Recommended program: Complex analysis

Don Marshall and Steffen Rohde

First Year
534 535 536 (Complex Analysis)
524 525 526 (Real Analysis)
554 555 556 (Linear Analysis)
Second Year
A one-year topics course in complex analysis
plus two of the following:
521 522 523 (Advanced Probability)
527 528 529 (Functional Analysis)
544 545 546 (Topology and Geometry of Manifolds)
537 538 539 (Several Complex Variables)
557 558 559 (Introduction to Partial Differential Equations)
A course in ergodic theory/dynamical systems, if offered
ADDITIONAL COMMENTS:
Somewhere learn about elementary homotopy theory and uniformization. It is sometimes covered in 536, but if it is left out of that course, you should take Topology and Geometry of Manifolds.