Office Hours: M 1:00--1:50 and W 5:15--6:15 HH 222, after class, and by appointment. You may email me or call (631-7165) to set up appointments.
Text: Cox, Little, and O'Shea, Ideals, varieties, and algorithms (4th edition)
Class Time: MWF 11:30--12:20, Pasq 116.
Course syllabus pdf file
We will study solutions of polynomial equations, and especially
the geometric properties of sets where a collection of polynomials
are zero. An interesting aspect of this field is the interplay between
algebra and geometry. For example, singularities of a curve can be studied using
the algebra of the ring of functions on the curve. Also, the number of intersection
points between two curves can be studied using properties of ideals,
which are nice subsets of polynomial algebras. We will review the
basic notions from algebra that are needed, such as rings, ideals,
and quotient rings, and see how these can be explicitly computed
in examples. We will also study the problem of intersection points
at infinity via projective varieties. Throughout the course, we
will introduce and develop commutative algebra.
My intention is to cover parts of chapters 1, 2, 3, 4, 5, 8, and 9
of Cox, Little, and O'Shea, but I won't necessarily do everything in order. I'll do my best to be clear about where you can read about the material I am
covering.
Exams :
Grades :
Assignments:
Homework and in-class problems will appear here, and also be distributed in class. Assignments with a date are due on the indicated date.