Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) | 
 enlarge | Authors: David Cox, John Little, Donal O'shea
Publisher: Springer
Category: Book
List Price: $59.95
Buy New: $34.99
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Rating:  6 reviews
Sales Rank: 745504
Media: Hardcover
Edition: 2nd
Pages: 556
Number Of Items: 1
Shipping Weight (lbs): 2
Dimensions (in): 9.2 x 6.4 x 1.4
ISBN: 0387946802
Dewey Decimal Number: 516.35
EAN: 9780387946801
Publication Date: February 24, 2006
Availability: Usually ships in 1-2 business days
Condition: New
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Product Description
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing a new edition of Ideals, Varieties and Algorithms the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple , Mathematica and REDUCE.
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| Customer Reviews: Read 1 more reviews...
Straightforward and lucidly written April 9, 2002
9 out of 9 found this review helpful
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.
Easiest introduction to Algebraic Geometry April 23, 2003
The Polar Bear (NY United States)
9 out of 10 found this review helpful
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.
Symbolic computation August 29, 2003
6 out of 6 found this review helpful
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!
The best book on the topic January 26, 2001
8 out of 9 found this review helpful
I learned the basics of Groebner bases from this book and its the best introductory book on this topic. Authors have explained all concepts with the help of examples which makes it readable for people from other fields also. It also talks about applications of Groebner bases to other fields. The book gives lot of exercises which help in understanding the contents more. I recommend that if you wish to learn Algebraic Geometry and Groebner bases then this is the book to start with.
Wonderful textbook. May 26, 1999
11 out of 18 found this review helpful
This is an exquisite textbook. It introduces the reader to a wonderful part of mathematics that is not very often taught at the undergraduate level. Without it being too involved, it covers a lot of material, explains difficult concepts with remarkable ease and involves applications that help the reader obtain a perfect idea for the subject. Highly recommended.
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