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 ∂/ ∂{\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.