 G J Chaitin Home Page  Greg Chaitin
From the author of Algorithmic Information Theory, Information, Randomness & Incompleteness, InformationTheoretic Incompleteness, The Limits of Mathematics, The Unknowable, Exploring Randomness, Conversations with a Mathematician, From Philosophy
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 Glitter Trap (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
You've probably looked at your distorted reflection in a shiny holiday ornament, but you may be surprised to learn what the reflections in a pyramid of silvery balls are like. The behavior of light in a stack of mirrored balls can help mathematicians
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 Global Analysis, Analysis on Manifolds  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to global analysis, which studies the global nature of differential equations on manifolds, that is, dynamical systems. In addition to local tools from ordinary differential equation
theory, global
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 The Global Schoolhouse  Global SchoolNet Foundation (GSN)
A site for teachers, parents, teens, and kids, with articles on telecommunication in the classroom, contests, events, projects, an alphabetical site index, and an annotated list of all articles. Formerly called FrEdMail (Free Educational Mail), GSN is
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 The Global Schoolhouse  Global SchoolNet Foundation (GSN)
The Global Schoolhouse focuses on projects for lifelong learning and uses the most powerful Internet tools, including live video, to link K12 classrooms to their communities and to other children around the world. Projects that discover and document
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 The Gods of Sugarscape  Ivars Peterson  Science News Online
Computer simulations furnish a means of gleaning insights into human social and economic behavior. The Sugarscape model is more a metaphor than a realistic depiction of society, but by providing insights into population growth, resource use, migration,
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 Goldbach's Prime Pairs  Ivars Peterson (MathTrek)
Prime numbers serve as building blocks in the mathematics of whole numbers. Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove. The Goldbach
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 The Golden ratio  MacTutor Math History Archives
Linked essay on the history of the golden ratio (golden number, golden section), from Euclid through Martin Ohm's book, Die reine ElementarMatematik. With references and other related web sites.
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 Golden Rectangle and Golden Ratio  Jim Loy
An introduction to the ratio involved in the Golden Rectangle, with a link to The Most Pleasing Rectangle Web Poll.
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 The Golden Section In Art, Architecture and Music  Ron Knott
An introduction with illustrations and references to some applications and occurrences of the Fibonacci series and the Golden Ratio in architecture, art and music. The constant Phi has been used to design architecture, from the Parthenon in Athens to
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 Google Scholar  Google Labs
Google Scholar is a subset of the larger Google search index, consisting of fulltext journal articles, technical reports, preprints, theses, books, and other documents. Use the Advanced Scholar Search to confine search results to engineering, computer
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 Government Affairs and Education (AMS)  American Mathematical Society
Government Affairs: news from Washington on science funding; calls for action; policy statements; recent statements by the mathematical community; federal budget information; how to contact Congress; science policy events; and a link to the AMS Committee
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 Graceful Graphs  Michael Brundage, Dept. of Mathematics, Univ. of Washington
A paper about current studies on graceful labeling of graphs. Of particular interest is the conjecture that all trees are graceful graphs. Includes: definition of a graceful graph; methods of labeling graphs; how many graceful graphs are there?; known
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 Graduate School in Your Future?  Dianne Prost O'Leary
Written by a former director of undergraduate studies attempting to smoothe the transition from undergraduate to professional, this document offers advice to students on entering, surviving, and thriving during graduate study and beyond. Graduate School
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 Grant Keady
Grant Keady, a member of the faculty of the University of Western Australia, Dept of Mathematics and Statistics, Western Australia, researches fluid dynamics and related subjects, with forays into computer algebra. Some of his papers are available online
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 Graphing Misinterpretations and MicrocomputerBased Laboratory Instruction, with Emphasis on Kinematics  Lisa Denise Murphy
A review of the literature and of several efforts to teach graph interpretation using various forms of technology. Line graphs showing the value of a variable over a period of time are used extensively in mathematics and the sciences. Students often misinterpret
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 Graph Theory and Linear Algebra [PDF file]  Stephen Kauffman
The author states: Discusses aspects of Graph Theory that I haven't been able to find on the internet except at Linear Spaces of a Graph, so I wrote up everthing I know about it. It hasn't been reviewed.
