Applied Combinatorics

by Alan Tucker

Book Overview

This is a revision of a one-semester survey of combinatorial analysis and graph theory, designed for mathematics and computer science majors. Three principal aspects of combinatorial reasoning are emphasized in this book: the systematic analysis of different possibilities, the exploration of the logical structure of a problem, and ingenuity. Keeping theory to a minimum, it uses numerical examples to demonstrate the combinatorial reasoning involved...

• Format: Hardcover
• Language: English
• ISBN: 0471863718
• ISBN13: 9780471863717
• Release Date: August 1994
• Publisher: Wiley
• Length: 447 Pages
• Weight: 1.78 lbs.

Customer Reviews

Neat problems

Combinatorics is one of those subjects that you get good at by doing lots of problems (to build creative muscle). See, there's a book called "Combinatorcs Through Guided Discovery" by Kenneth Bogart. Basically, the author attempts to have the reader discover combinatorics through first principles. My combinatorics professor used that book for our combinatorics class. Now while I learned a lot from doing those problems (and learned what it is like to be genuinely stressed), the exam questions my professor gave were necessarily more application problems that used the principles of combinatorics rather than problems designed to teach the fundamental principles (so the exam questions were trickier but shorter), so to prepare for exams and to apply what I learned, I needed a bunch of problems that allowed me to do this. This book is *filled* with such problems and I honed my combinatorial problem instinct by just assigning myself problem sets from this book and doing them with (and without) time limits. So that basically sums this book up: it has a TON of really good problems and if you really put the work in (and assuming you are reasonably mathematically talented), you'll walk away with much better problem solving skills than you did before you worked through the book. There's no branch of mathematics that really caters to the "problem solver" type of mentality than combinatorics and this book is just excellent to satisfy the need to just solve tricky problems. I do reccomend that if you're buying this for self-study/supplement that you do NOT buy this 5th edition and that you go buy a really cheap 3rd or 4th edition (what I did). I skimmed my prof's copy of the 5th edition and saw that 95% of the problems are the same, with a few added/reworded.

Jaime's review

it was prompt and in the condition stated. Those were my expectations, so good job.

Excellent for applications

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.

An almost ideal introduction book to combinatorics

There have been wonderfully written reviews of this book, but since this is really an excellent textbook, I am urged to praise again. Fully recommended.This book is easily and clearly written; covers almost every important basic concept and technic in graph theory and enumerative combinatorics, with neatly selected and wonderfully organised exercises. And I highly suggest the author give the references to those last exercises in every section, since each of them does lead into a theory.

Excellent undergraduate text

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.