I previously acted as a review instructor to help incoming students prepare for this written exam at Rutgers. General information about the written qualifying exams can be found here:

https://www.math.rutgers.edu/academics/graduate-program/program-requirements/requirements-for-the-doctoral-degree/written-qualifying-exam

The main reference for the review is Stein, E.M., & Shakarchi, R. Complex Analysis, Princeton University Press (2003).

You can find some of my materials from this time below:

• Collection of all exams pre-Fall 2026 can be found here.

• Solutions to select previous qualifying problems can be found here.
  (Be aware that there may be errors! Please feel free to email me if you find any or want to contribute any of your own answers)

• A brief systematic guide to contour integration can be found in Ahlfors' book or here.

• A nice explanation of the argument principle, both as a way to count zeroes and poles as well as a way to track the change in argument, can be found here.

• A conformal mapping visualizer can be found here.