Customer Reviews

Applied Combinatorics

5 star:		(8)
4 star:		(2)
3 star:		(1)
2 star:		(2)
1 star:		(1)

 

 

This book was assigned for a class in applied combinatorics, and in many instances I had to ask "why?"

The Positives: This book has the simplest introduction to building generating function models that I've ever come across, in regards to ordinary generating functions. The examples in this section really shine, and if you spend time on this section (Chapter 6.1) you shouldn't have too much trouble at all as you progress through the rest of the chapter. I cannot stress that enough! Master 6.1; the rest falls into place.

The intro to graph theory is just that: Tucker doesn't spend too much time on any major results, in fact treats Euler's polyhedral formula almost as an afterthought. I mean, I realize this is enumeration, but the fact that Euler's proof was really combinatorial in the first place is an excellent place to tie in a branch of mathematical study. The emphasis though are on graph problems and it gives an excellent study of two algorithms for solving the traveling salesman problem.

Binomial identities (the ultimate goal of chapter 5) aren't covered quite as comprehensively as I would have hoped. (see the book "Art of Combinatorial Proof") But the writing here is good and I only had to consult outside material on some of the problems.

The Negatives:

The treatment of recurrence relations are a joke. I mean, seriously! It starts out assuming you've spent time on Diff EQ (which I hadn't) and uses language such as 'obviously,' a damn dangerous word to anyone who studies math seriously!

In Homgeneous recurrence relations they introduce the general solution buried within the discussion and make the additional mistake of using the * symbol in the notation. Organization is my biggest gripe here, they should treat this solution like a theorem or do SOMETHING to make it stand out. I finally just complied my own chart for my notes because I got tired of flipping pages back and forth and scanning for what I wanted. Tucker also misses the fact that an explicit treatment of notation when multiple or complex roots should be in order.

For solving recurrence relations I went back to my trusty "Discrete and Combinatorial Mathematics" text from Grimaldi. Real theory, and plainly spoken. For an undergrad text I expect my hand to be held at least a little, and Tucker obviously thinks recurrence relations are no big deal.

They aren't once you know them. I'm in a class of mostly math majors and you should have seen their faces when in an Inhomogeneous solution the teacher finished with "...can be solved with partial fraction decomposition."

The final gripe is the lack of any solutions manual. Maybe that's the point. I'm supposed to look at a solution and reverse engineer it on my own; its just that many times I'm not getting the point in the first place and I need to see more solutions to different kinds of problems.

In conclusion, I will keep this book on my shelf. The problems are incredibly challenging, and once you can solve them with one method, you can go back and solve them with another, that's the fun part about combinatorics.

For other clear treatments, Grimaldi, Harris, and Bona.

Harris's book is at the upper end of the undergrad spectrum, but its brevity on some topics is especially excellent as its derivation of generating function models sped up my understanding of this crucial area.

Docked 1 star for retail price for such a thin tome, and 1 star for assorted problems.

For self-study, I'd recommend the Grimaldi text before you tackle this one, but this one is good if you just want a source of problems. Many of these books I suggest should be available in your school's library, to avoid racking up high book costs.

The book covers the fundamentals of graph theory and combinatorics (enumeration) and is designed for first courses for undergraduates.

The material is presented in a clear, friendly manner. The sections are short and specific and the emphasis is on problem-solving. Many examples are provided and constitute the majority of the book's volume. Each section ends with 20-30 exercises with answers (not full solutions) at the end of the book.

The book is excellent for computer science and applied math majors looking for a clear, application-based introduction to combinatorics and graph theory. It is also excellent for self-study.

The book's main flaw is that the proofs are not rigorous and are sometimes more intuitive than mathematical. For pure math students looking to explore graph theory and combinatorics in a more rigorous manner, other books (e.g. Diestel, "Graph Theory") will serve that purpose better.

Very briefly, Tucker loses you through examples rather than developing his theoretical discussions.

I've noticed that some people have said that this text is clearly written, to me, nothing could be further from the truth. He seems to have a great knack for over-complicating simple ideas. This may be a personality thing -- some people really identify with his approach, I do not. I think he gets bogged down in smoothing out the details of his examples and definitions and ends up obfuscating points where simple brevity not only would have sufficed, but would have been more illuminating.

Also, except by inference on the reader's part, it can be difficult to distinguish the important from the trivial . . . this is a very poor text for self-study. I think I'm going to check out what selections Springer offers covering these topics, I've had pretty good luck finding well-written texts with their UTM series.

This is one of the college textbooks which I saved from college and found to be an excellent source of reference for years to come. Combinatorics is the kind of math that every programmer needs to know from time to time, but if you're like me you will be a bit rusty everytime a new problem presents itself. I strongly recommend this book to both students and programmers who have yet to appreciate the value of the factorial function ;)

This book is a very clear introduction to combinatorics which provides a fundamental understanding of the material of elementary combinatorics using mathematics of college sophomore level. I have used exercises and sections of this text to review the subject for my engineering students in system design. It remains my book of choice for the elementary topics in combinatorics. I only wish that the Pigeon-hole and Ramsey Theorem were part of the content.

The book is really little, which allows me to practice theoretical combinatorics anywhere that I am, whether I am driving or walking down the middle of the hallway.

I am a math grad student taking graph theory this semester. As a math major, I understand that one should have the ability to "fill in the holes". You can overdo anything, however. This book is ruined by its lack of examples. Also, it is like the author is in a hurry when he is talking about key ideas. Definitions are often stated in a rushed way that confuses me. Yet, he rambles on when discussing less relevant things. In short, this is a very hard text to read. Easy exercises seem hard because little foundation has been laid. I only paid $17 for this book on amazon. I could not imagine paying $100 for it.

I will admit that this book is a good source for exercises. Also, the proofs are fairly readable, provided you can grasp the "under-explained" key concepts that are less than readable.

I covered the book as part of a final-year undergraduate mathematics course. This is certainly an undergraduate text, but I think that to fully appreciate the content, the reader should have a little past exposure to the basic concepts. These are usually covered in first-year maths or physics courses anyway.

The book is divided into two almost separate sections - one dealing with graph theory and one with combinatorics. Both make for good reading, and really equip the reader with practical problem solving skills for everyday situations.

I liked the fact that there were sufficient examples in all sections, and of a good complexity that showed the theory in action. Exercises were good and of a fair standard.

Overall, a very good text - get it.

God Alan Tucker is awesome. Not enough text books have lord of the rings references in my opinion. This one is totally worth while.

This is a very well done book. In my opinion, the staggering amount of exercises with solutions is worth the price of admission alone. In the chapter on basic counting principles, the solutions are left as pre-calculated answers (for example, the author will write 3*C(5,2) instead of 30).

This not only allows you to obtain the correct answer, but it also allows you to gain insight into *how to think* about a combinatorial problem - especially helpful for self study. It does not get too heavy-duty into theory, so a more rigorous supplement may be in order if that is the primary concern. Regardless, I would keep/purchase this book just for the problem sets - they are invaluable.