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Topic: Issai Schur

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	Issai Schur - Wikipedia, the free encyclopedia
		Issai Schur (January 10, 1875 in Mogilyov - January 10, 1941 in Tel Aviv) was a mathematician who worked in Germany for most of his life.
		Nevertheless he was dismissed from his chair in 1935 and, at the instigation of Bieberbach (who had previously sympathised with Schur regarding his treatment at the hands of the Nazis), he was forced to resign from the Prussian Academy in 1938.
		Schur eventually emigrated to Palestine in 1939, and had to endure the humiliation of living out his final years in poverty.
	en.wikipedia.org /wiki/Issai_Schur (245 words)

	Schur (Site not responding. Last check: 2007-09-07)
		Although Issai Schur was born in Mogilyov on the Dnieper, he spoke German without a trace of an accent, and nobody even guessed that it was not his first language.
		Schur returned to work on representation theory with renewed vigour and he was able to complete the programme of research begun in his doctoral dissertation and give a complete description of the rational representations of the general linear group.
		Schur had held an appointment before World War I which should have qualified him as a civil servant, but the facts were not allowed to get in the way, and he was 'retired'.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Schur.html (1639 words)

	issai schur (Site not responding. Last check: 2007-09-07)
		As a student of Frobenius, he worked on group representations but also in number theory and even theoretical physics.
		An ancillary result was the existence of the Schur decomposition which nowadays he is best known for.
		See also: Schur's lemma, Schur indicator, Schur index, Schur complement.
	www.yourencyclopedia.net /issai_schur.html (214 words)

	Encyclopedia: Schur multiplier
		In group theory, the Schur multiplier is the second homology group of a group G with coefficients in the integers,
		Schur multipliers are of especial interest when G is a perfect group, meaning a group equal to its own commutator subgroup.
		The Schur multiplier is due to Issai Schur, and can be said to represent the beginning of group cohomology.
	www.nationmaster.com /encyclopedia/Schur-multiplier (233 words)

	Schur (Site not responding. Last check: 2007-09-07)
		Schur was also interested in reducibility, location of roots and the construction of the Galois group of classes of polynomials such as Laguerre and Hermite polynomials.
		In 1922 Schur was elected to the Prussian Academy, proposed by Planck, the secretary of the Academy.
		Schur should not have been caught by this clause but the facts were not allowed to get in the way, and he was 'retired'.
	www.bg-rams.ac.at /intranet/Physik/history/Schur.html (1689 words)

	Schur multiplier - tScholars.com (Site not responding. Last check: 2007-09-07)
		In mathematics, more specifically in group theory, the Schur multiplier (sometimes multiplicator), named after Issai Schur, is the second homology group of a group G with coefficients in the integers,
		Schur multipliers are of especial interest when G is a perfect group (a group equal to its own commutator subgroup).
		The Schur multiplier is due to Issai Schur, and can be said to represent the beginning of group cohomology (or at least of the higher groups H
	www.tscholars.com /encyclopedia/Schur_multiplier (279 words)

	References for Schur (Site not responding. Last check: 2007-09-07)
		A Brauer and H Rohrbach (eds.), I Schur, Gesammelte Abhandlungen (Berlin, 1973).
		A Brauer, Gedenkrede auf Issai Schur, in A Brauer and H Rohrbach (eds.), I Schur, Gesammelte Abhandlungen (Berlin, 1973), v-xiii.
		M M Schiffer, Issai Schur : Some personal reminiscences, in H Begehr (ed.), Mathematik in Berlin : Geschichte und Dokumentation (Aachen, 1998).
	www-groups.dcs.st-and.ac.uk /history/References/Schur.html (135 words)

	Schur complement - Wikipedia, the free encyclopedia
		In linear algebra and the theory of matrices, the Schur complement (named after Issai Schur) of a block of a matrix within the larger matrix is defined as follows.
		The Schur complement arises as the result of performing a "partial" Gaussian elimination by multiplying the matrix M from the right with the "lower triangular" block matrix
		If M is a positive definite symmetric matrix, then so is the Schur complement of D in M.
	en.wikipedia.org /wiki/Schur_complement (236 words)

