Prove the Cauchy integral representation of analytic functions and use it to discover and prove advanced properties of analytic functions. How well did you achieve this learning goal in this course?
Relate properties of an analytic function to the geometry of the associated mapping, and use the geometry of analytic functions to solve function-theoretic problems (e.g., counting zeros) as well as prove results about mappings (e.g., one-to-one and onto properties of conformal mappings). How well did you achieve this learning goal in this course?
Master the proofs of several classical theorems in complex analysis, such as: the Riemann mapping theorem, theorems about elliptic functions, applications of analytic functions, and properties of the Riemann zeta function. How well did you achieve this learning goal in this course?