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Topic: Karl Weierstrass

	Weierstrass biography
		Weierstrass had made a decision to become a mathematician but he was still supposed to be on a course studying public finance and administration.
		Weierstrass attended Gudermann's lectures on elliptic functions, some of the first lectures on this topic to be given, and Gudermann strongly encouraged Weierstrass in his mathematical studies.
		The concepts on which Weierstrass based his theory of functions of a complex variable in later years after 1857 are found explicitly in his unpublished works written in Münster from 1841 through 1842, while still under the influence of Gudermann.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Weierstrass.html (2615 words)

	Karl Weierstrass - Wikipedia, the free encyclopedia
		Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the "father of modern analysis".
		Karl Weierstrass was born in Ostenfelde, Westphalia (today Germany).
		After that he studied mathematics at the University of Münster which was even to this time very famous for mathematics and his father was able to obtain a place for him in a teacher training school in Münster, and he later was certified as a teacher in that city.
	en.wikipedia.org /wiki/Karl_Weierstrass (439 words)

	[No title]
		This was because of a conflict with the mathematician and philosopher Leopold Kronecker.
		Weierstrass even considered the possibility of leaving Berlin for Switzerland to avoid the continuing conflict; but, since he did not wish his successor at the university to be chosen by Kronecker, he decided to stay.
		Weierstrass himself was no longer able to supervise the whole process so his students undertook the task of gathering and polishing up his lectures based on their own notes or transcripts.
	math.nist.gov /opsf/personal/weierstrass.html (3054 words)

	PlanetMath: Weierstrass function
		The Weierstrass function is a continuous function that is nowhere differentiable, and hence is not an analytic function.
		The function is named after Karl Weierstrass who presented it in a lecture for the Berlin Academy in 1872 [1].
		This is version 15 of Weierstrass function, born on 2002-01-03, modified 2005-02-28.
	planetmath.org /encyclopedia/WeierstrassFunction.html (222 words)

	BookRags: Karl Theodor Wilhelm Weierstrass Biography
		Karl Wilhelm Theodor Weierstrass was considered one of the greatest mathematical analysts of 19th century Europe.
		Weierstrass was directed by his father to attend the University of Bonn, where it was expected he would acquire an education in business and law.
		Weierstrass demonstrated that the integral of an infinite series is equal to the sum of the integrals of the separate terms when the series converges uniformly within a given region.
	www.bookrags.com /biography/karl-theodor-wilhelm-weierstrass-wom (1422 words)

	Karl Theodor Wilhelm Weierstrass
		Karl Weierstrass's father became a tax inspector when Karl was eight years old.
		Weierstrass was torn between the subject he loved and the subject his father wanted for him, and he spent 4 years of intensive fencing and drinking.
		Weierstrass published a full version of his theory of inversion of hyperelliptic integrals in his next paper in 1856.
	www.stetson.edu /~efriedma/periodictable/html/W.html (835 words)

	Karl Weierstrass
		Karl Theodor Wilhelm Weierstraß was born on October 31, 1815, in the village of Ostenfelde, which was located in what was then the Prussian province of Westphalia.
		For the first 14 years of Karl Weierstraß' life, his family was more or less constantly on the move.
		In 1829, Karl's father obtained an assistant's position at the tax office in the city of Paderborn (also in Westphalia), and the family could finally settle down.
	www.ualberta.ca /dept/math/gauss/fcm/History_People/Weierstrass_Karl/Weierstrass_byRunde.html (1990 words)

	10.11. Weierstrass, Karl (1815-1897)
		Karl Weierstrass was one of the leaders in rigor in analysis and was known as the "father of modern analysis." In addition, he is considered one of the greatest mathematics teachers of all-time.
		Karl Wilhelm Theodor Weierstrass was born October 31, 1815, in Ostenfelde, Westphalia, Germany.
		Karl was on the receiving end of lectures well past the age of forty.
	web01.shu.edu /projects/reals/history/weierstr.html (1271 words)

	Highbeam Encyclopedia - Search Results for Weierstrass,
		Weierstrass, Karl Wilhelm Theodor WEIERSTRASS, KARL WILHELM THEODOR [Weierstrass, Karl Wilhelm Theodor], 1815-97, German mathematician.
		He studied under Karl Weierstrass and taught (1869-1913) at the Univ. of Halle.
		She studied at the universities of Heidelberg and Berlin (under K. Weierstrass) and in 1874 received a Ph.D. in absentia from the Univ. of Göttingen for her remarkable thesis on partial differential equations.
	www.encyclopedia.com /SearchResults.aspx?Q=Weierstrass, (414 words)

	Weierstrass, Karl Wilhelm Theodor (1815-1897)
		In 1854 he published a paper, written 14 years earlier when he was fresh our of college, in Crelle's Journal, on Abelian functions which completed work that Niels Abel and Karl Jacobi had begun.
		Its importance was immediately recognized and Weierstrass was appointed a professor at the Royal Polytechnic School and a lecturer at the University of Berlin.
		He went on to give the first rigorous definitions of limit, derivative, differentiability, and convergence, and investigated under what conditions a power series will converge.
	www.daviddarling.info /encyclopedia/W/Weierstrass.html (203 words)