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 Graph Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to graph theory. A graph is a set V of vertices and a set E of edges  pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on
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 Graph Theory  Steven Locke; Dept. of Mathematical Sciences, Florida Atlantic University
A brief history of graph theory, with basic definitions and problem sets based on the texts. Topics investigated include: Automorphism Group, Bicentral Tree, Binding Number, Bond Space, Cage, Central Tree, Characteristic Polynomial, Chromatic Polynomial,
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 Grassmann's Theory of Dimension  Desmond FearnleySander
The theory of dimension for finitelygenerated linear spaces was created by Hermann Grassmann and is given in detail in Chapter 1 of his Ausdehnungslehre of 1862. The main part of the present paper is an annotated translation of the relevant portion of
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 The Greater Philadelphia Secondary Mathematics Project  The Greater Philadelphia Secondary Mathematics Project
A support site for the systemic implementation of professional development using nationally validated, exemplary, standardsbased secondary mathematics curricula in the Greater Philadelphia region. News and resources include edited dialogues about the
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 The Greatest Math Teacher Ever  Keith Devlin (Devlin's Angle)
An article about the individual who, Devlin suggests, could justifiably be described as the American university mathematician who, through his teaching, has
had the greatest impact on the field of mathematics... He was a pioneer in one of the most important
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 Greek Astronomy  MacTutor Math History Archives
Linked essay tracing the history of Greek astronomy from its beginnings with
Thales, in philosophy and timekeeping, through Pythagoras, Eratosthenes,
Hipparchus, Ptolemy, Plato, Aristotle, Aristarchus, and many others; with
references to relevant
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 Greek Mathematics and its Modern Heirs  SunSITE's Vatican Exhibit; Library of Congress
Classical roots of the scientific revolution. An essay on the history of Greek Math, with sample math problems. Covers Euclid's Elements and Optics, Archimedes' Works, Piero della Francesca's De quinque corporibus regularibus, and links to Ptolemy's Geography
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 Greek number systems  MacTutor Math History Archives
Linked essay on the history of the Greek number systems, notably the acrophonic system used in the first millennium BC, and the alphabetical numerals. With references and other related web sites.
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 Greek Science, Oral Report: Greek Mathematics  Chris Weinkopf
An oral report on the WWW, with links to relevant materials at the Perseus Project. The Four Divisions; Aristotelian Reclassification; Arithmetic; Geometry. Archytus, Plato, Aristotle, arithmetic as a function of logic, numbers as expressions of worth.
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 GreenHouse Gas Online
A site devoted to greenhouse gas and climate changerelated science, containing climate change news and links to the abstracts of hundreds of greenhouse gasrelated scientific papers. With discussions of the main types of greenhouse gas, and the global
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 The Greenwood Institute  Greenwood School
A dyslexia, learning disabilities, and literacy resource site, with links to Web resources and publications. Comprehensive training of literacy instructors for mainstream and specialized schools; support for home schooling; research support; and consulting
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 Greg Egan's Home Page
Information, illustrations, and Java applets that supplement some of the works of the science fiction author. The Applets Gallery includes groups of rotations in three dimensions and in four dimensions; Escher, inspired by the artist's conflicting orientation
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 Greg Kearsley's Personal Home Page  Greg Kearsley
Articles and papers include Learning and Teaching in Cyberspace; Educational Technology: A Critique of Pure Reason, The Virtual Professor: A Personal Case Study, Engagement Theory: A framework for technologybased teaching and learning, Online Education:
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 Gregory Buck  The New Yorker
"Like everyone else I know, when I go to the beach I think mathematics....I have had people ask me what it is like to do research in mathematics, and perhaps the answer is that it is like a snowstorm...." Seasonal posts by the Saint Anselm College professor
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 Grothendieck Circle  Leila Schneps
Alexandre Grothendieck's published articles, unpublished research, letters, and translations: The Cohomology Theory of Abstract Algebraic Varieties, Standard Conjectures on Algebraic Cycles, Hodge's General Conjecture Is False for Trivial Reasons, Groupes
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 Groupe Fractales (INRIA)  Benoît Leblanc and Frédéric Raynal
A group of researchers studying the application of fractal techniques to complex systems, especially signal processing. Introduction to the theoretical aspects of fractal analysis; genetic algorithms; introduction to timescale analysis, in French; applications,
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 Grouping: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on grouping practices, primarily as related to the education of gifted children.
