- 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: 15 customer reviews
- Amazon Best Sellers Rank: #228,086 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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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.