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Topic: Ferdinand Georg Frobenius

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	Ferdinand Georg Frobenius - Slider
		Ferdinand Georg Frobenius (October 26, 1849 – August 3, 1917) was a German mathematician, best-known for his contributions to the theory of differential equations and to group theory.
		Frobenius was born in Charlottenburg, a suburb of Berlin, and was educated at the University of Berlin.
		Group theory was one of Frobenius' principal interests in the second half of his career.
	enc.slider.com /Enc/F._G._Frobenius (204 words)

	Frobenius biography
		Georg was born in Charlottenburg which was a district of Berlin which was not incorporated into the city until 1920.
		Frobenius was only in Berlin for a year before he went to Zürich to take up an appointment as an ordinary professor at the Eidgenössische Polytechnikum.
		Frobenius collaborated with Schur in representation theory of groups and character theory of groups.
	www-history.mcs.st-and.ac.uk /history/Biographies/Frobenius.html (2015 words)

	Ferdinand Georg Frobenius Biography \| World of Mathematics
		German mathematician Ferdinand Georg Frobenius was a number theorist who made critical contributions to the study of group theory.
		Frobenius only remained in the position for a year when he decided to relocate to Zürich, Switzerland to teach mathematics at the Eidgenössische Polytechnikum (Federal Polytechnic) there.
		Frobenius remained in Zürich until 1892, when he returned home to Berlin to resume his position at the University as mathematics professor.
	www.bookrags.com /biography/ferdinand-georg-frobenius-wom (270 words)

	file_nav_name Encyclopedia Index (Site not responding. Last check: 2007-10-10)
		The Landgraviate of Hesse-Darmstadt came into existence in 1568, as the portion of George, youngest of the four sons of L...
		Ferdinand von Arnim (15 September 1814 in Treptow an der Rega near Berlin â“ 23 March 1866 in Berlin) was an a...
		Georg Ludwig Hartig (September 2, 1764 - February 2, 1837), German agriculturist and writer on forestry, was bo...
	www.brainyencyclopedia.com /topics/ludwig.html (2320 words)

	test (Site not responding. Last check: 2007-10-10)
		Ferdinand Georg Frobenius was born to a Protestant minister in Berlin.
		Frobenius then began to teach secondary students at his old school Joachimsthal Gymnasium (Gymnasium is the name for a Grammar School), before being offered an appointment as extraordinary professor in mathematics at his old University.
		Frobenius was of the old school of thought (a traditionalist) in terms of the study of “pure” mathematics.
	www.mathsyear2000.org /timeline/test-mathinfo.php?m=ferdinand-georg-frobenius (668 words)

	Frobenius
		Siegel, who knew Frobenius for two years from 1915 when he became a student until Frobenius's death, relates his impression of Frobenius as having a warm personality and expresses his appreciation of his fast-paced varied and deep lectures.
		Fuchs when Frobenius was elected to the Prussian Academy of Science in 1892.
		Dedekind in 1885 made an important contribution and Frobenius was able to construct a complete set of representations by complex numbers.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Frobenius.htm (1873 words)

	Georg Frobenius (Site not responding. Last check: 2007-10-10)
		Frobenius became assistant professor of mathematics at the University of Berlin in 1874 and in 1875 was appointed professor of mathematics at the Federal Polytechnic, Zürich.
		Frobenius' findings in abstract group theory were published in the paper "Über Gruppen von vertauschbaren Elementen" (1879; "Concerning Groups of Permutable Elements"), in collaboration with Ludwig Stickelberger.
		In collaboration with Issai Schur, he developed group theory by means of the theory of finite groups of linear substitutions.
	thales.cica.es /rd/Recursos/rd99/ed99-0289-02/biografias/gfrobenius.html (157 words)

	Sketching the History of Hypercomplex Numbers (Site not responding. Last check: 2007-10-10)
		George Peacock's (1791-1858) Report on the recent progress and present state of certain branches of analysis, stating for the first time the idea that algebras should be constructed axiomatically and without reference to their intended interpretation.
		George Boole (1815-1864) publishes The Mathematical Analysis of Logic, espousing a view of mathematics as a science of consistent symbolism, as opposed to numbers or magnitudes.
		Ferdinand Georg Frobenius shows, using algebraic topology, that quaternions are algebras which satisfy all properties of arithmetic save the commutative law of multiplication.
	history.hyperjeff.net /hypercomplex.html (1939 words)