	Karl Weierstrass (Site not responding. Last check: 2007-09-17)
		Weierstrass was the oldest son of a minor customs official, and his childhood is not particularly unusual.
		When Sonja Kovalevskaia came to Germany from Russia to study mathematics, she was not allowed to attend classes at the university because she was a woman, so Weierstrass privately tutored her for several years.
		Weierstrass' work had a great influence on 19th and 20th century mathematics, and several of his results are now a standard part of a typical calculus course, for example, the Weierstrass M-test for series and his example of a continuous but nowhere differentiable function.
	scidiv.bcc.ctc.edu /Math/Weierstrass.html (515 words)

	About WIAS - About Karl Weierstrass
		Bölling, R.: Briefwechsel zwischen Karl Weierstraß und Sofja Kowalewskaja.
		Many of them had studied in Berlin or, after having finished their studies, came to Berlin to attend lectures by Weierstrass or his colleagues Ernst Kummer and Leopold Kronecker at the Friedrich Wilhelm University.
		Therefore, a hither to unknown, or perhaps forgotten, portrait of Karl Weierstrass [to the right], which I recently discovered, may well be of interest.
	www.wias-berlin.de /main/about/weierstrass/index.html.en (768 words)

	Lindemann–Weierstrass theorem - Wikipedia, the free encyclopedia
		The theorem is named for Ferdinand von Lindemann and Karl Weierstrass.
		Weierstrass proved the above more general statement in 1885.
		The theorem, along with the Gelfond-Schneider theorem, is generalized by Schanuel's conjecture.
	en.wikipedia.org /wiki/Lindemann-Weierstrass_theorem (371 words)

	Wiestrass and Kovalevski (Site not responding. Last check: 2007-09-17)
		Karl Weierstrass is known as the father of modern analysis.
		Karl Weierstrass was born in Ostenfield, Bavaria, (which is now Germany) on October 31st, 1815 and he died in Berlin, Germany on February 19th, 1897.
		Weierstrass was very interested in the theory of functions, his interest was fueled by the desire to complete the works of Niels Abel, and Karl Jacobi.
	www.andrews.edu /~calkins/math/biograph/bioweier.htm (1247 words)

	NDSU Department of Mathematics: Who was Sonia Kovalevsky?
		Weierstrass was soon impressed by her ability and claimed that she had "the gift of intuitive genius" to a degree he seldom found among his advanced students.
		This was the first time that a woman had applied for a higher degree in mathematics, so Weierstrass requested that the university be particularly careful to uphold high standards in judging her.
		Although Weierstrass' letters kept her in touch with recent mathematical advances, she was on the verge of abandoning mathematics.
	math.ndsu.nodak.edu /sonia/sonia.shtml (581 words)

	19th century - Wikipedia, the free encyclopedia
		Italian naturalist novels are especially important in that they give a social map of the new unified Italy to a people that until then had been scarcely aware of its ethnic and cultural diversity.
		On February 21, 1848, Karl Marx and Friedrich Engels published the Communist Manifesto.
		Karl Weierstrass and other mathematicians also carried out the arithmetization of analysis.
	en.wikipedia.org /wiki/19th_century (2038 words)

	The Hindu : Karl Weierstrass (1790-1869): Father of mathematical analysis
		KARL WEIERSTRASS was born on October 31, 1815, at Ostenfelde, Germany.
		Weierstrass thoroughly enjoyed his school and completed the course in less than the prescribed time, leaving a brilliant academic record.
		Weierstrass matriculated (May 1839) at the Academy of Muenster and obtained his teacher's certificate in 1841, which equipped him for a career as secondary school teacher.
	www.hinduonnet.com /thehindu/2000/08/10/stories/08100006.htm (991 words)

	Karl Weierstrass - Scientists - German Archive: Karl Theodor Wilhelm Weierstrass (Weierstra?) (October 31, 1815 û ...
		Karl Weierstrass - Scientists - German Archive: Karl Theodor Wilhelm Weierstrass (Weierstra?) (October 31, 1815 û February 19, 1897) was a German mathematician who is often cited as the 'father of modern analysis'.
		Karl Theodor Wilhelm Weierstrass (Weierstra?) (October 31, 1815 û February 19, 1897) was a German mathematician who is often cited as the 'father of modern analysis'.
		Weierstrass also formulated the definition of limit and derivative still in use today.
	www.germannotes.com /archive/article.php?products_id=239&osCsid=3ff1d3d9fd0157586079ece6e2045eea (425 words)

	untitled (Site not responding. Last check: 2007-09-17)
		It is essentially a merit of the scientific activity of Weierstrass that there exists at present in analysis full agreement and certainty concerning the course of such types of reasoning which are based on the concept or irrational number and of limit in general.
		Weierstrass says that we can find a larger enough number of rectangles that their sum will be within one thousandth of a square inch of 25 square inches.
		Weierstrass' definition of the irrational numbers was important because it shifted the emphasis from an infinite series to a set where an irrational number could be defined to any degree of precision, with only a finite number of members of the set.
	www.angelfire.com /super/magicrobin/peirce.htm (7996 words)

