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	Mathematics - MSN Encarta
		Mathematics finally became a field in its own right with the development of calculus by English mathematician Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17th century and the creation of rigorous mathematical analysis during the 18th century by French mathematician Augustin Louis Cauchy and his contemporaries.
		Mathematics attempts to capture the complexity of a problem using mathematical notation (signs and symbols) and concepts (theorems and proofs).
		Pure mathematics is the study of abstract relationships, whereas applied mathematics applies mathematical analysis to real-world problems, such as the rate of global warming.
	encarta.msn.com /encyclopedia_761578291/Mathematics.html (1356 words)

	Mathematics
		The universe is merely an incarnation of mathematics.
		Mathematics occupies no space and is not located anywhere specifically, yet it's everywhere.
		Somewhere in the depths of mathematics there are truths, perhaps in the form of equations that can be set up and solved, which would explain how the universe can materialize from mathematics.
	www.numericalmathematics.com /mathemat.htm (388 words)

	Universe (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, and particularly in applications to set theory and the foundations of mathematics, a universe or universal class (or if a set, universal set) is, roughly speaking, a class that is large enough to contain (in some sense) all of the sets that one may wish to use.
		Implicitly, this is the universe that Georg Cantor was using when he first developed modern naive set theory and cardinality in the 1870s and 1880s in applications to real analysis.
		This concept of a universe is reflected in the use of Venn diagrams.
	en.wikipedia.org /wiki/Universe_(mathematics) (1776 words)

	Encyclopedia: Universe (mathematics) (Site not responding. Last check: 2007-10-15)
		In mathematics, a relatively complemented lattice is a lattice L in which for all a, b, c in L with a ≤ b ≤ c there is some x in L such that x ∨ b = c and x ∧ b = a.
		In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range).
		In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the models which underlie mathematical systems.
	www.nationmaster.com /encyclopedia/Universe-(mathematics) (3899 words)

	Learn more about Universe in the online encyclopedia. (Site not responding. Last check: 2007-10-15)
		In the first half of the 20th century, the word Universe was used to mean the whole spacetime continuum in which we exist, together with all the energy and matter within it.
		It is not known whether the Universe is finite or infinite in spatial extent and volume, although the majority of theorists currently favor an finite Universe.
		We live in the centre of the observable universe, in apparent contradiction to the Copernican principle which says that the Universe is more or less uniform and it has no distinguished centre.
	www.onlineencyclopedia.org /u/un/universe.html (1133 words)

	The lawful Universe - 1.2 Mathematics and quantification - part 1 of 2
		Roger Bacon once said ‘Mathematics is the door and the key to the sciences’.
		Given an equation that relates various quantities, the rules of mathematics allow that equation to be re-expressed in a number of different but logically equivalent ways, all of which are valid if the original equation was valid.
		Given two equations, mathematical reasoning allows them to be combined to produce new equations which are again valid if the original equations were valid.
	physicalworld.org /restless_universe/html/ru_1_21.html (414 words)

	Saint Michael's College - Mathematics
		Mathematics is intellectually stimulating because it demands clarity and precision.
		Mathematics majors are attractive to a wide variety of business and industrial firms, especially if the major is combined with some coursework in computer science, a natural science, economics or business; many find work in the actuarial field or as analysts in the computer or communications industry.
		Mathematics majors may prepare to teach at the secondary school level by simultaneously completing education courses, including a semester of student teaching, which leads to state certification.
	www.smcvt.edu /academics/mathematics (325 words)

	[No title]
		Mathematics has a beauty all its own and there is, for the mathematician, an aesthetic joy that comes from solving an important problem, no matter what value society may place on this activity.
		Mathematics may indeed reflect the operations of the brain, but both brain and mind are far richer in their nature than is suggested by any structure of algorithms and logical operations.
		Mathematics is effective when it becomes a hymn to this underlying order of consciousness and the universe, and when it expresses something of the truth inherent in nature.
	www.fdavidpeat.com /bibliography/essays/text/maths.txt (6983 words)