	Ferdinand Georg Frobenius (Site not responding. Last check: 2007-10-10)
		Georg Frobenius briefly attended the University of Göttingen, but he only studied there for one semester before returning to the city of his birth, Berlin.
		Then, in 1874 he was appointed to the University of Berlin as an extraordinary professor of mathematics, and in 1875 he became an ordinary professor at the Eidgen&oouml;ssische Polytechnikum.
		In his work in group theory, Frobenius combined results from the theory of algebraic equations, geometry, and number theory, which led him to the study of abstract groups.
	www.stetson.edu /~efriedma/periodictable/html/Fr.html (551 words)

	Ferdinand Georg Frobenius Biography \| scit_05123_package.xml
		In particular, his paper on group characters was of fundamental importance to this field.
		In 1897, learning of work on matrices by Molien, Frobenius successfully reformulated much of his own work.
		Ferdinand Georg Frobenius from Science and Its Times.
	www.bookrags.com /biography/ferdinand-georg-frobenius-scit-05123 (106 words)

	Burnside's lemma - Wikipedia, the free encyclopedia
		Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy-Frobenius lemma or the orbit-counting theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects.
		Its various eponyms include William Burnside, George Pólya, Augustin Louis Cauchy, and Ferdinand Georg Frobenius.
		William Burnside stated and proved this lemma (without attribution) in his 1897 about this formula, but mathematical historians have pointed out that he was not the first to discover it; Cauchy in 1845 and Frobenius in 1887 also knew of this formula.
	en.wikipedia.org /wiki/Cauchy-Frobenius_lemma (452 words)

	Earliest Known Uses of Some of the Words of Mathematics (S) (Site not responding. Last check: 2007-10-10)
		Sequence is found in 1891 in a translation by George Lambert Cathcart of the German An introduction to the study of the elements of the differential and integral calculus by Axel Harnack: "What conditions must be fulfilled in order that for continually diminishing values of &Deltax, the quotient...
		Georg Cantor (1845-1918) did not define the concept of a set in his early works on set theory, according to Walter Purkert in Cantor's Philosophical Views.
		SIMILAR (applied to a matrix) was introduced by Frobenius (as "ähnlich") in "Ueber lineare Substitutionen und bilineare Formen," J.
	hometown.aol.com /jeff570/s.html (13183 words)

	Matches for: (Site not responding. Last check: 2007-10-10)
		The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927).
		In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory.
		Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject.
	www.mathaware.org /bookstore?fn=20&arg1=hmathseries&item=HMATH-15-S (680 words)

	Frobenius Series Solution of D. E.
		Frobenius Series Solution of D. Method of Frobenius.
		There are some instances when only one Frobenius solution can be constructed.
		or if the roots differ by an integer, then only one Frobenius series solution can be found and other methods such as reduction of order must be used to create the second solution.
	math.fullerton.edu /mathews/n2003/frobeniusdiffeqns/FrobeniusSeriesProof/Links/FrobeniusSeriesProof_lnk_3.html (246 words)

	Frobenius Series Solution of a D. E.
		Caveat: There are some instances when only one Frobenius solution can be constructed.
		Use Frobenius series to solve the D. Solution 2.
		Use Frobenius series to solve the D. A solution is known to be the celebrated
	math.fullerton.edu /mathews/n2003/FrobeniusSeriesMod.html (373 words)

	Ring Theory: Rings, Ideals, Integral Domains, Fields - Numericana
		The latter relation comes from Newton's binomial formula, with the added remark that the binomial coefficient C(p,k) is divisible by p, if p is prime, unless k is 0 or p.
		It is a ring homomorphism, which is called the Frobenius map in honor of Georg Ferdinand Frobenius (1849-1917) who discovered the relevance of such things to algebraic number theory, in 1880.
		A subring is a ring contained in another, endowed with the same operations.
	home.att.net /~numericana/answer/rings.htm (1316 words)

	Earliest Known Uses of Some of the Words of Mathematics (C) (Site not responding. Last check: 2007-10-10)
		Central limit theorem is in the title of George Pólya's "Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem," Mathematische Zeitschrift, 8 (1920), 171-181 [James A. Landau].
		CHARACTER (group character) appears in title of the paper "Uber die Gruppencharactere" by Ferdinand Georg Frobenius (1849-1917), which was presented to the Berlin Academy on July 16, 1896.
		Georg Cantor (1845-1918) in "De la puissance des ensembles parfaits de points," Acta Mathematica IV, March 4, 1884, introduced (in French) the concept and the term "ensemble fermé [Udai Venedem].
	hometown.aol.com /jeff570/c.html (16077 words)

	MY TEACHERS' TEACHERS' TEACHERS'
		Moore (George Edward Moore) [4 Nov 1873-24 Oct 1958] was an English Realist Philosopher, and a leading anti-Idealist.
		Issai Schur's advisors were Georg Frobenius and Lazarus Fuchs.
		Georg Ferdinand Frobenius' advisors were Karl Weierstrass and Ernst Kummer.
	www.magicdragon.com /JVPteachers.html (5091 words)

