MATH 60413 Advanced Complex Analysis
Prerequisites: MATH 50403 and 50503, or equivalents. A rigorous development of the theory of complex analysis. Analytic functions, branches of functions, harmonic functions and Dirichlet problems. Complex integration, Cauchy's Integral Theorem, winding numbers, topology of the complex plane. Taylor series and Laurent series, singularities of analytic functions, and function theory on the extended plane. Conformal Mapping and Riemann Mapping Theorem.