Elemente Der Diskreten Mathematik: Zahlen Und Zählen, Graphen Und Verbände
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Die Grundidee des vorliegenden Lehrbuchs ist, wesentliche Elemente der diskreten Mathematik zu vermitteln, um die modernen Entwicklungen im Informationszeitalter kompetent mathematisch beurteilen zu k�nnen. Hierzu geh�ren das Verst�ndnis von Graphen, das Rechnen mit gro en Zahlen und das Rechnen modulo n. Die Autoren beginnen mit einer Darstellung der elementaren Zahlentheorie. Insbesondere wird die Verschl�sselung mit dem RSA-Verfahren erl�utert. Danach werden Absch�tzungen behandelt, die unerl�sslich sind, wenn man Objekte z�hlen oder Laufzeiten wichtiger Algorithmen verstehen m�chte. Diverse in der Praxis vollkommen zuverl�ssige Algorithmen nehmen den Zufall zu Hilfe, um �berhaupt zu einem Ergebnis zu kommen. Daher darf ein Kapitel zur diskreten Wahrscheinlichkeit nicht fehlen. Danach begibt sich der Leser ins Zentrum der diskreten Mathematik. Es werden Kombinatorik, erzeugende Funktionen und Graphentheorie behandelt. Zum Abschluss widmen sich die Autoren Ordnungsstrukturen und Verb�nden sowie booleschen Funktionen und Schaltkreisen.
Das Buch erg�nzt und vertieft Grundlagen und zeigt m�gliche Anwendungen auf. Es werden aber auch Themen behandelt, die �ber den Standardstoff hinaus gehen. Einen hohen Stellenwert nehmen Aufgaben und L�sungen ein. F�r alle wichtigen Aussagen geben die Autoren vollst�ndige Beweise an. Am Ende eines jeden Kapitels sind kurze Kapitelzusammenfassungen als Lern- und Merkhilfe hinzugef�gt.
Das ben�tigte Vorwissen ist gering. Die behandelten Grundlagen sind keine blo en Aneinanderreihungen von Definitionen und elementaren Zusammenh�ngen. Das Buch vermittelt ein tieferes Verst�ndnis f�r die behandelten mathematischen Zusammenh�nge und stellt Wissen, Techniken und Denkweisen vor, welche den Leser in die Lage versetzen, selbstst�ndig mathematische Probleme zu l�sen.
Volker Diekert and Manfred Kufleitner, University of Stuttgart, Germany; Gerhard Rosenberger, University of Hamburg, Germany.
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