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	Evariste Galois - Wikipedia, the free encyclopedia
		Galois at the age of fifteen from the pencil of a classmate.
		Galois revised his memoir and sent it to Fourier in early 1830, upon the advice of Cauchy, to be considered for the Grand Prix of the Academy.
		Galois' mathematical contributions were finally fully published in 1843 when Liouville reviewed his manuscript and declared that he had indeed solved the problem first proposed and also solved by Abel.
	en.wikipedia.org /wiki/Evariste_Galois (678 words)

	Galois theory - Wikipedia, the free encyclopedia
		In mathematics, Galois theory is a branch of abstract algebra.
		Galois theory not only provides a beautiful answer to this question, it also explains in detail why it is possible to solve equations of degree four or lower in the above manner, and why their solutions take the form that they do.
		The central idea of Galois theory is to consider those permutations (or rearrangements) of the roots having the property that any algebraic equation satisfied by the roots is still satisfied after the roots have been permuted.
	www.wikipedia.org /wiki/Galois_theory (1577 words)

	Evariste Galois
		A tragic hero to mathematicians, Galois brief, chaotic, and dire life on the fringes of the mathematical and political establishments lends easily to the great myth of Galois as the genius oppressed by the hostile, ignorant power structure of his day.
		However, Galois was arrested again on Bastille Day 1831 for possessing a weapon and wearing the uniform of the Guard, which had been ordered disbanded by a fearful Louis-Philippe.
		Using this theory, Galois gave an elegant proof of the mathematical theorem that states that the general quintic polynomial is not solvable, a problem of much interest in his day.
	www.iscid.org /encyclopedia/Evariste_Galois (1902 words)

	Learn more about Galois theory in the online encyclopedia. (Site not responding. Last check: 2007-11-07)
		Galois theory is that branch of abstract algebra which studies the symmetries of the roots of polynomials.
		Symmetries are usually expressed in terms of symmetry groups, and in fact the abstract notion of group was invented by Evariste Galois for the very purpose of describing symmetries of roots.
		In the modern approach, the formalism is changed somewhat, in order to achieve a precise and more general definition: one starts with a field extension L/K and defines its Galois group as the group of all field automorphisms of L which keep all elements of K fixed.
	www.onlineencyclopedia.org /g/ga/galois_theory.html (753 words)

	Galois theory - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		In mathematics, Galois theory is that branch of abstract algebra which studies the symmetries of the roots of polynomials.
		Symmetries are usually expressed in terms of symmetry groups, and in fact the very notion of a group of permutations was used by Evariste Galois (also Cauchy, and earlier by Ruffini) to describe symmetries of roots.
		In the modern approach, the setting is changed somewhat, in order to achieve a precise and more general definition: one starts with a field extension L/K and defines its Galois group as the group of all field automorphisms of L which keep all elements of K fixed.
	open-encyclopedia.com /Galois_theory (1078 words)

	Evariste Galois (1811 - 1832) (Site not responding. Last check: 2007-11-07)
		Galois is one of the most tragic and romantic figures of mathematics.
		Galois proved that no polynomial of degree greater than five could be solved analyticaly, a great outsanding problem of the day.
		Galois' early schooling was at the infamous lycee of Louis Grande in Paris.
	www.scs.ryerson.ca /~danziger/labs/galois.htm (507 words)

	Evariste Galois
		Galois tried to start his own school of mathematics, but got no students, so he joined the National Guard -- "If a carcass is needed to stir up the people, I will donate mine." Galois was jailed for supposedly threatening the King, but was found 'not guilty' by a jury.
		Galois took it violently and was disgusted with love, with himself, and with his girl." A few days later Galois encountered some of his political enemies and "an affair of honor," a duel, was arranged.
		Galois was shot in the intestines, and was taken to the hospital.
	scidiv.bcc.ctc.edu /Math/Galois.html (653 words)

	Galois (Site not responding. Last check: 2007-11-07)
		Galois' father was an important man in the community and in 1815 he was elected mayor of Bourg-la-Reine.
		Galois was invited by Poisson to submit a third version of his memoir on equation to the Academy and he did so on 17 January.
		Galois was wounded in the duel and was abandoned by d'Herbinville and his own seconds and found by a peasant.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Galois.html (1959 words)

	Evariste Galois (Site not responding. Last check: 2007-11-07)
		Galois must have been interested in politics when he was still attending the Louis-le-Grand, because Dupuy says in his biography, that besides the excellent education provided at the Polytechnique, Galois hoped to participate in the various political activities of this school.
		Galois irritated him with his proposals: He wanted to introduce uniforms, like the one at the Ecole Polytechnique, which were in military style.
		Evariste Galois was expelled from school on the 9th of December - publicly announced on the 4th of January - because of an anonymous letter to the "Gazette des écoles".
	www.evariste-galois.net (2898 words)

