A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Second Edition) - Softcover

Bona, Miklos

Softcover

ISBN 10: 9812568859 ISBN 13: 9789812568854

Publisher: Wspc, 2006

Synopsis

This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity.As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

About this title

About the Author

Miklos Bona received his PhD at Massachusetts Institute of Technology. He is a Professor of Mathematics at the University of Florida, where he has been inducted into the Academy of Distinguished Teaching Scholars. His research has been supported by the National Science Foundation, the National Security Agency, and the Howard Hughes Medical Institute. Miklos Bona has received teaching awards at the University of Florida and at the University of Pennsylvania. He is one of the Editor-in-Chiefs of the Electronic Journal of Combinatorics.

Review

"Miklos Bona's book is the best introductory combinatorics book that I have ever seen. It is extremely lively yet mathematically accurate, and the writing is lucid and very entertaining at the same time." -- Doron Zeilberger

"This is a very attractive textbook on combinatorics ... A special feature of this book is the extensive list of interesting exercises with complete solutions."

"The strong points of the book are in particular a very inviting style of exposition, in which developments are always well motivated and well illustrated by numerous examples, and the long list of exercises at the end of each chapter, with detailed solutions ... This is very pleasant and instructive reading."

Plentiful examples .... Bona does a supreme job of walking us through combinatorics -- Choice "Choice"

Edition details

• Publisher: Wspc
• Publication date: 2006
• ISBN 10: 9812568859
• ISBN 13: 9789812568854
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 492