Theoretical / proof-based
Complex analysis · Graduate · Math
Topics
Holomorphic and meromorphic functions
- Review of analytic functions; identity and open mapping theorems
- Singularities, residues, and the argument principle
- Normal families and Montel's theorem
- Riemann mapping theorem (proof outline)
- Elliptic functions (introduction)
Several complex variables (introduction)
- Holomorphic functions of several variables
- Hartogs phenomenon and domains of holomorphy (overview)
- Plurisubharmonic functions (introduction)
- Cauchy–Riemann equations in higher dimensions
- Stein manifolds (preview)
Riemann surfaces and advanced topics
- Riemann surfaces: definitions and examples
- Uniformization theorem (statement)
- Divisors, line bundles, and sheaves (introduction)
- Hodge theory on Riemann surfaces (optional)
- Nevanlinna theory (optional capstone)
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$1,162 · Complex analysis · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.