A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

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9789812568861: A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory
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This is a textbook for an introductory combinatorics course lasting 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 two editions, 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 to the talented and hardworking 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, Eulerian and Hamiltonian cycles, and planar graphs.The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures 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.

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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:

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

"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

"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"

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Bona, Miklos
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