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

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Item description for A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory by Miklos Bona...

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.

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Item Specifications...

Studio: World Scientific Publishing Company
Pages   469
Est. Packaging Dimensions:   Length: 1" Width: 6" Height: 9"
Weight:   1.54 lbs.
Binding  Softcover
Release Date   Oct 10, 2006
Publisher   World Scientific Publishing Company
ISBN  9812568867  
ISBN13  9789812568861  

Availability  0 units.

More About Miklos Bona

Register your artisan biography and upload your photo! Miklos Bona has an academic affiliation as follows - University of Florida Gainesville, USA UNIV OF FLORIDA AT GAINESVILLE.

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Product Categories

1Books > Subjects > Science > Mathematics > General
2Books > Subjects > Science > Mathematics > Pure Mathematics > Combinatorics

Reviews - What do customers think about A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory?

A Walk Through Combinatorics  Apr 20, 2008
I wish that all math books should be written the way this book offers with great examples w/solutions for students to try out first and then a set of supplemental problems that follow through for more practices.
Encompassing and Very Clear  Aug 23, 2007
This book goes step by step on the elementary subjects of Combinatorics, contains many of examples and solved exercises, such that the reader or any autodidact student can experience a meaningful studying experience.
Well structured book  Dec 3, 2005
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:

I hope the author will correct all those typos then this would be the very best textbook!
A Stroll Through the Old and New  Oct 17, 2002
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.


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