MATH 6120 Complex Analysis

Minimum Syllabus

1. Elementary Properties of Holomorphic Functions.
2. Cauchy-Riemann equation, mean value property, harmonic functions.
3. Schwarz lemma, maximum modules theorem.
4. Runge’s approximation theorem.
5. Conformal mapping, normal families of holomorphic functions, Riemann mapping theorem.
6. Mittag-Leffler theorem, Weierstrass theorem in existence of functions with prescribed zeroes.
7. Analytic continuation.

Optional Topics

Depending on the instructor, different optional topics are covered.

1. The equation ∂f / ∂{\bar z} = g.
2. Riemann surfaces.
3. Distribution theory.
4. Several complex variables.
5. Prime number theorem.
6. Introduction to complex dynamics.
7. Uniformization theorem.