Using Algebraic Geometry

This course, oriented towards beginning graduate and advanced undergraduate
students, will introduce some basic ideas from Algebraic Geometry, emphasizing
computational aspects and interactions with linear algebra and combinatorics.

We will cover roughly chapters 1-3 and 7 of the text:
"Using Algebraic Geometry" by D. Cox, J. Little and D. O'Shea, Second Edition,
with some additional material from "Solving Systems of Polynomial Equations"
and "Groebner bases and convex polytopes" by B. Sturmfels.

Our principal subject will be solving systems of polynomial equations,
both algebraically and geometrically. 
Two principal computational approaches are based on Groebner 
bases and resultants. For sparse systems solving, connection with
polytopes and toric varieties will be discussed.

Some homework will use Maple, 
but no prior experience with Maple is expected.

Prerequisites: Abstract and Linear Algebra.