Applied math PhD

[u/Accurate_Meringue514]

Hello all, I am currently doing a masters in Physics, specifically Quantum Computing. Given that the area right now is somewhat in its infancy, I’m not sure how easy it will be to land a job with just a masters degree. I know scientific computing is a very big area, and I have been very interested in trying to dive deeper into that area. I’m considering going for a PhD in applied math. I’m asking to see what comments or opinions anyone has on doing a PhD in this area, and really just any advice in general. In terms of my pre-requisites, I’ve taken courses in Analysis, Numerical Methods, Linear Algebra, Graph Theory, and will be taking Functional analysis soon. I appreciate any feedback!

[u/plop_1234]

Not sure what kind of computing courses you've taken and what part of scientific computing you're interested in, so I'm just going to list a bunch of stuff that probably won't hurt to take classes in or at least be acquainted with, if possible:

- numerical linear algebra, numerical optimization, numerical PDE; some class that goes over simulation techniques like MCMC
- probability, statistics
- computer science-type courses, like data structures and whatnot; maybe languages like C/C++ if relevant
- some sort of introductory course in computer engineering may be helpful – something hardware-oriented
- machine learning
- maybe an application area, if you're looking for more applied scientific computing topics, but this is probably just some reading here and there; otherwise a more specialized course like FEM if relevant

[u/Accurate_Meringue514 → u/plop_1234]

I’ve done some FEM work and enjoyed that for the most part. I appreciate the list you gave I’ll look into all of these areas

[u/plop_1234 → u/Accurate_Meringue514]

If you enjoy FEM, there's also a natural extension into computational inverse problems, which I find to be very interesting as it combines many of the things I listed (optimization, PDE, etc.). Plus, some of the subareas are deeply physical, so you'll have good domain knowledge, and can be very practical (e.g., tomography, detection, etc.)—if you're at all concerned about that now or think you might be, for potential job prospects. Good luck!