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Einfuhrung in Die Kombinatorik by Konrad Jacobs

Einfuhrung in Die Kombinatorik

by Konrad Jacobs
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Book cover type: Hardcover
  • ISBN13: 9783110167276
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: de Gruyter
  • Publisher Imprint: de Gruyter
  • Publication Date:
  • Pages: 418
  • Original Price: USD 49.0
  • Language: German
  • Edition: N/A
  • Item Weight: 767 grams
  • BISAC Subject(s): Discrete Mathematics, Combinatorics, and Reference

Ziel dieser vollständig überarbeiteten und erweiterten Neuauflage ist es, eine weitgehend elementare Einführung in ausgewählte Teile der Kombinatorik zu geben. Dabei wird stets versucht, nicht nur die Grundlagen darzustellen, sondern auch in jedem Kapitel exemplarisch einige tiefer liegende Resultate vollständig zu beweisen.

Highlights sind:

  • allgemeine Lösung des Kirkmanschen Schulmädchenproblems und mehr über Blockpläne
  • projektive Ebenen und Räume, einschlie lich des Freundschaftstheorems
  • Anwendungen in der Kryptographie, Authentikation von Nachrichten, Zugangskontrolle zu geheimen Informationen
  • Heiratssatz und eine Fülle verwandter Sätze, etwa über Flüsse auf Netzwerken
  • allgemeine Widerlegung der Eulerschen Vermutung über Paare orthogonaler lateinischer Quadrate
  • der Satz vom Diktator
  • verblüffende Eigenschaften der Morse-Thue-Folge
  • einige Perlen aus der Codierungstheorie, inklusive konkreter Anwendungen etwa bei Prüfziffersystemen
  • der klassische Satz von Ramsey und verwandte Ergebnisse
  • Partitionen und Abzählen, etwa das klassische Menage-Problem
  • Endliche Geometrie und Graphentheorie, insbesondere ein kurzer Beweis des Fünffarbensatzes und das Königsberger Brückenproblem

Das Buch wendet sich an Dozenten, die eine entsprechende Vorlesung über Kombinatorik halten, sowie an Studenten der Mathematik, denen das Buch als Begleitlektüre zu einer solchen Vorlesung oder zum Selbststudium dienen kann. Angesprochen sind auch Lehrer und Schüler in der gymnasialen Oberstufe, die im Rahmen eines Leistungskurses erste Einblicke in die reizvollen und teilweise sehr direkten Fragestellungen der Kombinatorik gewinnen wollen.

Konrad Jacobs ist emeritierter Professor am mathematischen Institut der Friedrich-Alexander-Universität Erlangen-Nürnberg.

Dieter Jungnickel ist Professor am Institut für Mathematik der Universität Augsburg.

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