Elemente Der Codierungstheorie by Gert Kadunz - Bookswagon
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Elemente Der Codierungstheorie

Elemente Der Codierungstheorie


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About the Book

Im täglichen Leben sind wir zunehmend von Codes umgeben, die mathematisch konstruiert werden. Sie sind teils leicht erkennbar (Strichcode, ISBN, IBAN, QR) und teils eher verborgen (GPS, WLAN, CD, DVD). In diesem Buch werden solche Codes vorgestellt. Es wird dargelegt, wie sie aufgebaut sind, wie sie funktionieren und welche Mathematik zu ihrer Entwicklung und Anwendung notwendig ist. Die Lesenden lernen, eigenhändig Codes zu erstellen, Fehler zu erkennen und zu korrigieren:

  • EAN, ISBN und deren Barcodedarstellung sowie die internationale Bankkontonummer IBAN werden erarbeitet.
  • Kleine QR-Codes werden mit den vorgestellten Methoden (Paritätsprüfung, Linearcode, Polynomcode, zyklischer Code und Reed-Solomon Code) anschaulich realisiert.
  • An der Herstellung einer Mini-CD mit einem CIRC-Code über einem kleinen Körper werden wesentliche Konstruktionsprinzipien von neuen Codes aus bestehenden Codes, wie z.B. Kürzen, Erweitern, Spreizen (Interleaving) und gekreuztes Spreizen (Cross-Interleaving) veranschaulicht.

Das Verstehen von Mathematik wird durch diese selbstständige Erstellung und Verwendung didaktisch maßgeschneiderter Codes wesentlich gefördert.

Ein besonderer Fokus des Buchs liegt auf elementaren Methoden des Rechnens mit ganzen Zahlen und Polynomen. Für diese benötigt man nur den Satz von der Division mit Rest als zentrale Aussage - daher können große Abschnitte bereits mit Lernenden der Sekundarstufe II erarbeitet und die Grundlagen wesentlicher Teile der Codierungstheorie von den Lernenden mathematisch korrekt erfasst werden. Für Ausführungen, zu deren Verständnis Kenntnisse notwendig sind, die über die Mathematik der Sekundarstufe II hinausgehen, liegt ein ausführlicher Anhang vor (Vektorräume, Matrizen, Rechnen in endlichen Körpern).


About the Author:

Hermann Kautschitsch lehrt und forscht an der Universität Klagenfurt zu Themen aus der Algebra und der Visualisierung von Mathematik in der Unterrichtspraxis.

Gert Kadunz lehrt und forscht an der Universität Klagenfurt zu ausgewählten Themen der Mathematikdidaktik.


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Product Details
  • ISBN-13: 9783662675199
  • Publisher: Springer
  • Publisher Imprint: Springer Spektrum
  • Language: German
  • Returnable: Y
  • ISBN-10: 3662675196
  • Publisher Date: 08 Nov 2024
  • Binding: Paperback
  • No of Pages: 384
  • Sub Title: Besser Sehen, Besser Hören, Besser Informieren


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