Foundations of Combinatorics with Applications (Dover Books on Mathematics) by Edward A. Bender (PDF)

Description

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics.The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.

User’s Reviews

Editorial Reviews: From the Back Cover The book provides a solid introductory course for mathematics and mathematical computer science students. Designed for use in a number of courses, this book is appropriate for rigorous lower division courses, upper division courses in engineering, science, and mathematics, and beginning graduate courses. The material has been fully class-tested and includes many helpful examples and exercises. A solutions manual is also available.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent book. Has an interesting focus or at least a few chapters on applications to programming (such as recursion, Rooted Planar Trees, graphs) which adds to most books on “classical” combinatorics.

⭐Had been renewing this item with the library for about 5/yrs. Have invented an algorithm for Sudoku that needed to be elevated mathematically so “Foundations of Combinatorics with Applications” became my bible. Plus, have paid enough late fees which would have afforded the purchase.

⭐Eine so gründliche Darstellung all dessen, was mit der Kombination Elementen zusammenhängt, findet man selten. Ohne große technische Voraussetzung nehmen die Autoren den Leser mit auf eine Reise durch das Reich der Kombinationen. Die Darstellung ist dicht, die Autoren verlangen viel eigenes Denken, sodass das Buch am besten geeignet ist für eine Gruppe von Studenten oder gleich für den Unterricht. Für letzteres sprechen auch die zahlreichen Aufgaben, von denen die Hälfte im Anhang auch gelöst werden. Die Reise beginnt mit simplen Zusammenstellungen (Permutationen etc.), geht über Generatorfunktionen, Graphentheorie hin zur ausführlichen Darstellung von Induktion und Rekursion. Allgemeine Prinzipien erleichtern die Analyse von Aufgabenstellungen, und pädagogisch besonders wertvoll ist der Zugang der Autoren zu einem Problem über mehrere Wege, die scheinbar nichts miteinander zu tun haben. So wird abstraktes Denken an konkrete Beispielen geschult.Das Buch ist besonders geeignet für Studenten der Informatik, da auf die Programmierung von Algorithmen besonderer Wert gelegt wird und auch einige Beispiele für Programmabschnitte zu finden sind. Wem der Stoff zu dicht oder zu hoch ist, dem empfehle ich, sozusagen zur Vorlektüre, zwei einfachere Einführungen: “Mathematics of Choice” von Ivan Niven, und “Graphs and their Uses” von Oystein Ore.

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