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Topic: E8 (mathematics)

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	Field (mathematics) Encyclopedia
		The mathematical discipline concerned with the study of fields is called field theory.
		A field is a commutative ring (F, +, *) such that 0 does not equal 1 and all elements of F except 0 have a multiplicative inverse.
		However, in many circumstances in mathematics, it is not appropriate to treat G as being uniquely determined by F, since the isomorphism above is not itself unique.
	www.hallencyclopedia.com /topic/Field_(mathematics).html (1677 words)

	Math research team maps E8 - MIT News Office
		MIT's David Vogan, a professor in the Department of Mathematics and member of the research team, presented the work Monday, March 19 to a standing-room-only crowd in Room 1-190.
		Additional team members include Dan Ciubotaru, the CLE Moore Instructor in MIT's Department of Mathematics, and Alfred Noel, a professor at the University of Massachusetts at Boston and an MIT visiting scholar.
		The connections in the graph, and the colors of the connecting edges, are shorthand describing the geometry of the structure.
	web.mit.edu /newsoffice/2007/e8.html (783 words)

	cbs11tv.com - Mathematicians Map 248-Dimension E8 Problem
		MIT's David Vogan, a professor in the Department of Mathematics and member of the research team, explained the structure is a study of symmetries in higher dimensions.
		"E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood," said Jeffrey Adams, project leader and a mathematics professor at the University of Maryland.
		The mapping of E8 may well have unforeseen implications in mathematics and physics that won't be evident for years to come.
	cbs11tv.com /technology/local_story_079142127.html (522 words)

	AIM math: Representations of E8
		Even after we understood the underlying mathematics it still took more than two years to implement it on a computer." And then there came the problem of finding a computer large enough to do the calculation.
		The goal of the Atlas project is to determine the unitary representations of all the Lie groups.
		The Atlas project is funded by the National Science Foundation through the American Institute of Mathematics.
	aimath.org /E8 (945 words)

	Library Tour
		For anyone studying the history of mathematics, it is crucial that you learn to use the resources in the library.
		The standard histories of mathematics by Boyer (QA21.B767) and Eves (QA21.E8 1976) are also here, but not the best available survey book, that by Victor Katz (you can borrow a copy from Dr. Shell or Dr. Rickey).
		The crest of the peacock : the non-European roots of mathematics / George Gheverghese Joseph.
	www.dean.usma.edu /math/people/rickey/hm/USMA-lib-tour.html (1531 words)

	History of Mathematics
		A history of mathematics; from antiquity to the beginning of the nineteenth century.
		The history of mathematics from antiquity to the present : a selective bibliography.
		The history of modern mathematics : proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989.
	www.ship.edu /~deensl/m400/resources.html (391 words)

	Inside WEAC
		The mathematics class has traditionally represented the primary arena for statistical projects and topics.
		Appropriate analysis of data and the collection of data are essential skills for all citizens.
		This workshop will examine several high school projects which originated in the mathematics class and ex-panded to the geography, physical science, social studies, consumer ed-ucation, and English classrooms.
	www.weac.org /aboutwea/conven97/work40.htm (118 words)

	jacal (Site not responding. Last check: 2007-11-06)
		JACAL is a symbolic mathematics system for the simplification and manipulation of equations and single and multiple valued algebraic expressions constructed of numbers, variables, radicals, and algebraic functions, differential, and holonomic functions.
		e8 : a:[[1, 0], [-1, 1]]; [1 0] e8: [ ] [-1 1] e9 : a^^3; [1 0] e9: [ ] [-3 1]
		e8; [1 0] e12: [ ] [0 1] e13 : e10.
	www.swiss.ai.mit.edu /~jaffer/jacal.html (4818 words)

	PhysOrg.com: General Science news
		Dutch researcher Joris van den Berg has developed a mathematical model to predict the movement of sand waves.
		Using mathematical theory, UC Irvine scientists have shed light on one of cancer’s most troubling puzzles -- how cancer cells can alter their own genetic makeup to accelerate tumor growth.
		The theorists who first created the mathematics that describe the behavior of the recently announced "invisibility cloak" have revealed a new analysis...
	science.physorg.com /sub_Mathematics (673 words)

	News about E8 \| The n-Category Café
		You may have heard some hype about this, because it’s a really big calculation, and the American Institute of Mathematics has coaxed a lot of science reporters to write about it — in part by comparing it to the human genome project.
		Re: News about E8 “The trick for getting compact Lie groups from the distance function on their maximal torus is something kids learn in grad school.”….describing them as kids made me read that as grade school…for a moment there I thought something was seriously wrong with my primary education.
		Re: News about E8 Sure, a classification of all possible gradings of all simple Lie algebras would be interesting, and perhaps such a classification already exists.
	golem.ph.utexas.edu /category/2007/03/news_about_e8.html (5220 words)

	The New Math » Blog Archive » Mathematicians Map E8
		This achievement is significant both as an advance in basic knowledge and because of the many connections between E8 and other areas, including string theory and geometry.
		The magnitude of the calculation is staggering: the answer, if written out in tiny print, would cover an area the size of Manhattan.
		Mathematicians are known for their solitary work style, but the assault on E8 is part of a large project bringing together 18 mathematicians from the U.S. and Europe for an intensive four-year collaboration.
	www.thenewmath.com /2007/04/08/mathematicians-map-e8 (280 words)

	[No title]
		H -spaces analogous to E8 mod 3 Dedicated to the memory of Masahiro Sugawara James P. Lin Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112, U.S.A. email:jimlin@euclid.ucsd.edu Abstract Let p be an odd prime.
		Mathematics Subject Classification (2000): 55N22, 55P35, 55P45, 55Q25, 55R05, 55S05, 55S10, 55T10 0 Introduction In this note we begin a study of the following questions.
		H-spaces analogous to E8 mod 3 17 13.
	hopf.math.purdue.edu /LinJP/Lin=HspaceAnalog1.txt (3044 words)

	Mathematics (Site not responding. Last check: 2007-11-06)
		Groups, Rings, and Fields: I define these important mathematical terms here, and give a few interesting examples of groups.
		Sphere Packing: On this page, I include some diagrams of the face-centered cubic packing of spheres, as well as packings of circles in two dimensions, and I also include a diagram illustrating the E8 packing of hyperspheres in eight dimensions.
		Gödel's Proof and the Halting Problem: This page tries to discuss, very briefly, what is perhaps the most profound of mathematical discoveries.
	www.quadibloc.com /math/matint.htm (246 words)

	Clay Mathematics Institute
		These three symbols represent to a modern mathematician three Dynkin diagrams, but in a sense they have been known to mathematicians for hundreds of years.
		When the Greeks classified the regular solids, they were really showing they knew about E6, E7 and E8 and when the 19th century geometers got excited about the 27 lines on a cubic surface or the 28 bitangents to a quartic curve they were really studying E6 and E7 in their own terms.
		The talk will aim to show how E6, E7 and E8 lie at the heart of some very concrete mathematics.
	www.claymath.org /programs/outreach/academy/colloquium2005.php (1046 words)

	physics - Simple Lie group (Site not responding. Last check: 2007-11-06)
		In mathematics, a simple Lie group is a Lie group which is also a simple group.
		These groups, and groups closely related to them, include many of the so-called classical groups of geometry, which lie behind projective geometry and other geometries derived from it by the Erlangen programme of Felix Klein.
		The exceptional groups account for many special examples and configurations in other branches of mathematics.
	physics.usc.edu /~bars/symmetries/SimpleLieAlgebra.htm (465 words)

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