Customer Reviews

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra

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This is the 3rd edition of a popular reference on the subject. There was some production error with earlier version of the book. Even with the latest version, the authors have provided 14-page worth of corrections for the 1st printing of the 3rd edition. See www.cs.amherst.edu/~dac/iva/3ed1.pdf.
So buyers may be better off waiting for a corrected later version from the publisher.

This book explains the concepts well and the proofs are written carefully and clearly. This is a math book, so you should expect the usual Definition-Theorem-Proof format, but the exposition is progressive, and the material is very well motivated. I had to implement an algorithm for the computation of Groebner bases, and I borrowed this book from the University library to learn about the Buchberger algorithm and related topics, and thanks to this book I was able to understand this algorithm and its correctness proof without the help of anyone. Of course Buchberger's algorithm is only a small part of this book, and you can find a lot of important topics in it.
Finally, note that the second part of Madhu Sudan's Algebra and Computation course at MIT follows this book closely. So at least one top expert in the field seems to have a good opinion of the book.

I actually haven't gone through the entire book, but the parts that I did go through were interesting. The book was (I thought) a little confusing to understand, but that may just be because it is for higher level abstract math. Lost of proofs and interesting things if your interested in abstract math!