  This tutorial illustrates how to use Grayson and Stillman's computer algebra
system, Macaulay2, to study schemes. The examples are taken from the homework
for an algebraic geometry class given at the University of California, Berkeley
in the fall of 1999. This graduate course was taught by the second author with
assistance for the first author. Our choice of problems follows the material in
Eisenbud and Harris' textbook, The Geometry of Schemes.