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 Grouping Practices (NCREL)  Pathways to School Improvement
"Grouping practices  especially tracking  often have the effect of reducing equity." This article explores the negative effects of tracking and touches on cooperative learning. From the North Central Regional Educational Laboratory (NCREL).
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 Groupoid Home Page  Ramsay, Chiaramonte, Woo, Renault, Ramazan; Institute of Mathematics of the Romanian Academy
Papers on groupoids; other sources on groupoids; bibliography; an address book of mathematicians interested in groupoids; and future conferences.
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 Groups, Graphs, and Paul Erdös  Ivars Peterson (MathLand)
The relative isolation that Andrew Wiles sought in solving Fermat's Last Theorem is certainly not the rule in mathematical research. Doing mathematics is really a remarkably social process. The abundance of meetings, conferences, workshops, colloquia,
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 Group Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to group theory. Group theory can be considered the study of symmetry: the collection of symmetries of some
object preserving some of its structure forms a group; in some sense all groups arise this
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 Gsystems  Vladimir Ladma
A paper presenting an algebraic theory of musical chord structures that seeks to provide a simple algorithm for generating these structures.
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 Guessing the Prime Number Theorem and Treacherous Logic (Math Chat)  Frank Morgan, MAA Online
The Prime Number theorem says that the probability P(x) that a large integer x is prime is about 1/log x. At about age 16 Gauss apparently conjectured this estimate after studying tables of primes. Greg Martin suggested to me a heuristic way to approach
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 Guidelines for Educational Uses of Networks  Learning Resource Server (LRS), College of Education, Univ. of Illinois at UrbanaChampaign
A starting set of papers with guidelines for how to use networks in powerful ways for education. Topics include telecommunication, virtual communities, global literacy, acceptable use policies, and neworkbased learning environments.
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 Guy Kindler  The Official Site  Guy Kindler
A mathematics Ph.D. student at Tel Aviv University. Math puzzles are ranked from easy to tough. A paper on approximation and various resources for a seminar on computational models may be downloaded in PostScript format. Related PowerPoint presentations
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 GVU Center  Jarek Rossignac; Georgia Tech
The Graphics, Visualization & Usability Center, envisioning a world in which computers are used as easily and effectively as are automobiles, stereos, and telephones, and collaborating on research projects in Visualization, Animation, VR, Design,
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 Habits of mind: an organizing principle for mathematics curriculum (Connected Geometry)  Cuoco, Goldenberg, Mark; Education Development Center, Inc. (EDC)
A curriculum the goal of which is not to train large numbers of high school students to be university mathematicians, but rather to allow high school students to become comfortable with illposed and fuzzy problems, to see the benefit of systematizing
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 Hales Proves Hexagonal Honeycomb Conjecture (Math Chat)  Frank Morgan, MAA Online
Professor Thomas Hales of the University of Michigan has announced a proof of the Hexagonal Honeycomb Conjecture, which says that regular hexagons provide the leastperimeter way to enclose infinitely many unit areas in the plane. This may partly explain
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 Hamiltonian Circuit Algorithm  Ashay Dharwadker
A new algorithm for finding Hamiltonian circuits in graphs with a
constructive proof of Dirac's theorem, applications to finding Knight's
Tours and a demonstration program, by Ashay Dharwadker.
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 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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