Courses to take during pure math masters to keep data science and applied work as a possibility I was wondering what courses you can take in a pure math masters to preserve the opportunity to go into data science, economics, policy research or other applied work while preserving the opportunity to do pure math PhD later (keeping in mind that I can't take on a ton of extra coursework and would prefer to take classes that have some overlap on the math side, e.g. PDEs?). Are there standard computer science, statistics and/or applied math classes that give enough of a background to find data science work? I'll also take suggestions of any sort of course progression online, e.g. on Coursera, that could be helpful to do in parallel with my degree and are geared towards people with theoretical backgrounds but I worry that online courses won't be enough for employers.
Thanks!
 A: I'm not sure about your specific program, but I think a good grounding in probability is a good background for later classes (online or otherwise) in statistics and data science, and your school should have versions that count towards pure math.  There might also  be a more theoretical class on optimization theory, after which you can pick up the numerical analysis skills on your own.
A: What a great question!
Offering only my own experience: I work in operations research, taken broadly as the science of better (versus the narrow scope of optimisation). One of the things I get a buzz from is when I can take a “vertical slice”, from engaging with a client on something that’s going matter to them, down through to some new insight in theory.
Compare with Ian Stewart’s 17 Equations That Changed The World - get the book and read it.  For me, this book showed that the best “pure” maths all started applied.
My grounding in pure maths was in real analysis and group theory (the latter was a strength at the uni I attended). Ironically I didn’t take any courses in probability & statistics, even though the client work I have ended up doing has called on probability theory a lot (for stochastic processes). But the foundations were there (I really really needed that real analysis background ).
What I think this means for you:  Try and learn more about the work that you want to do, and the maths / computation / analysis problems that could arise.  So for example, if you’re into discrete maths then you may orient to crypto and cyber security (systems & policy).  But if more into probability theory then it could be the data sciences.
In all cases, make sure that you’re very fluent on at least one modern computational computer software system.  Python is good.  So is R.  MATLAB was mine, and I have colleagues for whom Mathematica is their choice.
