General Topology vs Complex Analysis?

[galois]

Hi all. I'm applying for Fall 2019 to mostly statistics programs, but a couple applied math as well. I'm currently working full time,  but I think I have time in my schedule to take one class at the local college where I live. I can chose between Complex Analysis and General Topology.

Complex Analysis: This course provides a proof-based introduction to Complex Analysis. Topics include the complex number system, analytic and harmonic functions, power series, integrations, residue theory, analytic continuation, conformal mapping, and applications.

General Topology: This course provides an introduction to general topology. Topics include the generation of topological spaces, continuity, connectedness, compactness, separation and countability.

Thoughts on which I should take to best prep me up for next Fall? My motivation is mostly to shake off the dust, but I'd also like to consider what knowledge will be most valuable to me. (I have taken a "Complex Functions" course where I learned many of the common things you'd see in an introductory class, but it was not taught in an analysis style, so as to be more accessible to students outside the department. I have not studied topology formally.)

[Stat Assistant Professor]

Either of those would look good on a transcript, so take the one that interests you more. In either case, you would get a lot of good practice with doing mathematical proofs, which will be an essential skill in at least the coursework phase of a PhD program (if you end up doing something more "applied" for your thesis research, you might not need to bog down in so many theorems, but a lot of the core courses tend to be theoretical).

I don't think you need to know much about either for statistics research... you do sometimes see imaginary numbers and Cauchy's integral formula (namely stuff related to Fourier series), and some concepts from topology, like countability and compactness (namely as they apply to parameter spaces), etc., but I wouldn't say a very deep understanding of either complex analysis or topology is needed in most cases. However, the technical skills gained from doing proofs in these classes will definitely be helpful.

Edited January 5, 2019 by Stat PhD Now Postdoc