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

by Miklos Bona

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 three 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.New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them.The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.The previous edition of this textbook was also translated into Korean and adopted at various schools.

Genres: Mathematics, Textbooks, Nonfiction, Science

616 pages, Hardcover

First published June 1, 2002

Reviews

[Luci · Rating 5 out of 5]

bloody interesting... used this as a textbook a few years back and would like to revisit if I have time in the future.

[Henry Lembeck · Rating 3 out of 5]

If it weren't for the obscene amount of typos, I would give the book 5 stars. However, the book becomes incredibly difficult to read at times due to these typos, which force the reader to doubt himself. An egregious example of a typo occurs in the chapter on complexity theory. Here, Bona gives an example of a Turing Machine which is supposed to determine if a number is divisible by 3. Unfortunately, the machine may stay at the "start" state indefinitely, therefore never halting. There are also typos in some of the end-of-chapter equation lists.

The typos, in my opinion, warrant a 2 star deduction from an otherwise 5 star book.

[Shozab Qasim · Rating 5 out of 5]

I new a large chunk of the material prior to reading the book - however, the presentation was pretty good. I definitely recommend it for a first course!

[Raymond Ying · Rating 4 out of 5]

Difficult but good, very insightful and useful

[Travis Johnson · Rating 4 out of 5]

I liked this book a lot more than my other combinatorics text by Brualdi. Bona has a great pace and good examples.