Are other upper-division math courses besides real analysis helpful?

[Lp_space]

I am a junior year student in one of the top 10 universities in the US and I am planning on applying to Statistics PhD for 2021 entry. I am looking for your advice to further strengthen my profile. Currently I have taken linear algebra, the undergraduate real analysis sequences and the mathematical statistics sequences. Next year, I have the option to take more upper-division math courses such as abstract algebra, complex analysis and geometry. I also have the option to take the graduate mathematical statistics sequences and possibly some other stat courses like GLM and stochastic processes. For the purpose of admission, which option looks better? 

[Geococcyx]

I'm not the expert, so look for future posts for more veteran forum members, but I can at least give a first pass.

In a vacuum, yes, the other upper-division math courses are helpful.  Getting high grades in proofs-based classes will be helpful to your profile.  However, I also think the graduate math stat sequence would be helpful, particularly if it's taught out of Casella and Berger (or so my impression would be, from this forum).  As for the other stat courses, if they're at the grad level then they might be helpful, but if they are undergrad then I don't know that they'd do much for you.  

If you are just trying to give yourself the strongest possible admissions profile for a Stat PhD, then I'd personally recommend taking the graduate math stat sequence plus an upper-division math course or two (there are some applications of algebra and geometry in statistics, for instance).  This is with me not being sure what level the other stat classes are at, but I think this is probably the most reasonable option overall.  If you have low grades in past proofs-based classes, then the importance of other upper-division math courses requiring proofs would probably increase.

 

[bayessays]

No specific math course, beyond RA, will help you enough in admission where you should worry. I'd say beyond mastering basic probability, knowing some optimization/numerical analysis/linear algebra is going to get you the most use during your program though, so it will help to learn that.  Taking advanced abstract algebra or complex analysis might make you slightly better at proofs in some general sense, but if you don't actually want to take it, it's not really going to help you.

 

Edit: obviously taking graduate math stat will likely be the most directly useful, although topics vary between schools quite a bit.  If you go to a school with a good PhD program, acing the grad math stats and getting a good letter would be a big plus

Edited June 23, 2019 by bayessays