A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Second Edition) [Paperback]

Miklos Bona (Author)

Book Description

Publication Date: October 9, 2006 | ISBN-10: 9812568859 | ISBN-13: 978-9812568854 | Edition: 2

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.

Editorial Reviews

Review

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

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. --This text refers to the Hardcover edition.

Product Details

• Paperback: 492 pages
• Publisher: Wspc; 2 edition (October 9, 2006)
• Language: English
• ISBN-10: 9812568859
• ISBN-13: 978-9812568854
• Product Dimensions: 9 x 6.3 x 1.3 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (10 customer reviews)
• Amazon Best Sellers Rank: #1,068,543 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

26 of 27 people found the following review helpful:

4.0 out of 5 stars A Stroll Through the Old and New, October 16, 2002

By 

Christopher Frenzen (Monterey, CA USA) - See all my reviews

This review is from: A Walk Through Combinatorics (Hardcover)

Combinatorics often, but not always, involves finite sets, and the ideas of counting. But the subject of combinatorics has indeed become very large, and it has worked its way into many others parts of mathematics, computer science, science, and engineering. Bona's book, `A Walk Through Combinatorics', is a text designed for an introductory course in combinatorics. It covers the traditional areas of combinatorics like enumeration and graph theory, but also makes a real effort to introduce some more sophisticated ideas in combinatorics like Ramsey Theory and the probabilistic method.

The book is very exciting to read, and the author has a wonderful sense of humor: in Chapter 3 he introduces the idea of a permutation by the example of n people arriving at a dentist's office at the same time. They must decide the order in which they will be served. How many orders are possible?

The problems are a great strength of this text. Each chapter ends with a set of exercises with solutions. These tend to be very interesting and often quite challenging. A set of supplementary exercises follows. These tend to be a little easier, though not always, and make good homework assignments. The supplementary exercises do not have solutions, but a solutions manual is available to instructors.

The book walks through four parts: I. Basic Methods; II. Enumerative Combinatorics; III. Graph Theory; IV. Horizons. I particularly like the fourth part which includes Ramsey Theory, subsequence conditions on permutations, the probabilistic method, and partial orders and lattices. A glimpse of these subjects can whet the walker's appetite for more challenging terrain.

I would have liked to give this book 5 stars, but it suffers from a lack of clarity in some places. For example, the discussion of example 2.2 in Chapter 2 on induction just does not read clearly or make sense as it is written. Though an instructor can figure out what is missing, it would be much harder for a student to do so. And figure 13.1 on the colors of the edge of a triangle in Chapter 13 on Ramsey Theory is mislabeled. Again, this could steer an unwary student off the path of understanding. But these defects are minor compared to the riches contained in this text. The author has chosen his subjects carefully, illustrated them well and provided a wealth of wonderful exercises. And he has given the reader a glimpse of some of the less traditional and newer areas of combinatorics at the end of the book.

12 of 12 people found the following review helpful:

4.0 out of 5 stars Well structured book, December 2, 2005

By 

Rui Jiang (BELLEVUE, WA USA) - See all my reviews
(REAL NAME)   

This review is from: A Walk Through Combinatorics (Paperback)

The best thing I like about this book, is that it has carefully selected subjects and rich set of exercises with detailed solutions. For the first several chapters, there are even more pages devoted to exercises+answers than the text. I think it is better to learn math by doing exercises than memorizing lots of theorems.

I would have given it 5 stars if there were not so many typos. It is annoying because a lot of times when I puzzled about something, it turns out be a typo. There are several versions of errata online, and none of them is complete. :) You can find them here:

http://www-math.mit.edu/~apost/courses/18.314/

I hope the author will correct all those typos then this would be the very best textbook!

5 of 5 people found the following review helpful:

5.0 out of 5 stars Can't say it enough - I wish I had this book when I was beginning to learn combinatorics, November 12, 2008

By 

PC (L.A., CA United States) - See all my reviews

This review is from: A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Second Edition) (Paperback)

Wow, what an awesome book it is (even with so many good introductory books on combinatorics). I really like the fact that (i) the author engaged the reader on solving the problems early [combinatorics is as much about problem solving as theory building]; (ii) the great number of problems + solutions; and (iii) the selection of topics.

I cannot help but repeat here (foreword by Richard Stanley) - "I only wish that when I was a student beginning to learn combinatorics there was a textbook available as attractive as Bona's."