Using Algebraic Geometry


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Mod-01 Lec-01 What is Algebraic Geometry?

The context of Using Algebraic Geometry is not a traditional course in classical algebraic geometry. The audience is expected to consist of graduate students interested in computational aspects of algebraic geometry and others with some mathematical maturity who are curious to know what all the hype surrounding computational algebraic geometry is really about. In other words, the text is written for outsiders, whether they intend to eventually be insiders or not. The goal is to give a good overview of the several algorithms and ideas which make up the contents of the tool bag of computational algebraic geometry and their applications to combinatorics, coding theory and integer programming.


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This reviewer thinks that the part of the intended audience consisting of graduate students interested in research in computational algebraic geometry will find this to be a very useful book. The many exercises throughout the text, and the mere fact that this is a very good and detailed overview of the subject will definitely make it desirable for this group. Mathematicians with some previous exposure to classical algebraic geometry may also find in Using Algebraic Geometry a practical guide to the computational aspects of the subject.


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However, for the group of outsiders who do not really have much experience in algebraic geometry and who only wish to catch a glimpse of what is going on and how to make sense of this new phenomenon, this reviewer would in fact suggest the authors' previous book, the undergraduate text Ideals, Varieties, and Algorithms. This latter text is, unarguably, for undergraduates, but it is also much easier to digest and hence more appropriate for reading on the side if one is not really planning to jump in and start doing reseach in the subject.

In case our outsider finishes Ideals, Varieties and Algorithms and wishes to learn more, Using Algebraic Geometry is a fine second book. Skip to main content. Search form Search.

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Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Physical Description xii, p. Series Graduate texts in mathematics ; Subjects Geometry, Algebraic.

Summary This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grobner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds.

It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases.

Using algebraic geometry

The book does not assume the reader is familiar with more advanced concepts such as modules. Contents Ch. Introduction Ch. Solving Polynomial Equations Ch. Resultants Ch. Computation in Local Rings Ch.

Using Algebraic Geometry

Modules Ch. Free Resolutions Ch. Polytopes, Resultants, and Equations Ch. Integer Programming, Combinatorics, and Splines Ch. Algebraic Coding Theory. Notes Bibliography: p Includes bibliographical references p. View online Borrow Buy Freely available Show 0 more links Set up My libraries How do I set up "My libraries"? Australian National University Library. Open to the public.

Using Algebraic Geometry by David A. Cox

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Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry
Using Algebraic Geometry Using Algebraic Geometry

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