Using Algebraic Geometry

Graduate Texts in Mathematics #185

by David A. Cox, Donal O'Shea, John B. Little

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 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. 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."

Genres: Mathematics

12 pages, Paperback

First published January 1, 1998

About the author

David Archibald Cox (born September 23, 1948 in Washington, D.C.) is an American mathematician, working in algebraic geometry.

Cox graduated from Rice University with a Bachelor's degree in 1970 and his Ph.D. in 1975 at Princeton University, under the supervision of Eric Friedlander (Tubular Neighborhoods in the Etale Topology). From 1974 to 1975, he was assistant professor at Haverford College and at Rutgers University from 1975 to 1979. In 1979, he became assistant professor and in 1988 professor at Amherst College.

He studies, among other things, étale homotopy theory, elliptic surfaces, computer-based algebraic geometry (such as Gröbner basis), Torelli sets and toric varieties, and history of mathematics. He is also known for several textbooks. He is a fellow of the American Mathematical Society.

From 1987 to 1988 he was a guest professor at Oklahoma State University. In 2012, he received the Lester Randolph Ford Award for Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First.