	03 Aug History: This Date
		During World War II, US General George S. Patton, 57, slaps an Army private hospitalized for battle fatigue, accusing the young man of cowardice.
		Led by two wealthy brothers, Jacob and George Donner, the emigrants initially followed the regular California Trail westward to Fort Bridger, Wyoming.
		Sir Roger David Casement, the Irish-born diplomat who in 1911 was knighted by King George V, was executed for his role in Ireland's Easter Rebellion.
	www.geocities.com /jcanu/history/h4aug/h4aug03.html (7016 words)

	03 Aug History: This Date
		During World War II, US General George S. Patton slaps an Army private hospitalized for battle fatigue, accusing the young man of cowardice.
		The expedition returned to Spain in March of 1493, and Columbus was received with the highest honors by the Spanish court.
		Casement, an Irish Protestant who served as a British diplomat during the early part of the twentieth century, won international acclaim after exposing the illegal practice of slavery in the Congo and parts of South America.
	www.safran-arts.com /42day/history/h4aug/h4aug03.html (7637 words)

	Amazon.com: Frobenius, Burnside, Schur and Bauer: Pioneers of Representation Theory: Books: Charles W. Curtis (Site not responding. Last check: 2007-10-10)
		Frobenius, Burnside, Schur and Bauer: Pioneers of Representation Theory (Hardcover)
		Keep connected to what's happening in the world of books by signing up for Amazon.com Books Delivers, our monthly subscription e-mail newsletters.
		The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849--1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852--1927).
	www.amazon.com /Frobenius-Burnside-Schur-Bauer-Representation/dp/0821890026 (718 words)

	Publisher description for Library of Congress control number 2005019571
		During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised the following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,,an, find the largest natural number (called the Frobenius number and denoted by g(a1,,an) that is not
		formula giving the Frobenius number and algorithms to calculate it.
		The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.
	www.loc.gov /catdir/enhancements/fy0637/2005019571-d.html (179 words)

	The Mathematics Genealogy Project - Georg Frobenius
		Click here to see the students listed in chronological order.
		According to our current on-line database, Georg Frobenius has 17 students and 4213 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.ams.org /html/id.phtml?id=4642 (78 words)

	Markoff numbers (references)
		Conway and R. Guy, The Book of Numbers, pp.
		ISBN 0-387-97993-X. Frobenius, Über die Markoffschen Zahlen, Sitzungsberichte der Königlich Preußischen Akadamie der Wissenschaften zu Berlin, (1913), pp.
		The original journal may be hard to locate; a copy of the paper appears as chapter 96 in Band III of Ferdinand Georg Frobenius Gesammelte Abhandlungen, Springer-Verlag, Berlin, 1968.
	www.minortriad.com /mref.html (294 words)

	Literary Encyclopedia: Contemporaries for Castration Complex
		1893 Meredith, George -- Lord Ormont and his Aminta
		1894 Shaw, George Bernard -- Arms and the Man
		1898 Meredith, George -- Odes in Contribution to the Song of French History
	www.litencyc.com /php/contemporaries.php?rectype=2&uid=1601 (1719 words)

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		Hugh Woodin Adalbold II of Utrecht Jean-Victor Poncelet Carle David TolmÃ© Runge Teiji Takagi Hugh MacColl William Whiston Luther Welsh Igor Shafarevich John Adair (surveyor) William George Penney Delfino Codazzi Hillel Furstenberg Ernst Sigismund Fischer SÃ¡ndor CsÃ¶rgÅ‘ Hypatia of Alexandria Walter A. Shewhart Warren Weaver Peter Donnelly Daniel Schwenter Lyndhurst Giblin M.
		Redfield George Jerrard John Coates Allan Joseph Champneys Cunningham Warren Mitofsky Ahmad bin Musa David H. Bailey Francesco Brioschi Henry Richmond Droop Piotr SmoleÅski Yves Marie AndrÃ© Johann Matthias Hase J.
		Seshadri Howard Percy Robertson Aleyamma George Graham Priest StanisÅaw JaÅkowski StanisÅaw Åojasiewicz Luis Caffarelli Rolf Nevanlinna Theodor Vahlen Walter Bodmer A.
	www.math.ucla.edu /~aoleg/wp/mathlists/output.txt (1511 words)

	Food For Thought: Biographies F
		Falkenhayn, Erich Georg Anton Sebastian von (Prussian general)
		Fugger, Anton (German financier, merchant; son of Georg)
		Fugger, Georg (German financier, merchant; son of Jakob)
	www.junkfoodforthought.com /bio/bio_F.htm (686 words)

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