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Home > Mathematics and Science Textbooks > Mathematics > Topology > Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie
Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie

Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie


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About the Book

Die Knotentheorie hat sich im letzten Jahrzehnt zu einem der aktivsten Forschungsgebiete in der Mathematik entwickelt. Eine Vielzahl neuer Ergebnisse wurde gefunden, die sich nicht nur in der Topologie, sondern auch in anderen Gebieten der Mathematik und sogar in anderen Naturwissenschaften wie der Physik und der Biologie fruchtbar einsetzen liessen. Diese erstaunliche Entwicklung hat eine beachtliche Zahl von Buchveroffentlichungen zur Knotentheorie zur Folge gehabt, wobei eine historische Darstellung bislang noch nicht vorliegt. Dieses Buch schliesst diese Lucke und spannt den Bogen von Gauss bis zur heutigen Knotentheorie. Allgemein verstandliche und mathematisch anspruchsvolle Abschnitte sind klar zu unterscheiden.

Table of Contents:
1 Einleitung.- 1.1 Vier Episoden.- 1.2 Themen einer Geschichte der Knotentheorie.- 1.3 Die Perspektive: Eine Geschichte des mathematischen Handelns.- 1.4 Eine kurze Übersicht.- Erster Teil: Mathematisierung.- 2 Der Praktische Umgang Mit Knoten und die Anfänge der Analysis Situs.- 3 Der Beitrag von Carl Friedrich Gauss Zur Mathematisierung der verkettungen und knoten.- 4 Ätherwirbel, Knoten und Atome.- 5 Ein Periodisches System der Knoten? Peter Guthrie Tait und die ersten knotentafeln.- 6 Sackgassen und Neue Wege: Knoten und Zöpfe in der Mathematik des Ausgehenden 19. Jahrhunderts.- Zweiter Teil: Knotentheorie in der mathematischen Moderne.- 7 Der Anbruch der Mathematischen Moderne und die Disziplinäre Schwelle der Topologie.- 8 Ein Anderer Weg in die Mathematische Moderne: Wilhelm Wirtinger, Poul Heegaard Und Heinrich Tietze.- 9 Poincarésche Räume, Knoten, Gruppen: Max Dehn.- 10 Berechenbare Invarianten und Elementare Begründung: Kurt Reidemeister.- 11 Überlagerungen, Homologie und Ein Knotenpolynom: James Waddell Alexander.- 12 Ein Erstes Paradigma? Knotentheorie Nach 1930.- A Taits Tafeln Alternierender Knoten.- B Verzeichnisse.- B1 Chronik.- B2 Chronologische Bibliographie bis 1945.- B3 Weitere Literatur.

About the Author :
Dr. Moritz Epple lehrt Geschichte der Mathematik an der Universität Mainz.


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Product Details
  • ISBN-13: 9783322802965
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 240 mm
  • No of Pages: 449
  • Sub Title: Kontexte und Konstruktionen einer modernen mathematischen Theorie
  • ISBN-10: 3322802965
  • Publisher Date: 22 Jan 2012
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Width: 170 mm


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Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie
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