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Encyclopedia > Karl Weierstraß

Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815February 19, 1897) was a German mathematician who is often cited as the "father of modern analysis". He was born in Ostenfelde, Westphalia (today Germany) and died in Berlin, Germany. October 31 is the 304th day of the year (305th in leap years) in the Gregorian Calendar, with 61 days remaining, as the final day of October. ... 1815 was a common year starting on Sunday (see link for calendar). ... February 19 is the 50th day of the year in the Gregorian Calendar. ... 1897 was a common year starting on Friday (see link for calendar). ... Mathematics, often abbreviated maths in Commonwealth English and math in American English, is the study of abstraction. ... Westphalia (in German, Westfalen) is a (historic) region in Germany, centred on the cities of Dortmund, Münster, Bielefeld, and Osnabrück and now included in the Bundesland of North Rhine-Westphalia (and the (south-)west of Lower Saxony). ... Berlin (pronounced: , German ) is the capital of Germany and its largest city, with 3,387,404 inhabitants (as of September 2004); down from 4. ...

Karl Weierstraß

Karl Weierstrass was the son of Wilhem Weierstrass, a government official, and Theodora Vonderforst. His interest in mathematics began while he was a Gymnasium student, and was sent to the University of Bonn upon graduation to prepare for a government position. Because his studies were to be in the fields of law, economics, and finance, he was immediately in conflict with his hopes to study mathematics. He resolved the conflict by paying little heed to his planned course of study, but continued private study in mathematics. The outcome was leaving the university without a degree. His father was able to obtain a place for him in a teacher training school in Muenster, and he later was certified as a teacher in that city. During this period of study, Weierstrass attended the lectures of Christoph Gudermann and became interested in elliptic functions. The main building, viewed from the Hofgarten. ... Münster: Prinzipalmarkt Münster is a city in North Rhine-Westphalia, Germany. ... In complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. ...

After 1850 Weierstrass suffered from a long period of illness, but was able to publish papers that brought him fame and distinction. In 1857 he took the chair of mathematics at the University of Berlin. There is no institution called the University of Berlin, but there are four universities in Berlin, Germany: Humboldt University of Berlin (Humboldt-Universität zu Berlin) Technical University of Berlin (Technische Universität Berlin) Free University of Berlin (Freie Universität Berlin) Berlin University of the Arts (Universität der Künste Berlin) This is...

Selected papers

  • Zur Theorie der Abelschen Functionen (1854)
  • Theorie der Abelschen Functionen (1856)

See also

The Bolzano-Weierstrass theorem in real analysis states that every bounded sequence of real numbers contains a convergent subsequence. ... In mathematical analysis, the Heine-Borel theorem states: A subset of the real numbers R is compact iff it is closed and bounded. ... In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on an interval [a,b] can be uniformly approximated as closely as desired by a polynomial function. ... The Weierstrass-Casorati theorem in complex analysis describes the remarkable behavior of holomorphic functions near essential singularities. ... In mathematics, the Weierstrass function was the first example found of a kind of function with the property that it is continuous everywhere but differentiable nowhere. ... In mathematics, the Weierstrass M-test is an analogue of the comparison test for infinite series, and applies to a series whose terms are themselves functions of a real variable. ... In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic... In mathematics, the Lindemann-Weierstrass theorem states that if α1,...,αn are algebraic numbers which are linearly independent over the rational numbers, then are algebraically independent over the algebraic numbers; in other words the set has transcendency degree n over . ...

External links

  • Biography (http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Weierstrass.html)
  • University of St Andrews' page (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Weierstrass.html)
  • Weierstraß' students (http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=7486)
  • Digitalized versions of Weierstraß' original publications (http://www.bbaw.de/bibliothek/digital/struktur/autoren/weierstr/treffer.htm) are freely available online from the library of the Berlin Brandenburgische Akademie der Wissenschaften (http://www.bbaw.de/bibliothek/digital/).



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