	Think Maths
		With this kind of ubiquitous occurrence of the same mathematical patterns, it is no wonder that physical scientists get carried away and declare them to lie at the very basis of space, time and matter.
		Your behaviour is caused by mathematical rules applied to your constituent atoms, in the context of everything that is happening around you, but you can't do the calculations to check that because they're too messy and too lengthy.
		From this point of view, mathematical patterns that arise in high-level descriptions of living organisms are evidence that biology, too, is mathematical at heart.
	www.fortunecity.com /emachines/e11/86/thinkmat.html (2870 words)

	Resource: Private Universe Project in Mathematics
		The Private Universe Project in Mathematics demonstrates and honors the power and sophistication of these ideas, and explores how mathematics teaching can be structured to resonate with children's sophisticated thinking.
		This workshop offers the rare opportunity to follow the mathematical development of one group of students throughout grades 1-12, and to observe teachers in the process of redefining what mathematics is for themselves and for their students.
		An unprecedented long-term study conducted by Rutgers University followed the development of mathematical thinking in a randomly selected group of students for 12 years - from 1st grade through high school - with surprising results.
	www.learner.org /resources/series120.html (352 words)

	Readings, Films, and Paper--MAT 222 (Site not responding. Last check: 2007-10-15)
		These out-of-class activities are provided to support two of the course objectives (to expand personal perspectives on the history and role of mathematics in society, and to appreciate better the concepts that form the foundation of science and technology).
		It was the state-of-the-art mathematical research in the 17th century.
		Mathematics is the tool for investigating these questions and the language for communicating the answers.
	www.wlc.edu /academics/mat/calc/mat222_readings.html (653 words)

	* Universe - (Astronomy): Definition (Site not responding. Last check: 2007-10-15)
		The study of the origin of the universe, or cosmos, is known as cosmogony, and that of its structure and evolution,...
		The expanding universe is a model of the universe in which galaxies are receding from one another at a speed proportional to their separation - it is based on the observed Doppler redshift of distant galaxies...
		Hypothesis that the universe began as nothingness, from which matter and energy arose by a process analogous to the appearance of virtual particles from a vacuum.
	www.bestknows.com /astronomy/universe.html (2052 words)

	Is mathematics a science?
		Mathematics is certainly a science in the broad sense of "systematic and formulated knowledge", but most people use "science" to refer only to the natural sciences.
		Since mathematics provides the language in which the natural sciences aspire to describe and analyse the universe, there is a natural link between mathematics and the natural sciences.
		There is also the argument that mathematics is "not really accessible enough to be an art and not immediately useful enough to be a science" [1], but this assumes that art is accessible and science is useful.
	euclid.trentu.ca /math/sb/misc/mathsci.html (1478 words)

	NSERC - The Mathematics of the Universe
		Very little of Dr. Jeffrey's brand of mathematics is accessible to the outsider – a title that applies to anyone outside the rarefied field of symplectic geometry.
		It's the mathematics that is at the heart of studying phase space, the combination of location, motion and time that is used to describe the behaviour of everything big and small in the Universe (other than gravity, an exception left to Einstein's theory of general relativity).
		But symplectic geometry is a happy exception," says Dr. Lisa Jeffrey, a professor of mathematics at the University of Toronto and the recipient of a 2004 NSERC Steacie Fellowship.
	www.nserc.ca /news/2004/p040311_bio5.htm (806 words)

	ScienceDaily: Help Page (Site not responding. Last check: 2007-10-15)
		Enzyme Inhibitor Produces Stable Disease In Patients With Advanced Solid Cell Cancers (November 15, 2006) -- Preliminary trials of a MEK enzyme inhibitor have shown that it is capable of producing long-lasting stable disease in patients with advanced solid cancers.
		Pattern Of Human Ebola Outbreaks Linked To Wildlife And Climate (November 15, 2006) -- A visiting biologist at the University of California, San Diego and her colleagues in Africa and Britain have shown that there are close linkages between outbreaks of Ebola hemorrhagic fever in human...
		Math Model Could Aid Study Of Collagen Ailments (November 15, 2006) -- An MIT researcher's mathematical model explains for the first time the distinctive structure of collagen, a material key to healthy human bone, muscles and other tissues.
	www.sciencedaily.com /news/computers_math/mathematics (1165 words)