	Search Results for Schur
		Schur had solved the problem for the case n = 1, where the matrices are over a prime field, and the case of n = 2 had been solved in the 1930s.
		Schur held weekly problem hours, and in these sessions he would give the students difficult problems most of which Frobenius or Schur himself had solved, but occasionally he gave the class an open problem which he did not know how to solve.
		Schur gave him the topic for his dissertation On the various ways of expressing an orthogonal matrix in terms of parameters and conducted his oral examination in November 1933.
	www-history.mcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=Schur&CONTEXT=1 (3591 words)

	Schur Family Crest
		The surname Schur is a habitation name which forms a broad category of surnames that were derived from pre-existing names for towns, villages, parishes, or farmsteads.
		In continental Europe, the most ancient recorded family crest was discovered upon the monumental effigy of a Count of Wasserburg in the church of St. Emeran, at Ratisobon, Germany...
		In the Schur coat of arms as in all coat of arms the crest is only one element of the full armorial achievement.
	www.houseofnames.com /xq/asp.fc/qx/schur-family-crest.htm (581 words)

	Schur
		There were unaware at that time that the second cohomology group with coefficients in the nonzero complex numbers is the Schur multiplier, and therefore that Schur had made some of the first steps forty years earlier.
		In 1922 Schur was elected to the Prussian Academy, proposed by
		Pressure was put on Schur to resign from the Prussian Academy to which he had been honoured to be elected in 1922.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Schur.htm (1539 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		Subject: Studies in Memory of Issai Schur Date: Friday, December 06, 2002 9:48 AM Joseph A.; Melnikov A.; Rentschler R. (Eds.): Studies in Memory of Issai Schur 2003 Approx.
		Many techniques are inspired by the great works of Issai Schur who passed away some 60 years ago.
		This is a unified presentation consisting of an extended biography of Schur---written in collaboration with some of his former students---as well as survey articles on Schur's legacy (Schur theory, functions, etc).
	www.scicomp.uni-erlangen.de /letter/v03n04/b3 (163 words)

	Schur's lemma - Encyclopedia Glossary Meaning Explanation Schur's lemma (Site not responding. Last check: 2007-09-07)
		Schur's lemma - Encyclopedia Glossary Meaning Explanation Schur's lemma.
		In mathematics, Schur's lemma is now a generic term applied to theorems on the commutant of a module M that is simple.
		The original case may have been for linear representations of a finite group G over the complex number field C.
	www.encyclopedia-glossary.com /en/Schurs-lemma.html (263 words)

	Richard Dagobert Brauer, February 10, 1901—April 17, 1977 \| By J. A. Green \| Biographical Memoirs
		Schur had been a pupil of G. Frobenius, and had graduated at Berlin in 1901; he had been "ordentlicher Professor" (full professor) there since 1919.
		In [4], he and Emmy Noether characterized Schur's "splitting fields" of a given irreducible representation * of a given finite dimensional algebra, in terms of the division algebra associated to *.
		Schur suggested, in lectures at Berlin, an "arithmetic" approach: a given rational prime p generates, in the integral group ring of ZG of a given finite group G, an ideal whose prime divisors, in a suitable order containing ZG, correspond to the types of irreducible representations of G over a field of characteristic p.
	www.nap.edu /readingroom/books/biomems/rbrauer.html (5666 words)

	Issai Schur (Site not responding. Last check: 2007-09-07)
		Issai Schur (January 10, 1875 in Mogilyov - January10, 1941 in Tel Aviv) was a mathematician who worked in Germany for most of his life.
		As a student of Frobenius, he worked on group representations but also in numbertheory and even theoretical physics.
		An ancillary resultwas the existence of the Schur decomposition which nowadayshe is best known for.
	www.therfcc.org /issai-schur-239453.html (162 words)