	Weierstrass, Karl (Theodor Wilhelm)
		In 1841 Weierstrass obtained his teacher's certificate and began a 14-year career as a teacher of mathematics at the Pro-Gymnasium in Deutsche Krone (1842-48) and at the Collegium Hoseanum in Braunsberg (1848-56).
		Weierstrass' work on the theory of functions was guided by his desire to complete the work begun by Niels Abel of Norway and Karl Jacobi of Germany, primarily Abel's theorem that the number of independent integrals of algebraic functions is finite and Jacobi's discovery of multiple periodic functions of many variables.
		Weierstrass contributed few papers to scholarly journals; his work was embodied in his lectures, which were collected in Gesammelte Abhandlungen, 8 vol.
	www.phy.bg.ac.yu /web_projects/giants/weiers~1.htm (484 words)

	Weierstrass, Karl Wilhelm Theodor - HighBeam Encyclopedia (Site not responding. Last check: 2007-09-17)
		WEIERSTRASS, KARL WILHELM THEODOR [Weierstrass, Karl Wilhelm Theodor], 1815-97, German mathematician.
		He demonstrated (1871) a function that is continuous throughout an interval but that possesses no derivative anywhere in the interval.
		Find newspaper and magazine articles plus images and maps related to "Weierstrass, Karl Wilhelm Theodor" at HighBeam.
	www.encyclopedia.com /html/w/weierstr.asp (164 words)

	Weierstrass Karl Theodor Wilhelm - Search Results - MSN Encarta (Site not responding. Last check: 2007-09-17)
		Weierstrass Karl Theodor Wilhelm - Search Results - MSN Encarta
		Weierstrass, Karl Theodor Wilhelm (1815-1897), German mathematician, who helped to found the modern theory of functions.
		Jaspers, Karl (1883-1969), German philosopher, one of the originators of existentialism, whose work, which comprised 30 books, influenced modern...
	uk.encarta.msn.com /Weierstrass_Karl_Theodor_Wilhelm.html (115 words)

	MS.350
		Karl Theodor Wilhelm Weierstrass was born in Osterfelde, Westphalia
		Karl Theodor Wilhelm Weierstrass died in Berlin February 19, 1897.
		Bierman, Kurt-R., "Weierstrass, Karl Theodor Wilhelm," in: Charles
	www.library.jhu.edu /collections/specialcollections/manuscripts/msregisters/ms350.html (440 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		Weierstrass' paper with his proof of the Weierstrass Theorem on density on algebraic polynomials in the space of continuous real-valued functions on any finite closed interval.
		Weierstrass, K., Sur la possibilité d'une représentation analytique des fonctions dites arbitraires d'une variable réelle, J.
		This is the translation of the Weierstrass 1885 paper and, as the original, it appeared in two parts and in subsequent issues, but under the same title.
	www.math.technion.ac.il /hat/wei.html (189 words)

	[No title]
		Weierstrass also has a function named after him: the Weierstrass elliptic function, which I explained in "week13".
		Weierstrass asked for a question on elliptic functions, and wound up writing a paper which Gudermann assessed "...
		For example, Weierstrass invented uniform convergence and proved that the limit of a uniformly convergent series of continuous functions is continuous.
	math.ucr.edu /home/baez/twf_ascii/week166 (2346 words)

	KOVALEVSKY, S.(1850-1891) and NOETHER, A.E.(1882-1935)
		Konigsberger had earlier studied under Karl Weierstrass of the University of Berlin, and his enthusiastic reports of his mentor instilled in Kovalevsky a desire to study under the great teacher.
		She accordingly approached Weierstrass directly, who, upon receiving a strong recommendation from Konigsberger, accepted her as a private student.
		Kovalevsky soon became Weierstrass' favorite pupil, and he repeated his university lectures to her.
	library.thinkquest.org /22584/temh3005.htm (826 words)

	Earliest Known Uses of Some of the Words of Mathematics (A)
		Abelian function appears in the title "Zur Theorie der Abelschen Functionen" by Karl Weierstrass (1815-1897) in Crelle's Journal, 47 (1854) reprinted in Werke I, p.
		Weierstrass' first publications on Abelian functions appeared in the Braunsberg school prospectus (1848-1849) reprinted in Werke I, p.
		Weierstrass later exploited this idea in his theory of functions of a complex variable, retaining Lagrange’s term "analytic function" to designate, for Weierstrass, a function of a complex variable with a convergent Taylor series." (pp.
	hometown.aol.com /jeff570/a.html (7427 words)

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