Elementare Methoden Der Kombinatorik: Abzählen -- Aufzählen -- Optimieren

Name: Elementare Methoden Der Kombinatorik: Abzählen -- Aufzählen -- Optimieren
Brand: Vieweg+teubner Verlag
SKU: 9783519025290
Price: 3089.0 INR
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by Rainer Danckwerts , Dankwart Vogel , Klaus Bovermann

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ISBN13: 9783519025290
Binding: Paperback
Subject: N/A
Publisher: Vieweg+teubner Verlag
Publisher Imprint: Vieweg+teubner Verlag
Publication Date: November 1, 1985
Pages: 208
Original Price: EUR 42.05
Language: German
Edition: 1985
Item Weight: 304 grams
BISAC Subject(s): Engineering (General)

About The Book

Die Kombinatorik als eigenstiindige mathematische Disziplin ist recht jung. Anders als die Geometrie, die im Altertum fiir die Landvermessung im Niltal lebensnot- wendig war, erscheinen eigenstiindige kombinatorische Untersuchungen erst viel spiiter. Euler und Bernoulli liisten mittels analytischer Methoden Abziihlprobleme (z.B. Geldwechselprobleme), die in natiirlicher Weise in der damals entstehenden Wahrscheinlichkeitsrechnung vorkamen. In der ersten Hiilfte unseres Jahrhunderts wurden verstiirkt algebraische und gra- phentheoretische Methoden entwickelt. So ziihlte z.B. Polya die Anzahl der Alko- hol-Molekiile. Dank dieser neuen Ansiitze verschoben sich die Untersuchungen weg von der reinen Abziihlung von Objekten. Vielmehr weitete sich die Kombinatorik zu der Untersuchung der endlichen Strukturen aus. Die Existenz gewisser endlicher Konfigurationen war von Interesse, wie z.B. die von Gewinnstrategien bei Nim- Spielen. Dabei traten zusiitzlich Auflistungs- und Optimierungsprobleme auf. Das Problem, einen kiirzesten Weg vom Start zum Ziel durch ein Netzwerk zu finden, ist ein typisches Optimierungsbeispiel. Die bei diesen Problemen anfallenden groBen Datenmengen konnten erst mit Hilfe von Rechnern richtig verarbeitet werden. Der Einsatz von Rechenanlagen er- miiglichte aber nicht nur die Handhabung umfiinglichen Datenmaterials. Er erfor- derte vielmehr ein neues Verstiindnis der "Liisung" eines Problems. Statt einer Forme! war nun ein Algorithmus gefragt.

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