# Grad school preparation: Should I take a probability class?

• Schools
I am (hopefully!) going to be entering grad school in the fall. I will be going for a PhD in applied mathematics. Many grad schools recommend that you take a course in probability before entering (it is strongly hinted that doing so will improve your odds of admission). Here's where the wrinkle comes in. I'm double majoring in math and physics. Within the physics department, I have had several classes that utilized and derived probability distributions (e.g. quantum mechanics, statistical mechanics, thermodynamics). As a result, I've had a good deal of probability in my time as an undergraduate. In addition, I took AP Statistics waaaay back in my junior year of high school, so I've had a "formal" statistics class. Here is the course description of my school's Introduction to Probability class (listed as Statistics 4321, so it's an upper level course):

Introduction to the theory of probability, counting rules, conditional probability, independence, additive and multiplicative laws, Bayes Rule. Discrete and continuous random variables, their distributions, moments and moment generating functions. Multivariate probability distributions, independence, covariance. Distributions of functions of random variables, sampling distributions, central limit theorem
The only thing in this description that I have not had in some class or another is moments and moment generating functions. So my question is: Should I take this formal probability class in order to show that I've had it and maybe learn a couple of things I didn't know before but largely hit on topics I've already covered, or should I take a different class? Moreover, would not taking this class damage my grad school applications?

Thanks so much for your opinions!

If grad schools are explicitly saying that it helps your application, who are we to contradict them?

In addition, I took AP Statistics waaaay back in my junior year of high school, so I've had a "formal" statistics class.
All due respect to your high school teachers, I don't think this counts.

or should I take a different class? Moreover, would not taking this class damage my grad school applications?
Is there some reason you *don't* want to take probability? What would you take instead?

The course looks quite good to me, ideas in statistics will surely come in useful at some point if you're studying an applied subject. Not only that, I'd say that probability/statistics are both underestimated/understudied/under-appreciated by undergraduate students in general, at least it is in my experience within the UK. Unless there's some dream course you'd be missing out on in place of this one, I say take it. There's no harm in reinforcing the ideas you've learned in physics from a mathematicians point of view, and you may well have to take another probability/stats class in grad school so this would be good preparation.

If you have a physics undergraduate and are applying to a Ph.D. in applied math, then it will help your application a lot if you have coursework in probability and statistics. Probability and statistics is something that is extremely weak in the undergraduate physics curriculum.

Part of the reason I think (and the admissions committees) seem to think that a course on probability and statistics would be useful is that you learn what it is that you don't know.

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If grad schools are explicitly saying that it helps your application, who are we to contradict them?
+1

All due respect to your high school teachers, I don't think this counts.
+1

I have a PhD in physics, and I have taken several probability classes offered by mathematics departments. There is no comparison. The probability you pick up along the way is a) very superficial, and b) lacking in rigor and proofs.

Yes, take Probability. I'm taking it in the Spring.