Using Algebraic Geometry

David A. Cox, John Little, Donal O'Shea - Collection Graduate Texts in Mathematics

568 pages, parution le 15/10/2004 (2^eme édition)

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Résumé

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner 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 Gröbner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text.

Written for: Graduate mathematics students, mathematicians, computer scientists, engineers

L'auteur - David A. Cox

DAVID A.COX is a professor of mathematics at Amherst College. He pursued his undergraduate studies at Rice University and earned his PhD from Princeton in 1975. The main focus of his research is algebraic geometry, though he also has interests in number theory and the history of mathematics. He is the author of Primes of the Form x² + ny², published by Wiley, as well as books on computational algebraic geometry and mirror symmetry.

L'auteur - John Little

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Sommaire

Introduction
Solving Polynomial Equations
Resultants
Computation in Local Rings
Modules
Free Resolutions
Polytopes, Resultants, and Equations
Integer Programming, Combinatorics, and Splines
Algebraic Coding Theory
The Berlekamp-Massey-Sakata Decoding Algorithm

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	David A. Cox, John Little, Donal O'Shea
Collection	Graduate Texts in Mathematics
Parution	15/10/2004
Édition	2^eme édition
Nb. de pages	568
Format	15,5 x 23,5
Couverture	Broché
Poids	825g
Intérieur	Noir et Blanc
EAN13	9780387207339
ISBN13	978-0-387-20733-9