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Enumerative Combinatorics, Vol. 1 (Cambridge Studies in Advanced Mathematics)
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Enumerative Combinatorics, Vol. 1 (Cambridge Studies in Advanced Mathematics) Customer Reviews
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♥♥♥♥♥
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Very challenging, very deep
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This is an excellent book on combinatorics, but it is quite difficult to understand--written for experts, not novices. The author often chooses a more general framework in which to present things, and this can make the material quite difficult to follow. But the rewards for the diligent reader are great. Occasionally I question how Stanley chooses to present a certain topic, but usually if I look closely enough, I see that there are deep reasons for his choice of notation or presentation.
Some of the material in this book is easier than others; some of it depends on earlier chapters, but some stands on its own. People interested in partially ordered sets and lattices may want to jump ahead to that chapter--much of this chapter stands on its own, and it is an excellent exposition of that topic, and I think somewhat easier to understand than the rest of the book.
The most precious thing about this book is that the author manages to provide several comprehensive frameworks for solving large classes of enumeration problems. Combinatorics seems a hodge-podge subject to many mathematicians, but Stanley manages to see it as a unified subject with a number of general theories and common techniques. This book is truly the only text I have ever read that has this perspective on the subject.
I would recommend this book only to someone who has a strong background in mathematics and wants a challenging text that can take them to a deeper level of understanding. Students of combinatorics may want to take this book out of the library and read the introductory pages; there are some particularly useful comments right at the beginning. As a final note, the exercises in this book are also helpful and of diverse difficulty levels--and Stanley classifies the exercises by their difficulty level. People who find this book difficult to follow may want still benefit from some of the easier exercises. Students wanting an easier-to-follow text might want to check out Cameron's "Combinatorics", or Wilf's "Generatingfunctionology". As a final note I would like to remark that this book is very reasonably priced, especially when you consider the wealth of material it contains. |
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