Using Algebraic Geometry

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. One of the aims of this text is to illustrate the various uses of algebraic geometry and to highlight the more recent applications of Groebner bases and resultants. In order to do this, an introduction to some advanced algebraic objects and techniques is provided.