# Math 6283 - Several Complex Variables

Lecture: TR 10:30–11:45am in MSCS 428

Problem session: F 1pm–2pm in MSCS 428

## Lecture Notes:

In lieu of a textbook, we will be using my lecture notes, which can be downloaded below. They will be updated frequently, so probably best to read them online or print out only the relevant new bits. I will be putting them together as the semester is going so they will never be complete and new stuff will be added only as I prepare each lecture. I will probably be fixing typos and still updating them even after lecturing on a particular material.

## Homework:

1. (For Jan 31): Let's look at all exercises in the notes until the complex chain rule for next week. That is, all exercises up to exercise 1.2.7.
2. (For Feb 7): Exercises in the notes until exercise 1.3.2. (Make sure to look at the current pdf, I've just updated it and added a few exercises)
3. (For Feb 14): Exercises in the notes until exercise 1.4.8.
4. (For Feb 21): Exercises in the notes until exercise 1.6.1.
5. (For Feb 28): Exercises in the notes until exercise 1.6.7.
6. (For Mar 7): Exercises in the notes until exercise 1.6.12.
7. (For Mar 28): Exercises in the notes until exercise 2.4.25 (numbering changed).
8. (For Apr 4): Exercises in the notes until exercise 2.5.7.
9. (For Apr 11): Exercises in the notes until exercise 3.2.2.
10. (For Apr 18): Exercises in the notes until exercise 3.3.5.
11. (For Apr 25): Exercises in the notes until exercise 3.4.7.

## Useful Books for Reference:

1. Albert Boggess, CR manifolds and the tangential Cauchy-Riemann complex, CRC Press, 1991, MR1211412.
2. John P. D'Angelo, Several complex variables and the geometry of real hypersurfaces, CRC Press, 1993, MR1224231.
3. Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall Inc., 1965, MR0180696.
4. Lars Hörmander, An introduction to complex analysis in several variables, North-Holland Publishing Co., 1990, MR1045639.
5. Steven G. Krantz, Function theory of several complex variables, Wadsworth & Brooks/Cole Advanced Books & Software, 1992, MR1162310.
6. Walter Rudin, Function theory in the unit ball of Cn, Springer-Verlag, 1980, MR601594.
7. Hassler Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., 1972, MR0387634.