Book,
Using Algebraic Geometry
Graduate Texts in Mathematics Springer, First edition, (1998)
DOI: 10.1007/978-1-4757-6911-1
Abstract
In recent years, the discovery, of new algorithms for dealing with polynomial equations, coupled with their implementation on inexpensive yet fast computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods and techniques have also given rise to some exciting new applications of algebraic geometry.
One of the goals of this book is to illustrate the many uses of algebraic geometry, and to highlight the more recent applications of Groebner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques more advanced than one typically encounters in a first course, but which are nonetheless of great utility. This book is accessible to nonspecialists and to readers with a diverse range of backgrounds.
This book is written at the graduate level and hence assumes the reader knows the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
