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Mathematics Einf¨¹hrung in die Kombinatorik
Posted on 2010-04-12
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More Dieter Jungnickel ¡°Einf¨¹hrung in die Kombinatorik" Ziel dieser vollst?ndig ¨¹berarbeiteten und erweiterten Neuauflage ist es, eine weitgehend elementare Einf¨¹hrung in ausgew?hlte Teile der Kombinatorik zu geben. Dabei wird stets versucht, nicht nur die Grundlagen darzustellen, sondern auch in jedem Kapitel exemplarisch einige tiefer liegende Resultate vollst?ndig zu beweisen. Highlights sind: allgemeine L?sung des Kirkmanschen Schulm?dchenproblems und mehr ¨¹ber Blockpl?ne projektive Ebenen und R?ume, einschlie?lich des Freundschaftstheorems Anwendungen in der Kryptographie, Authentikation von Nachrichten, Zugangskontrolle zu geheimen Informationen Heiratssatz und eine F¨¹lle verwandter S?tze, etwa ¨¹ber Fl¨¹sse auf Netzwerken allgemeine Widerlegung der Eulerschen Vermutung ¨¹ber Paare orthogonaler Lateinischer Quadrate der Satz vom Diktator verbl¨¹ffende Eigenschaften der Morse-Thue-Folge einige Perlen aus der Codierungstheorie, inklusive konkreter Anwendungen etwa bei Pr¨¹fziffersystemen der klassische Satz von Ramsey und verwandte Ergebnisse Partitionen und Abz?hlen, etwa das klassische Menage-Problem Endliche Geometrie und Graphentheorie, insbesondere ein kurzer Beweis des F¨¹nffarbensatzes und das K?nigsberger Br¨¹ckenproblem Das Buch wendet sich an Dozenten, die eine entsprechende Vorlesung ¨¹ber Kombinatorik halten, sowie an Studenten der Mathematik, denen das Buch als Begleitlekt¨¹re zu einer solchen Vorlesung oder zum Selbststudium dienen kann. Angesprochen sind auch Lehrer und Sch¨¹ler in der gymnasialen Oberstufe, die im Rahmen eines Leistungskurses erste Einblicke in die reizvollen und teilweise sehr direkten Fragestellungen der Kombinatorik gewinnen wollen. "
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