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I asked my research group recently what they wished they had learned before they started work on a PhD. Here are some of the responses.

More mathematics. Particular topics they named included real analysis, functional analysis, measure theory, algebra, linear algebra. That would have been my response also. I still wish I knew more mathematics than I do. I did quite a lot of mathematics as an undergraduate, but every year I need to learn some more.

More English. Most of my group speak English as a second language, so this is understandable. I don’t think there is any short-cut when trying to master a new language — just speak, read and write in it as much as possible.

More about efficient programming, especially memory issues, avoiding do-loops in R, developing complex code. I think a basic programming course using R should be a compulsory unit in modern statistics and econometrics undergraduate degrees. Surely everyone needs to know how to code in R these days. That said, we don’t have such a subject at Monash yet. If you need help in this area, there are some good texts available including Introduction to Scientific Programming and Simulation Using R by Jones, Maillardet & Robinson.

More nonparametric smoothing and Bayesian statistics (as distinct from classical statistics). I think this is a legacy of undergraduate curricula not keeping up with statistical development. However, there will always be some areas of statistics that you have not covered but find you need. When you do statistical research you should expect to have to master some areas on you own, either because it was not covered in your formal training, or because the topic didn’t exist when you did your formal coursework. The trick is to find a good textbook and give yourself the time to read it carefully.

I’m interested if any readers have additions for this list.

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