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Rating: 
Summary: This is for people who likes to COUNT
Review: Gosh! This is for people who count, what else does combinatorist do? Before people dismiss me as somebody who dont know hoot about math: I actually took a class with R. Stanley (the author) in college, and had actually used this book (vol 1 though) as a text. The material is highbrow (I agree on the 'hardcore' math part, as some people say) but the main theme of the book is on how to 'count' -- needless to say not in the sense of everyday counting, but in the sense that 'topology' is 'coffee-donut transformation' and 'analysis' is 'honors calculus'. You have to be able to count combinatorially, and comfortable with combinatorial proof to actually learn from this. I like the fact that Stanley asks for combinatorial proof to a some given problems, marking them as unsolved -- he really elevates the status of combinatorial proof, a proof method other mathematicians might dismiss as 'handwaving'. Of course, there are the numbered exercises, according to the level of difficulty: [1] for trivial, [5] unsolved. I saw a professor working in differential topology for 40 years referring to this book -- and first year undergrads thumbing through for exercises marked [1] to solve in spare time. This is a book for all levels of mathematicians: I am sure even the armchair amateur mathematicians can grasp the material after a hard day's thought. I dont see this book as any less than a definitive text on enumerative combinatiorics.
Rating:
Summary: A Masterpiece on Enumerative Combinatorics
Review: I agree with the other reviewers. The book is a masterpiece on enumerative combinatorics. However, I am not so sure that it is a good book for a beginner. If you are a beginner, then you should read another book first, like John Riordan's book on "Combinatorial Analysis." Stanley's book is best suited for an advanced student who has a high level of mathematical mental maturity. The reason I say this is that in a few places Stanley's formalism, which is entirely appropriate for professional exposition, actually obscures the underlying simplicity of the mathematical ideas. We have all seen this in research papers, where a mathematician takes a trivial idea and "obsures" the underlying simplicity with too much formalism. However, for an advanced student, the book has a high density of important ideas and methods.
Rating:
Summary: People who like to COUNT?!? People who like hard-core math.
Review: There was an earier review that claimed this book is for "people who like to count." That's a little silly. This book is a rigorous math text. And it's glorious. It's probably my favorite text. But it's not light reading at all.I spent a semester actively reading and working on this book with my advisor. I read this book and worked on research, 50/50 split on my time. I got through 2.5 of the 4 chapters, and I'm damn proud of myself. It's a great book, but if you didn't know that 'enumerative' was for "people who like to count", you probably want a different text.
Rating:
Summary: People who like to COUNT?!? People who like hard-core math.
Review: There was an earier review that claimed this book is for "people who like to count." That's a little silly. This book is a rigorous math text. And it's glorious. It's probably my favorite text. But it's not light reading at all. I spent a semester actively reading and working on this book with my advisor. I read this book and worked on research, 50/50 split on my time. I got through 2.5 of the 4 chapters, and I'm damn proud of myself. It's a great book, but if you didn't know that 'enumerative' was for "people who like to count", you probably want a different text.
Rating:
Summary: A Classic!
Review: This book is a must for anyone who likes how to count. In addition to the superb exposition of deep and important mathematics, it contains so many intriguing problems, some of them even puzzle-like. Read this book cover-to-cover or open it at a random page. Either way you would love it!
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