**Several
Complex Variables:Math 567, Spring 2012**

**Instructor **John E. M^{c}Carthy

**Class **
MWF 3.00-4.00 in 216 Cupples I

**Office **
105 Cupples
I

**Office Hours** MF 11:00-12:00, W 9:15 -10:00

**Phone **
935-6753

**Prerequisites** The
pre-requisites for the course are 5021-5022 and 5051-5052.

Interested students who are taking 5022 and
5052 concurrently are welcome.

**Content**

We shall
cover the basic theory of holomorphic functions of
several variables.

Historically, there
have been five different approaches to their study, each one being useful

for different sorts
of questions. These are methods of power series, integral kernels, sheaf
theory,

d-bar, and operator
theory. We shall try to give the flavor of all five methods.

**Basis for Grading**

Grades are based on attendance and class participation.

**Bibliography**

The following is a brief bibliography you may find useful.

R.C.
Gunning * Introduction to holomorphic
functions of several variables, Vols. I-III*

L. Hormander * An introduction to complex analysis in
several variables*

S.G.
Krantz * Function Theory of Several Complex Variables*