Using Algebraic Geometry (original) (raw)

Overview

Authors:

• John Little 1,
• Donal O’Shea 2

1. David Cox
   1. Department of Mathematics and Computer Science, Amherst College, Amherst, USA
2. John Little
   1. Department of Mathematics, College of the Holy Cross, Worcester, USA
3. Donal O’Shea
   1. Department of Mathematics, Statistics and Computer Science, Mount Holyoke College, South Hadley, USA

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About this book

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 Gr"obner 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 Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

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Table of contents (9 chapters)

1. Introduction

   • David Cox, John Little, Donal O’Shea
     Pages 1-23

2. Resultants

   • David Cox, John Little, Donal O’Shea
     Pages 71-129

3. Modules

   • David Cox, John Little, Donal O’Shea
     Pages 179-233

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Authors and Affiliations

• Department of Mathematics and Computer Science, Amherst College, Amherst, USA

David Cox

• Department of Mathematics, College of the Holy Cross, Worcester, USA

John Little

• Department of Mathematics, Statistics and Computer Science, Mount Holyoke College, South Hadley, USA

Donal O’Shea

Bibliographic Information

• Book Title: Using Algebraic Geometry
• Authors: David Cox, John Little, Donal O’Shea
• Series Title: Graduate Texts in Mathematics
• DOI: https://doi.org/10.1007/978-1-4757-6911-1
• Publisher: Springer New York, NY
• eBook Packages: Springer Book Archive
• Copyright Information: Springer Science+Business Media New York 1998
• eBook ISBN: 978-1-4757-6911-1Published: 17 April 2013
• Series ISSN: 0072-5285
• Series E-ISSN: 2197-5612
• Edition Number: 1
• Number of Pages: XII, 503
• Topics: Algebraic Geometry, Combinatorics

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