PhD in Probability

[Pi is Exactly 3]

I am currently a Masters student in statistics, hoping to eventually do research in applied probability. Two fields that particularly interest me are Mathematical Biology and Mathematical Physics, but of course this isn't set in stone.

 

I was wondering what I should do to prepare myself for applications to PhD programs in probability. Should I apply to applied math departments or statistics departments? Also, what kind of courses should I take? I have the option of taking two of the following graduate courses (I will definitely be taking graduate real analysis):

 

1) Complex Analysis

2) Functional Analysis

3) PDEs

4) Numerical Analysis

5) Statistical Mechanics

6) Mathematical Physics

7) Combinatorics

 

I should note that my school's functional analysis course has both real and complex analysis as prerequisites. Any advice would be greatly appreciated. 

Edited June 21, 2014 by Pi is Exactly 3

[Stat Assistant Professor]

You could apply to both math and stat departments if your interests are in probability.

 

I vote for PDEs (there is some cool research going on now about stochastic differential equations and stochastic PDEs). I'd also recommend a graduate-level one year probability-statistics sequence (if you have not already taken it).

[Pi is Exactly 3]

You could apply to both math and stat departments if your interests are in probability.

 

I vote for PDEs (there is some cool research going on now about stochastic differential equations and stochastic PDEs). I'd also recommend a graduate-level one year probability-statistics sequence (if you have not already taken it).

 

Thanks for the response! I've been told that probability theorists are generally scattered in different departments (applied math, statistics, operations research, engineering, etc.), but are mostly found in math departments. 

 

My program requires the probability-statistics sequence, as well as a few other applied statistics courses, so I will definitely be taking those courses. Thanks for the PDEs suggestion. 

 

I've also been told that Numerical Analysis is probably the least important of the above sequences, but wouldn't it be important for applied math applications?

Edited June 21, 2014 by Pi is Exactly 3

[StatsGuy92]

Thanks for the response! I've been told that probability theorists are generally scattered in different departments (applied math, statistics, operations research, engineering, etc.), but are mostly found in math departments. 

 

My program requires the probability-statistics sequence, as well as a few other applied statistics courses, so I will definitely be taking those courses. Thanks for the PDEs suggestion. 

 

I've also been told that Numerical Analysis is probably the least important of the above sequences, but wouldn't it be important for applied math applications?

 

Yeah I've taken Numerical analysis a few semesters ago and I would say that it is rather unimportant/irrelevant in probability/statistics.

Basically you learn different algorithms to approximate the solution of non-linear equations or complicated differential equations, but nowadays most of these calculations are done by any standard computer package with mathematical applications (even Excel!).

Numerical analysis is probably most important for people who study computer science with a concentration on the computational aspects of software.