	Zhang,
		This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility.
		The eight chapters of the book cover themes and variations on the Schur complement, including its historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis.
		Preface.- Historical Introduction: Issai Schur and the Early Development of the Schur Complement.- Basic Properties of the Schur Complement.- Eigenvalue and Singular Value Inequalities of Schur Complements.- Block Matrix Techniques.- Closure Properties.- Schur Complements and Matrix Inequalities: Operator-Theoretic Approach.- Schur Complements in Statistics and Probability.- Schur Complements and Applications in Numerical Analysis.- Bibliography.- Notation.- Index.
	www.yurinsha.com /383/p9.htm (784 words)

	Schur decomposition -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-07)
		In the mathematical discipline of (The part of algebra that deals with the theory of linear equations and linear transformation) linear algebra, the Schur decomposition or Schur triangulation (named after (additional info and facts about Issai Schur) Issai Schur) is an important (additional info and facts about matrix decomposition) matrix decomposition.
		If A is a square matrix over the (A number of the form a+bi where a and b are real numbers and i is the square root of -1) complex numbers, then A can be decomposed as
		Furthermore, if A is (additional info and facts about positive definite) positive definite, the Schur decomposition of A is the same as the (additional info and facts about singular value decomposition) singular value decomposition of the matrix.
	www.absoluteastronomy.com /encyclopedia/S/Sc/Schur_decomposition.htm (190 words)

	What is Issai Schur? : Abaara fun facts and uncommon knowledge (Site not responding. Last check: 2007-09-07)
		Issai Schur (January 10, 1875 in Mogilyov - January 10, 1941 in Tel Aviv) was a
		Schur decomposition which nowadays he is best known for.
		Schur multiplier, Schur indicator, Schur index, Schur complement,
	www.abaara.com /pac/Issai_Schur (172 words)

	Issai Schur - Encyclopedia, History, Geography and Biography
		Issai Schur - Encyclopedia, History, Geography and Biography
		As a student of Ferdinand Georg Frobenius, he worked on group representations but also in combinatorics and even theoretical physics.
		This page was last modified 00:14, 27 May 2005.
	www.arikah.net /encyclopedia/Issai_Schur (222 words)

	schur.html (Site not responding. Last check: 2007-09-07)
		Issai Schur proved the first Ramsey Theorem (way before Ramsey).
		He proved that if you color the integers from 1 to n by r-colors, you are GUARANTEED (if n is not too small) a monochromatic triple {x,y,x+y}.
		If the number of colors is 2, Ron Graham, in SOCA 96' (Tianjin, June 1996), offered 100 dollars for the asymptotic minimal number of these Schur triples.
	www.math.rutgers.edu /~zeilberg/mamarim/mamarimhtml/schur.html (176 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		Main notions Abstract: The concept of a Schur ring goes back to a seminal paper by Issai Schur (1933), where Schur proved that a cyclic group of a composite order is a B-group (B stands for Burnside).
		In other words it was proved that each primitive overgroup of a regular cyclic group Z_n of a composite order n in the symmetric group of degree n is a doubly transitive permutation group.
		The name "Schur ring" (briefly S-ring) was coined by followers of Schur, in particular by H.Wielandt.
	www.math.technion.ac.il /~techm/20001213191020001213kli (244 words)

	Citations: Uber die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionen ... (Site not responding. Last check: 2007-09-07)
		Any representation of one may be made into a representation of the other by multiplying by i all the matrices corresponding to elements not in the subgroup of index two.
		Since that time S functions and P functions have appeared in a number of topics: functions of the KP and BKP hierarchies of soliton equations [13, 40] irreducible characters of the Lie algebras gl n and the Lie superalgebras Q(n) 35] cohomology of grassmannians and isotropic grassmannians....
		Schur, I. Uber die Darstellung der symmetrischen und der alternierenden Gruppen durch gebrochene lineare substitutionen.
	citeseer.ist.psu.edu /context/496945/0 (2570 words)

