Helpful Math?

[discreature]

A lot of things I hear seem to suggest that math background is vital for Stats Ph.D admission, but this usually boils down into just Calculus, Linear Algebra, Real Analysis, and Probability. I was wondering what additional math courses would be helpful? I'm a math major who has completed these courses but still has over a year to go. There are some more advanced stochastic processes courses and some upper-div real analysis courses I'm interested in, but I wonder if this will have diminishing returns. In that case, would it be useful to take more stats methods courses? Or do admissions committees like any sort of math (e.g. Abstract Algebra, Number Theory)?

[Stat Assistant Professor]

Calculus I-III, Linear Algebra, and Real Analysis are the bare minimum you need for most Statistics PhD programs. However, more math beyond the bare minimum is always helpful in boosting your application. So strong performance in classes like abstract algebra, number theory, and complex analysis are definitely viewed positively by adcoms, as they signal mathematical maturity even if these subjects are not directly applicable to statistics. I would thus encourage you to take more math to boost your application. The only upper division statistics classes that are very helpful for Statistics PhDs are Calculus-based probability and statistical inference (at the undergrad level). These might make the first-year Casella & Berger mathematical statistics sequence somewhat easier. 

Some of the more "relevant" upper division math classes to Statistics are numerical analysis, advanced (proof-based) linear algebra, and optimization.  

[StatsG0d]

Totally agree with @Stat Assistant Professor, and I would add that taking some CS classes will also be useful. In particular, Object Oriented Programming and Data Structures / Algorithms will help you out a lot, even if they don't boost your application (they will make your dissertation life easier).