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Bernhard Riemann 1826-1866: Wendepunkte in Der Auffassung Der Mathematik

Bernhard Riemann 1826-1866: Wendepunkte in Der Auffassung Der Mathematik

          
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About the Book

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."


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Product Details
  • ISBN-13: 9783034898546
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Edition: Softcover reprint of the original 1st ed. 1996
  • Language: German
  • Returnable: Y
  • Spine Width: 19 mm
  • Weight: 471 gr
  • ISBN-10: 3034898541
  • Publisher Date: 06 Oct 2011
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 348
  • Series Title: Vita Mathematica
  • Sub Title: Wendepunkte in Der Auffassung Der Mathematik
  • Width: 152 mm


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