Yu.Burman

Complex analysis

1. Local properties of holomorphic functions.
1. Complex differentiation
2. The domain preservation principle
3. Schwartz lemma
2. Global properties of holomorphic functions.
1. Liouville theorem (there are no bounded holomorphic functions)
2. Picard theorem
3. Complex curves
1. Riemann uniformization theorem
2. Classification of elliptic curves
3. Genus of a curve