	Mark Wilson's Home Page - Science/Thesis (Site not responding. Last check: 2007-09-07)
		SCHUR provided a computational environment where the entities being manipulated were partitions.
		I spent a reasonably happy year puttering around within SCHUR adding a number of features (like that damn plethysm operator, which I recall as being horribly complex).
		SCHUR was (and is still?) a tool for theoretical Physicists in the same way that I imagine MatLab or Mathematica are.
	www.geocities.com /SiliconValley/Park/9541/science/thesis.html (241 words)

	Schur's theorem - Encyclopedia, History, Geography and Biography
		In mathematics, Schur's theorem is either of two different theorems of the mathematician Issai Schur.
		In Ramsey theory, Schur's theorem states that for any partition of the positive integers into a finite number of parts, one of the parts contains three integers x, y, z with
		Moreover, for every positive integer c, there exists a number S(c), called Schur's number, such that for every partition of the integers
	www.arikah.net /encyclopedia/Schur%27s_theorem (128 words)

	Issai Schur -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-07)
		Issai Schur -- Facts, Info, and Encyclopedia article
		An ancillary result was the existence of the (additional info and facts about Schur decomposition) Schur decomposition which nowadays he is best known for.
		See also: (additional info and facts about Schur's lemma) Schur's lemma, (additional info and facts about Schur multiplier) Schur multiplier, Schur indicator, Schur index, (additional info and facts about Schur complement) Schur complement, (additional info and facts about Schur's theorem) Schur's theorem.
	www.absoluteastronomy.com /encyclopedia/I/Is/Issai_Schur.htm (224 words)

	Read about Schur's theorem at WorldVillage Encyclopedia. Research Schur's theorem and learn about Schur's theorem here! (Site not responding. Last check: 2007-09-07)
		In mathematics, Schur's theorem is either of two different theorems of the mathematician
		In Ramsey theory, Schur's theorem states that for any
		Schur's number, such that for every partition of the integers
	encyclopedia.worldvillage.com /s/b/Schur%27s_theorem (121 words)

	Read This: Pioneers of Representation Theory
		Its goal is to acquaint the reader with the history of the theory of representations of finite groups through a detailed analysis of the major papers of the founders of the discipline (Frobenius, Burnside, Schur, and Brauer) and other mathematicians.
		His treatment of Schur is more leisurely and detailed, but it is still not an easy road to travel.
		Most textbooks contain the archeological remains of this process of development (with names like "Schur's Lemma" and "Maschke's Theorem" adorning their major results) and, sandwiched in between the latest and greatest proofs, some authors will note the existence of this development in brief casual asides.
	www.maa.org /reviews/pioneers.html (1223 words)

	Arizona by Ann Heinrichs, ISBN 0756503337 And Studies in Memory of Issai Schur by Anthony Joseph, ISBN 0817642080
		Arizona by Ann Heinrichs, ISBN 0756503337 And Studies in Memory of Issai Schur by Anthony Joseph, ISBN 0817642080
		This unified presentation consists of an extended biography of Issai Schur, written in collaboration with some of his former students, as well as survey articles on Schur's legacy.
		Additionally, there are 25 articles covering the areas of orbits, crystals and representation theory, with special emphasis on canonical bases and their crystal limits, and on the geometric approach linking orbits to representations and Hecke algebra techniques.
	www.alpharetta-rv-rentals.com /arizona.htm (156 words)

	Studies in Memory of Issai Schur -- Books (Site not responding. Last check: 2007-09-07)
		This volume is dedicated to the memory of Issai Schur.
		Finally, leading mathematicians in the representation theory of the symmetric groups, of semisimple and affine Lie algebras and of Chevalley groups have contributed original and outstanding articles.
		These concern many areas inspired by Schur's work as well as more recent developments involving crystal and canonical bases, Hecke algebras, and the geometric approach linking orbits to representations.
	cadgate.com /book/un/817642080 (294 words)

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