	NOVA \| The Elegant Universe \| Imagining Other Dimensions \| PBS
		He can't be at the center of a circle and move in a direction that allows him to remain equidistant to every point of the circle's circumference—unless he moves into the third dimension.
		That is, for the equations that describe superstring theory to begin to work out—for the equations to connect general relativity to quantum mechanics, to explain the nature of particles, to unify forces, and so on—they need to make use of additional dimensions.
		It turns out that, before superstring theory existed, two mathematicians, Eugenio Calabi of the University of Pennsylvania and Shing-Tung Yau of Harvard University, described six-dimensional geometrical shapes that superstring theorists say fit the bill for the kind of structures their equations call for.
	www.pbs.org /wgbh/nova/elegant/dimensions.html (1174 words)

	Course List, Mathematics, Saint Michael's College
		Mathematics is intellectually stimulating because it demands clarity and precision.
		Mathematics majors are attractive to a wide variety of business and industrial firms, especially if the major is combined with some coursework in computer science, a natural science, economics, or business; many find work in the actuarial field or as analysts in the computer or communications industry.
		Mathematics majors may prepare to teach at the secondary schoool level by simultaneously completing Education courses, including a semester of student teaching, which leads to state certification.
	joshua.smcvt.edu /math/courses.html (2895 words)

	Science Show - 18/11/00: Mathematics Gene
		And not despite its peculiarities but because of them, the mental universe of mathematics has provided human beings with many of their deepest insights into the world around them.
		Now modern scientific approaches to how the brain deals with numbers and other aspects of mathematics shows that really there are separate parts of the brain that deal with maths on the one hand, deal with reasoning on the other deal and deal with language on the third hand.
		The Maths Gene is a mathematics book that could just as easily be seen as a very significant work on linguistics or equally a study of evolutionary biology.
	www.abc.net.au /rn/science/ss/stories/s212670.htm (3373 words)

	Is Math a Young Man's Game? - No. Not every mathematician is washed up at 30. By Jordan Ellenberg (Site not responding. Last check: 2007-10-15)
		Mathematical progress is supposed to occur not through decades of experience and toil but all at once, in a numinous blaze, to a born genius.
		Galois laid down the foundations of modern algebra as a teenager, with enough spare time left over to become a well-known political radical, serve a nine-month jail sentence, and launch an affair with the prison medic's daughter; in connection with this last, he was killed in a duel at the age of 21.
		Jordan Ellenberg is an assistant professor of mathematics at Princeton University.
	slate.msn.com /id/2082960 (1568 words)

	CM Series
		Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.
		Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination.
		To sum up, Mathematics are a necessary part of every man's education; they must be taught by those who know; but they may not engross the time and attention of the scholar in such wise as to shut out any of the score of 'subjects,' a knowledge of which is his natural right.
	www.amblesideonline.org /CM/6_1_10_09.html (770 words)

	Tool Factory Press
		Mathematics, Art, History, and Science meet in the highly-acclaimed CD-ROMs, and teachers and students alike are thrilled to finally find software titles that reach into the fascinating realm of subjects such as Art History and Astronomy.
		Life, the Universe, and Mathematics is an interactive program that explores the "elegant geometrical laws" at work in the universe.
		Both Life, the Universe, and Mathematics and Art and Mathematics are appropriate for high school study and higher learning.
	www.toolfactory.com /Press/virtual_press_release.htm (615 words)

	What is Mathematics?
		The purpose of this writing is to present a brief summary of types of mathematical thought that have surfaced since the ancient Greeks realized that humans have the mental capacity to reason.
		All of mathematics is derivable from principles of logic.
		Mathematical laws are not discovered by studying nature; rather, they are found in the recesses of the human mind.
	www.herkimershideaway.org /writings/whatmth.htm (1657 words)