	Galois
		During that same year, 1830, during the revolution, Galois was expelled from school for publicly criticizing the director of his school for failing to support the Revolution.
		Galois was denied entry into a prestigious school and attended a much inferior one.
		In that same year Galois was arrested for political offenses and spent most of the rest of the year and a half of his life in prison.
	www.math.wichita.edu /history/men/galois.html (742 words)

	.:: Galois Field Arithmetic Library ::.
		The branch in mathematics known as Galois theory (pronounced as "gal-wah") which is based on abstract algebra was discovered by a young brilliant french mathematician known as Evariste Galois.
		Galois theory is used to describe and generalize results seen in these fields, for example the AES algorithm can be represented with just a few lines of mathematics using Galois theory and some other related abstract algebra.
		Galois fields are setup by intially defining the size of the field which means how many elements will exist within the field, and also the values those elements will posses.
	www.partow.net /projects/galois (689 words)

	The Galois group of a polynomial
		A method for deciding whether the Galois group is abelian...
		Determining the Galois group of a rational polynomial...
		Computing the Galois group of a polynomial using linear differential equations...
	www.scienceoxygen.com /math/294.html (91 words)

	galois
		The story of Evariste Galois (Oct 25, 1811 to May 31, 1832) is a tragic one.
		At age 19, Galois sent three papers on theory of equations to Augustin Louis Cauchy at the Academy of Science, who valued Galois' papers highly and recommended Galois revise them into one paper in order to be considered for the Grand Prize in Mathematics at the Academy.
		Galois was shot in the abdomen and died the next day, apparently from peritonitis.
	www.geocities.com /galois_e/page/galois.html (833 words)

	Galois representations and elliptic curves (Site not responding. Last check: 2007-11-07)
		Galois theory is essentially the "complete" theory of the roots of polynomial equations in one variable.
		Galois' brilliant insight was that one can know essentially "everything" there is to know about the roots of polynomial equations by considering a new object, a group, namely the group of all "reasonable" permuations of those roots.
		F is Galois if E is the field obtained by adjoining to F all roots of some irreducible polynomial with coefficients in F. The Galois group of E over F, Gal(E/F), is the group of automorphisms of E that leave F fixed (i.
	www.mbay.net /~cgd/flt/flt07.htm (3077 words)

	Galois Theory (Site not responding. Last check: 2007-11-07)
		Galois theory is one of the jewels of mathematics.
		This undergraduate text develops the basic results of Galois theory, with Historical Notes to explain how the concepts evolved and Mathematical Notes to highlight the many ideas encountered in the study of this marvelous subject.
		Section 13.2 discusses how to compute the Galois group of a quintic polynomial and in Example 13.2.13 mentions the problem of finding the roots of a quintic that is solvable by radicals.
	www.cs.amherst.edu /~dac/galois.html (621 words)

	MC449 Galois Theory
		Galois theory is one of the first examples of methods from one branch of Mathematics being applied to solve problems in an apparently completely different area.
		The main theorem of Galois theory is one of the most beautiful theorems in all of mathematics, and extensions and applications of Galois theory are the subject of major research activities in algebra, geometry and analysis.
		Appreciate the significance of the Galois group of a polynomial as a group of permutations of the roots.
	www.mcs.le.ac.uk /Modules/Modules01-02/node76.html (641 words)

	Galois theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Modern approach by ((physics) a theory that explains a physical phenomenon in terms of a field and the manner in which it interacts with matter or with other fields) field theory
		The notion of a (Click link for more info and facts about solvable group) solvable group in (The branch of mathematics dealing with groups) group theory allows us to determine whether or not a polynomial is solvable in the radicals, depending on whether or not its Galois group has the property of solvability.
		One of the great triumphs of Galois Theory was the proof that for every n > 4, there exist polynomials of degree n which are not solvable by radicals—the (Click link for more info and facts about Abel-Ruffini theorem) Abel-Ruffini theorem.
	www.absoluteastronomy.com /encyclopedia/G/Ga/Galois_theory.htm (1239 words)

