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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) Hardcover – February 24, 2006

ISBN-13: 978-0387946801 ISBN-10: 0387946802 Edition: 2nd

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Hardcover, February 24, 2006
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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 556 pages
  • Publisher: Springer; 2nd edition (February 24, 2006)
  • Language: English
  • ISBN-10: 0387946802
  • ISBN-13: 978-0387946801
  • Product Dimensions: 9.2 x 6.4 x 1.4 inches
  • Shipping Weight: 2 pounds
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #644,938 in Books (See Top 100 in Books)

Editorial Reviews

Review

"I consider the book to be wonderful...The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging...offers the heart and soul of modern commutative and algebraic geometry." -The American Mathematical Monthly

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Most Helpful Customer Reviews

12 of 12 people found the following review helpful By A Customer on April 8, 2002
Format: Hardcover
Having just finished using this text in the course of an undergraduate seminar, I can attest to the fact that the authors' style is outstanding - they are able to synthesize an enormous amount of material in this volume and present it in a manner that is highly accessible to almost all students of mathematics. The presentation of important theorems (for example, Hilbert's Nullstellensatz and Basis Theorem) along with just the right amount of copncrete examples makes for a book of superb quality. All-around, I highly recommend this volume to anyone who has an interest in learning about Algebraic Geometry.
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10 of 10 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on May 26, 2001
Format: Hardcover
I don't have the second edition of this book but did read the first, and the authors do a fine job of introducing the reader to the computational side of algebraic geometry. I will forego a chapter by chapter review therefore, but no doubt the second edition (which I do not own) is as well-written as the first. I would recommend it to anyone interested in the many applications of algebraic geometry and to those who need to understand how to compute things in algebraic geometry. The good thing about this book is that it gives a concrete flavor to a highly abstract subject. Algebraic geometry, through its applications to coding theory, cryptography, and computer graphics, is fast becoming the subject to learn. It is no longer just an esoteric, high-brow subject but one that is taking on major importance in the information age. Even without applications though it is a fascinating subject, and readers will get a taste of this in this book.
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11 of 12 people found the following review helpful By The Polar Bear on April 23, 2003
Format: Hardcover
This is the easiest introduction to algebraic geometry and commutative algebra, the authors had done a great job in writing a book that assume very little from the readers. To learn some algebraic geometry, you can either start with this book, or you can spend a year to read a lot of background materials in algebra and then go to a Graduate Text like Harris' book. Of course, if you want to be an expert in algebra, you eventually need a lot of background, what this book can help you is to offer you a quick start, much quicker than you would ever imagine.
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7 of 7 people found the following review helpful By David L. Elliott on August 28, 2003
Format: Hardcover Verified Purchase
This book explains and illustrates the algorithms used by symbolic math packages such as Mathematica, Maple, CoCoA, MatLab, MuPAD,... to solve problems involving polynomials in many variables, and along the way teaches the elements of real algebraic geometry-- most mathematics texts concentrate on the complex-variable version. It is not just for undergraduates; electrical engineers, for instance, should see it. Lots of pictures!
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