Choosing Courses for my Junior Year

[discreature]

Hello All. I'm going to be applying to Stats Ph.D programs in Fall 2021 (for hopeful admission to Fall 2022). Right now though, I'm planning my classes out for Junior Year and I've got a few hang-ups. Basically, Between the following set of classes I can choose one (all likely taught fall):

• Measure-Theoretic Probability Theory (First required probability class for Ph.Ds) 
  • Likely the one that would "look best" when applying, but also the most time consuming. Furthermore, I don't think it's super expected that I take this since it's Ph.D Level? I guess there's some worry that I should be focusing on the fundamentals before going this deep.
• Abstract Algebra (Group and Ring Theory)
  • Probably the one that's least relevant to Stats, but I haven't taken Algebra before and I plan to take the Math GRE (intend to apply to Stanford) and feel that this could do good for my score. Also, at the very least this might convey mathematical maturity?
• Linear Dynamical Systems (Would be my first applied Linear Algebra course, and the required prereq for our optimization course)
  • Probably the one I'm most interested to take at this stage. Covers some signal processing stuff, and I think it would be good to have a strong performance in Linear Algebra that is recent (my previous Linear Algebra course will have been almost 2 years old when I apply)

And also can choose one between the following set of classes (all likely taught winter):

• Functional Analysis
  • Seemingly helpful for Stats? Not super direct, but I think also probably flexes Lin Alg and mathematical maturity.
• Number Theory
  • Same argument as Abstract Algebra.

Also,  notably, I'll likely take the courses not taken this year next year (so the fall courses might appear on some applications depending on due dates). Let me know if you have any thoughts on these choices or any other questions! Thank you in advance.

[kingsdead]

Hey full disclosure; I'm not yet a grad student so I don't know how much you should value what I have to say. But IMO, abstract algebra isn't too important for the subject test. It's never more than a few questions - you can always get >90th percentile by doing well on the other questions. So I definitely wouldn't recommend taking abstract algebra (or number theory) just for the sake of doing well on the subject test. If you have some personal interest in the classes, that's different, but those classes aren't particularly relevant for statistics unless you do something specialized like algebraic statistics.

Between the others, it sounds like you could spread them out between fall 2020 and fall 2021. I think you'd get more out of functional analysis if you have a better measure theory background first, but I don't think the ordering is particularly important.

Just my $.02!

Edited July 2, 2020 by kingsdead