	Tony Rothman's Article on Evariste Galois (Site not responding. Last check: 2007-11-07)
		Galois was not among those expelled, nor is it known if he was even among the rebels, but we may guess that the arbitrariness of the provisor and the general severity of the school's regime made a deep impression on him.
		Galois was asked to repeat his third year because of his poor work in rhetoric Bell writes, "His mathematical genius was already stirring," and "He was forced to lick up the stale leavings which his genius had rejected"[17].
		Galois was the hero of the moment, and the artillerists adjourned to the street to celebrate their exhuberance by dancing all night.
	godel.ph.utexas.edu /~tonyr/galois.html (13825 words)

	The life and times of Évariste Galois
		This article is not intended to examine the work of Galois but rather to consider the extraordinary times that Galois lived in and to show the influence of world events on mathematics.
		From this point the monarchy of Louis 16th was in major difficulties as the majority of Frenchmen composed their differences and united behind an attempt to destroy the privileged establishment of the church and the state.
		However in 1826 Galois was asked to repeat the year because his work in rhetoric was not up to the required standard.
	www.maths.tcd.ie /~butler/greats/galois.html (1999 words)

	Evariste Galois' Biography (Site not responding. Last check: 2007-11-07)
		Galois concluded that not all permutations of the roots of a polynomial may be reasonable.
		Galois knew he had a very slim chance in the duel, so he spent all night writing the mathematics which he didn't want to die with him, often writing "I have not time.
		Galois proved that no such general method could be found, at least using a purely algebraic formula.
	www.andrews.edu /~calkins/math/biograph/biogaloi.htm (1725 words)

	Galois Theory IV (Site not responding. Last check: 2007-11-07)
		Galois extensions: splitting fields, normal extensions, separability, structure of finite fields.
		The Galois group: Fundamental Theorem, group of a polynomial; Fundamental Theorem of Algebra; cyclotomic extensions.
		Solubility by radicals: cyclic extensions, soluble polynomials have soluble Galois groups and conversely, solving the cubic, quartic, insolubility of the general equation of degree n, n ³ 5.
	www.maths.adelaide.edu.au /pure/courses03/Galois_IV_03.html (124 words)

	Algebraic homotopy, Galois theory and Descent
		Janelidze in 1989 published a new purely categorical approach to Galois theory which again included both covering space theory, and classical Galois theory, and the SGA1 approach of Grothendieck, but also was applicable to classification problems in other parts of algebra and topology.
		As one would expect, mixes of Galois theory and descent are being applied back in algebraic geometric settings with results on ringed topoi, whilst work by Brown continues to look at essential obstructions to extending local to global information measurable by monodromy groupoids generalising the fundamental group.
		The corresponding Galois theory and resulting algebraic homotopy is being studied at Bangor, not only for the potential application within equivariant homotopy and the theory of orbifolds, but also as a test bed for methods relating to Grothendieck's programme.
	www.informatics.bangor.ac.uk /public/mathematics/research/cathom/intas99.html (1107 words)

	Galois' commentators
		For instance, Kronecker was first to describe the Galois group not in terms of permutations on the roots of an equation, but as a group of automorphisms of the coefficient field with adjoined quantities.
		Weber presented Galois Theory in terms of group theory and field theory, making very few references to equations, so that the theory could also be applied to other areas than the solvability of equations.
		Today's formulations (see [6] or [7]) of the Fundamental Theorem of Galois Theory are equivalent to Artin's; their aim is to reveal the parallel structure of the extension field and its automorphism group.
	www-groups.dcs.st-and.ac.uk /~history/Projects/Brunk/Chapters/Ch3.html (2035 words)

	Galois theory at opensource encyclopedia (Site not responding. Last check: 2007-11-07)
		de:Galoistheorie fr:Théorie de Galois Galois theory is that branch of abstract algebra which studies the symmetries of the roots of polynomials.
		The Galois group of L over K is S, by a basic result of Artin.
		This is called the inverse Galois problem, and is usually posed for extensions of the rational number field Q.
	wiki.tatet.com /Galois_theory.html (1018 words)

	PlanetMath: infinite Galois theory (Site not responding. Last check: 2007-11-07)
		be a Galois extension, not necessarily finite dimensional.
		comes equipped with a natural topology, which plays a key role in the statement of the Galois correspondence.
		This is version 2 of infinite Galois theory, born on 2002-05-18, modified 2002-05-18.
	planetmath.org /encyclopedia/KrullTopology.html (220 words)

	PlanetMath: fundamental theorem of Galois theory (Site not responding. Last check: 2007-11-07)
		be a finite dimensional Galois extension of fields, with Galois group
		"fundamental theorem of Galois theory" is owned by djao.
		This is version 3 of fundamental theorem of Galois theory, born on 2002-01-05, modified 2004-01-19.
	planetmath.org /encyclopedia/FundamentalTheoremOfGaloisTheory.html (152 words)

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