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A Walk Through Combinatorics 1st Edition

4.3 out of 5 stars 14 customer reviews
ISBN-13: 978-9810249007
ISBN-10: 9810249004
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Editorial Reviews

Review

"It is extremely lively yet mathematically accurate, and the writing is lucid and very entertaining at the same time." -- Doron Zeilberger Rutgers University

...A very inviting style of exposition, in which developments are always well motivated and illustrated by numerous examples. -- Zentralblatt MATH

A very attractive textbook on Combinatorics. -- Monatshefte fur Mathematik

From the Inside Flap

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. --This text refers to an alternate Hardcover edition.

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Product Details

  • Hardcover: 424 pages
  • Publisher: World Scientific Publishing Company; 1st edition (June 15, 2002)
  • Language: English
  • ISBN-10: 9810249004
  • ISBN-13: 978-9810249007
  • Product Dimensions: 9.3 x 6.4 x 1.1 inches
  • Shipping Weight: 1.7 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #3,728,127 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: 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.
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Format: 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:

[...]

I hope the author will correct all those typos then this would be the very best textbook!
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Format: 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."
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Format: Paperback Verified Purchase
If looking to improve your combinatorial problem solving or better grasp the scope of the field, "A Walk Through Combinatorics" is a slim, suitable solution. It is not, however, a full primer. Although it acquaints the reader with several topics, it seems little concerned with their unified development. For example, partitions and generating functions share an important connection not discussed. Induction is presented without elucidating strong induction or the well-ordered principle.

The book does not use a sequential approach, equally to its credit as its criticism as a learning tool. Of course, some chapters cohere out of necessity (e.g. binomial identities and compositions come after counting principles) but you can largely jump in wherever you wish, which is good for quickly gaining a working definition with an sample application or two. But there are also numerous unexpected forward references, which is hard to forgive in a mathematics textbook. The closing chapter section on computability however, is an appreciated capstone.

Practice problems lie mostly at what the intended audience would probably call the "challenging" level. This is fine, because Bona has meticulously worked out solutions for many of the problems in each chapter. I have not taken a precise count (ironically) but solutions appear to comprise at least half of the book's pages. If you can understand the explanatory parts of the chapter and the brief examples given, taking the time to work through the practice sets will reinforce the foundation well.

One thing I will never understand is why discrete math textbooks insist on a probability unit, Bayesian or otherwise.

Take the title seriously. This is a "walk" through the subject, and you don't get a chance to sit and analyze in one spot on a gentle pedestrian stroll: the major landmarks are tagged with introductory information, and you get to see a lot of them.
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Format: Paperback
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.
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Format: Paperback
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.
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