Endliche Körper
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Endliche Körper: Verstehen, Rechnen, Anwenden(Springer-Lehrbuch)

Endliche Körper: Verstehen, Rechnen, Anwenden(Springer-Lehrbuch)


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About the Book

In jedem Handy, CD-Player und Computer steckt ein Chip, der lineare Gleichungssysteme über einem endlichen Körper blitzschnell löst, um fehlerbehaftetes Datenmaterial zu korrigieren; dieses Buch erklärt das mathematische Innenleben eines solchen Chips. Endliche Körper sind Zahlenbereiche (sog. Galoisfelder) mit nur endlich vielen Zahlen, die man aber addieren, subtrahieren, multiplizieren und dividieren kann. Das Hauptanliegen des Buches ist es, auf elementare Weise zu erklären und zu üben, wie diese Rechungen ausgeführt werden. Es wendet sich an jeden, dem die mathematischen Sprache nicht fremd ist und der wissen möchte, wie endliche Körper funktionieren. Vorausgesetzt wird eine gewisse Vertrautheit mit Grundbegriffen der linearen Algebra, wie sie etwa in einer Vorlesung Ingenieurmathematik geübt werden. Obwohl der Text zielgerichtet ist, bietet er auch eine elementare Einführung in die Algebra, denn endliche Körper können ohne algebraische Begriffe – Gruppe, Vektorraum, Ring, Körper und Polynom – nicht erklärt werden.

Table of Contents:
Der Ring der ganzen Zahlen.- Der Polynomring.- Die Teilbarkeit.- Der erweiterte Euklidische Algorithmus.- Nullstellen von Polynomen.- Zyklische Gruppen.- Die multiplikative Gruppe und die diskrete Fouriertransformation.- Das Rechnen in endlichen Körpern.- Erweiterungskörper.- Existenz und Eindeutigkeit von endlichen Körpern.- Irreduzible Polynome.- Reed–Solomon Codes.

Review :
Aus den Rezensionen: "Zur Entschlüsselung digitaler Informationen, die geeignet codiert, aber durch Übertragungsfehler entstellt wurden, hat die Theorie der endlichen Körper eine sehr praktische Bedeutung gewonnen. Der Autor destilliert dieses Gebiet aus dem allgemeinen algebraischen Zusammenhang, in das es üblicherweise verwoben ist, völlig heraus und entwickelt mit minimalem Begriffsaufwand zielgerichtet das Instrumentarium … Der … Text verlangt keinerlei das Schulwissen übersteigende Vorkenntnisse. Trotz der sehr konkreten Ausrichtung … bietet der Band auch einen ersten, in der Schule nutzbaren Einblick in algebraische Strukturen und Methoden." (Wolfgang Grölz, in: ekz-Informationsdienst Einkaufszentrale für öffentliche Bibliotheken, 2007, Issue 21)


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Product Details
  • ISBN-13: 9783540795971
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Edition: Revised edition
  • Language: German
  • Returnable: Y
  • Series Title: Springer-Lehrbuch
  • Width: 155 mm
  • ISBN-10: 3540795979
  • Publisher Date: 01 Sep 2008
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 178
  • Returnable: Y
  • Sub Title: Verstehen, Rechnen, Anwenden


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