Customer Reviews

Combinatorics and Commutative Algebra (Progress in Mathematics)

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Great book - just be ready to get hold of some other books to fill in the details. If you're not entirely comfortable with the stuff in chapter 0 concerning modules (projectivity, injectivity), tor and ext, and homology from topology, maybe find a quick introduction to these elsewhere - while its certainly possible to learn about these things from chapter 0 of this book, it's not exactly the most painless way to do it. It was my first book on the subject, then I got Miller and Sturmfels: it would make more sense to reverse that order. Better still, get both simultaneously, and when the Stanley becomes a bit dense refer to M+S. I really loved this book, but it was damn hard at times!

For those looking for a thorough introduction to the theory in this book, I would suggest a look at Miller and Sturmfels recent book on combinatorial commutative algebra or the book on Cohen-Macaulay rings by Bruns and Herzog. This is a great book, but I don't think it was intended as a beginners first book . Instead its style concentrates on presenting results found in research-articles ( prior to this book, there doesn't seem to have been any texts giving an overview of the theory ). It is great for looking up results, reading the needed prerequisites without going into details and finding important references.