Customer Reviews

A Walk Through Combinatorics

5 star:		(4)
4 star:		(4)
3 star:		(1)
2 star:		(0)
1 star:		(1)

 

 

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.

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!

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."

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.

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.

This is a good book on combinatorics. The problems constitute the real meat of this text. They range from the elementary to the very challenging. The first set of exercises has solutions. A set of supplementary exercises (without solutions) follows. This is a suitable book for self-study. Another combinatorics book worth looking at is Martin's Counting:The Art of Enumerative Combinatorics.

Let me start by saying that I was never good at Permutations and Combinations in high school. With the intention of changing that, I bought this book (the Kindle version, which is based on the Second Edition) some time ago to try to teach myself combinatorics. However, I wasn't really able to progress beyond Chapter 4 (there are 18 chapters in all) as the problems become way too difficult. Perhaps if there were exercises after each section rather than after each chapter, that would make learning a lot easier.

Yesterday I bought "Combinatorics and Graph Theory" by John M. Harris et al and hope I will have better luck with it.

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 rigorous unified development. For example, partitions and generating functions share an important deep 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 example application or two. But there are also numerous unexpected forward references, which is hard to forgive in a math textbook. The closing chapter section on computability however, is an appreciated capstone to the largely abstract topic list.

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 sufficiently, 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.

I love this book. It's very interesting through out the book. Each section goes from very basic stuff to advance stuff which makes it's easy for you to follow.

Each chapter of the book, there are about 20+ problems with detail solutions in the book (Yes, I am not kidding-SOLUTION). It's perfect for people who want to practice and check their work or finding some hint when you are stuck.
It's a great way to learn how to solve combinatoric problems.

Moreover, it also have the supplementary problems ( this one with no solution), for people who want to challenge themselves more.

It's a great book for those who are new to combinatoric and want to find their way in. And it has so many difficult levels that you won't be bored. Recommended!!!

This is an excellent book! The author explains the subject in such a clear and intelligent way that it's hard to not understand what he's trying to tell you. The book is nicely organized, and there are lots, lots, lots of exercises -- all with solutions. Having solutions available is really important to people learning for themselves, since it would be impossible to actually develop confidence in the skills they're trying to develop without these answers (there's no other easy way to check if progress is being made -- you either ask someone, which may not be available, or you check the answer).

Excellent first course in Combinatorics; requires highschool math, some familiarity with summations and products (sigma and pi notation), but other than that it develops everything you'll need.