- Paperback: 312 pages
- Publisher: World Scientific Publishing Company (July 1, 1992)
- Language: English
- ISBN-10: 9810211392
- ISBN-13: 978-9810211394
- Product Dimensions: 6 x 0.6 x 9 inches
- Shipping Weight: 15.2 ounces (View shipping rates and policies)
- Average Customer Review: 4.5 out of 5 stars See all reviews (13 customer reviews)
- Amazon Best Sellers Rank: #248,497 in Books (See Top 100 in Books)
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Principles and Techniques in Combinatorics
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"This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses." Mathematical Reviews
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Top Customer Reviews
When I found this tome here on Amazon it was at the behest of a reviewer that stated the strength of this book in the explanation of Recurrence Relations. I can't agree further. The text assigned for my class was Tucker's Applied Combinatorics book, and to be frank, it's a fairly decent text that does have an incredibly strong introduction to Generating Functions that goes down as one of the finest I have encountered. However, this book also discusses sequence creation using generating functions, something that Tucker leaves out. This book is a *true* introduction to combinatorics, explicitly detailing every step of every proof--something direly missing in most other texts of this type. Most people taking this class have only had a rudimentary sampling of proof techniques (comp-sci majors usually take combinatorics) and this book helps fill in the missing gaps left in slightly higher-flyers such as Tucker's.
But the reason this one is such a gem in recurrence relations is that it goes in depth in teaching you HOW TO MODEL with this tool. Tucker assumes you can do that already. His chapter on modeling is light on problems and doesn't explain the examples as clearly as this one does. This book also shows some incredibly creative problem solutions that crafty high-schoolers have devised (being olympiad trainers) that help you think about other implications in things such as Pascal's triangle. It does a great job of improving mathematical thinking and if I didn't enjoy Tucker's chapter on generating functions so much I would sell that thing in a heartbeat.
In studying for my combinatorics final I have also found that its plain explanations of other material from earlier chapters would have saved me (a whole lot) of 'head against the wall bashing.'
This book underlines the difference in how people who trained in education write books vs. people who typically write college textbooks. I know its typical as a native english speaker to think twice when buying a book written by a foreign sounding name, but trust me, you get the thing you always hope for in a math textbook. (Clarity, blessed, beautiful, sweet sweet clarity!)
If you're a student who enjoys--but struggles with--higher math, this is the book to get, hands down.
One valuable feature of this text that I didn't see mentioned is the selection of topics. A lot of combinatorics texts rarely devote an entire chapter to recurrence relations. To the extent of my knowledge, examples of texts with limited coverage are Stanley (vol 1), Riordan, Harris-Hirst-Mossinghoff, Comtet, Bona and Camina-Lewis. Generating functions and recurrence relations often work side-by-side, so the additional coverage allows one to get more mileage from the material on generating functions. Also, recurrence relations are often slick ways to find inductive structure in a problem, which leads to proofs -- even if they aren't what you want, computationally.
One downside is the typesetting and the paper-back materials. The typesetting is overly dark and isn't very elegant. The pages of the book are almost stiffer than the covers, so this makes reading the text rather uncomfortable. World Scientific rarely makes books that are superior to Springer, Cambridge with respect to materials and appearance.