	Is There Scientific Evidence for the Existence of God? How the Recent Discoveries Support a Designed Universe
		Much of the essential design of our universe is embodied in the scaling of the various forces, such as gravity and electromagnetism, and the sizing of the rest mass of the various elemental particles such as electrons, protons, and neutrons.
		In a universe where water is the primary medium for the chemistry of life, the temperature must be maintained between 0° C and 100° C (32° F to 212° F) for at least some portion of the year.
		To choose to believe that there is a naturalistic explanation for (a) the mathematical forms encoded in the laws of nature, (b) the precise specification of the nineteen universal constants and (c) the remarkable initial conditions required for star formation and the simplest living systems is to believe in a miracle by another name.
	www.leaderu.com /real/ri9403/evidence.html (9933 words)

	The Universe may be a Mystery, but it's no Secret!
		Worldwide traditions looked to the archetypal patterns of mathematics and nature for their compelling designs.
		He taught youngsters for twelve years in public and private schools at the Middle School and Elementary school levels, and was a Fulbright-Hayes Scholar in India studying ancient mathematics and sciences.
		Michael is the author of "A Beginner's Guide To Constructing The Universe: The Mathematical Archetypes Of Nature, Art and Science" (HarperPerennial paperback 1995), five "Constructing The Universe Activity Books" and numerous articles concerning mathematics in nature and art.
	www.constructingtheuniverse.com (774 words)

	Math Links
		In your solitude go to this Mathematics Museum in Japan; they greet you with a badly performed and loud midi music but they give you very stable solitary waves in a solution of the Soliton equations.
		If you are sent to this finite universe, instead of trying to reach its boundary, get on its various surfaces.
		The birthplaces of famous mathematicians are shown at the MacTutor History of Mathematics Archive.
	www.mcs.csuhayward.edu /~malek/Mathlinks/Mathlinks.html (1128 words)

	Amazon.com: Books: Theories of Everything: The Quest for Ultimate Explanation (Site not responding. Last check: 2007-10-15)
		So much of mathematics, physics, philosophy, and other disciplines have, even if it is unspoken, a sense of unity at heart, in which this belief plays a part.
		In discussing symmetries in the universe and the idea of creation ex nihilo, Barrow brings in ideas of overall net roation and electric charge to the universe (where is the evidence for these?), and basic conservation principles, in part to dispute the idea that creation ex nihilo somehow violates a cosmological principle.
		Barrow expands into mathematics (of course, incompleteness theorems, that gem of philosophical speculation that is so often misapplied beyond its narrow purview, is here), biological ideas of organising principles (is this natural or a fluke, or did it require an outside intervention?), time and space difficulties and paradoxes, and more.
	www.amazon.com /exec/obidos/tg/detail/-/0198539282?v=glance (2842 words)

	God's Equation :: Wayward Puppy (Site not responding. Last check: 2007-10-15)
		While occasionally the review of some of the equations involved was a nice refresher I got virtually nothing new out of this book.
		After reading the enjoyable but far overreaching The Mystery of the Aleph : Mathematics, the Kabbalah, and the Search for Infinity I didn’t have the highest of expectations from Aczel but I must say I still felt let down.
		Narrative style survey histories of the sciences are what Aczel does best but when he attempts to go beyond that his limits quickly become apparent.
	www.waywardpuppy.com /archives/2005/03/gods_equation.html (285 words)

	Universe (mathematics) (Site not responding. Last check: 2007-10-15)
		Instead, one can work with the individual Boolean lattices PA, where A is any relevant set belonging to S; then PA is a subset of S (and in fact belongs to S).
		is the universe of ordinary mathematics; it is a model of Zermelo set theory, the axiomatic set theory originally developed by Ernst Zermelo in 1908.
		Transfinite iteration of the superstructure yields Goedel's constructible universe L
	www.ukpedia.com /u/universe-mathematics-.html (1323 words)

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