 MacTutor Math History Archives
Linked essay on the history of electoral systems.
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 A history of Zero  MacTutor Math History Archives
Linked essay on the development of the concept of zero. There are two important but different uses of zero: one as a empty place indicator in our placevalue number system, and one as a number itself in the form we use it as 0. There are also different
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 Hoagies' Gifted Education Page  Carolyn K.
Research, reviews, professional and social organizations, internet explorations, and other resources for gifted children and their parents and educators. Math items available in all subsections of the site.
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 Holistic Numerical Methods Institute  Autar Kaw
Open courseware, books, primers, journal abstracts, PowerPoint presentations, multiple choice tests, and other resources supporting a typical course in Numerical Methods for undergraduates majoring in science, technology, engineering and mathematics (STEM).
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 Home Page for Laura Taalman  Laura Taalman
Course materials, mentored projects, publications, and more from Taalman, a professor of mathematics at James Madison University. Taalman's interests range from singular algebraic geometry and knot theory to games, puzzles, and 3D printing. The Puzzles
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 Homepage Michel Delord  Michel Delord
Une site opposé "à la spirale qui prétend faciliter la compréhension en allégeant les savoirs fondamentaux.... [et] à la justification de cette spirale qui sépare l'intelligence conceptuelle de ses manifestations
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 Home Page of Andrei Toom, André Toom  Andrei Toom, Department of Statistics, Federal University of Pernambuco, Recife, Brazil
The home page of one of the developers of the ToomCook, or Toom3 algorithm, a method of multiplying two large integers. Toom's Englishlanguage mathematics articles, published in journals such as the Journal of Statistical Physics, include "NonErgodic
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 Homepage of Keith Matthews  Dept. of Mathematics, Univ. of Queensland, Australia
Matthews is a Senior Lecturer whose professional interests are number theory, teaching, and traversing the World Wide Web to uncover things of interest to number theorists for the Number Theory Web. Links to mathematical interests, gateways (mainly mathematical)
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 Home Page of Persi Diaconis  Persi Diaconis
Download PDF and PostScript papers, organized by coauthor or by year of publication, such as Asymmetric onedimensional constrained Ising model; Random walk on trees and matchings; and Mathematical developments from the analysis of Riffleshuffling.
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 Homepage & Papers  Dr. Peter Singer
Dr. Singer is associated with the MeVisCenter for Diagnostic Systems and Medical Visualization at the Univ. of Bremen, Germany. His interests and publications include: mathematics of finance; Fourier analysis; fractals; medical image processing; stochastic
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 Home Run Numbers  Ivars Peterson (MathTrek)
The integers 61 and 62 have been very much in the news this summer. On the majorleague baseball front, Mark McGwire hit his 62nd home run on Sept. 8, and Sammy Sosa matched that total on Sept. 13, surpassing the record of 61 home runs in a season held
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 Home Schooling: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on homeschooling, in particular in the context of the education of gifted children.
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 Homeschool Math Contests  Haddon Fox
A list of dozens of math contests open to individuals and which do not require gathering up teams  a requirement that often poses a challenge for homeschoolers. homeschoolmathcontests.com also lists many more regional meets sponsored by colleges and
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 The Honeycomb Conjecture  Ivars Peterson  Science News Online
Mathematician Thomas C. Hales of the University of Michigan at Ann Arbor has formulated a proof of the socalled honeycomb conjecture, which holds that a hexagonal grid represents the best way to divide a surface into regions of equal area with the least
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 Hopf Topology Archive  Clarence Wilkerson, Dept. of Mathematics, Purdue University
The Hopf archive contains freely available articles and preprints as dvi, ps, text, or lj.gz files. Some short abstracts and a search engine are included, as well as pictures of topologists and some useful links concerning topology.
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 How Banks Work  HowStuffWorks
An illustrated article describing the functions of banks, what you would have to do to start your own bank, and why we should (or shouldn't) trust them with our hard earned cash.
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 How do I tell a real difference from random variation?  Max Janairo
This paper presents the concepts necessary to understand what the methodologies of hypothesis testing and confidence intervals accomplish, and provides an introduction to the use of these concepts to answer particular questions in medicine. Some problems
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 How do we know about Greek mathematicians?  MacTutor Math History Archives
Linked essay examining how the dates of Diocles given in the MacTutor archive have been determined, and other ways to gain information about the ancient Greek mathematicians, with references and other related web sites.
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 How do we know about Greek mathematics?  MacTutor Math History Archives
Linked essay illustrating the way that Greek mathematical texts have come down to us by looking first at perhaps the most famous example, Euclid's Elements, and Archimedes' palimpsest, with references and other related web sites.
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 How to Compute One Billion Digits of Pi (Organic Mathematics Proceedings)  D. H. Bailey, J. M. Borwein, P. B. Borwein
Ramanujan, Modular Equations, and Approximations to Pi  Bailey, Borwein and Borwein. Abstract: This article follows up one small thread of Ramanujan's work which has found a modern computational context, namely, one of his approaches to approximating
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 How to Compute Planetary Positions  Paul Schlyter
A description of how to compute the positions for the sun and moon and the major planets, as well as for comets and minor planets, from a set of orbital elements. The algorithms have been simplified as much as possible while still keeping a fairly good
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 How to Correctly View a Flatland Painting  Mark Schlatter
A paper with Java illustrations: Given a two dimensional painting of a three dimensional object, you can use geometry to find the ideal viewing locationthe position where the image appears most three dimensional. This site reviews that geometry (using
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 How to Fix an Election  Ivars Peterson (MathTrek)
Voting sounds like a simple matter. Just pick a candidate, then count the ballots and announce the tally. When there are three or more candidates (or choices), however, the results may not actually reflect the true preferences of the voters.
Suppose
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 How To Get Into the Newspapers  Keith Devlin (Devlin's Angle)
A lecture to Devlin's readers with good advice on how to write math clearly enough and other important things to do to get an article published in the newspapers.
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