advice before i embark on my graduate studies in applied math I'll be pursuing my graduate studies in applied math this fall. I'm hoping to gather advice in order to help me somewhat plan my courses as well as provide insight as to what is realistic or not.
i do not have very strictly defined research interests but somehow I want to dabble on differential equations and probability, i.e. stochastic differential equations. I am still unsure as to what field I intend to apply SDEs to but if all else fails, my fallback would have to be math. finance or theoretical SDEs.
As much as possible, I do not want to pursue a math. finance research career. Although among many fields in applied math, this is I believe the most convenient for me since learning the rudiments of finance is not very complicated. I have taken a few finance courses in my undergrad degree and most of them seem intuitive.
Now I am pondering about looking into the applications of SDEs in the sciences. while I never liked biology in high school, and probably don't remember anything about it, neuroscience sort of appeals to me since SDE applications are still relatively young compared to, say, physics.
My concern here is...whether I end up choosing to apply SDEs to biology or physics (of which I don't have any background also except for high school stuff which I forgot :( ) will I still be able to learn the basics I need in fields where I hope to employ SDEs during the course of my PhD? What I'm asking is - is it realistic to cover this during the 2-3 years of coursework considering that I also have to take graduate math courses?
Is anyone here concentrating on mathematical biology for their PhD studies but had very minimal biology background when they started their PhD? Or physics perhaps?
Thanks and help and advice very very much appreciated!
 A: I don't know about graduate studies, but I can share some of what I encountered during my undergraduate work. I suppose that's a bit like a child giving advice to an adult, but here's my opinion, for what it's worth...
I once took a course on mathematical modeling of biological systems (mostly ODE models, but we did a chapter on stochastic modeling as well). The class was more or less evenly split between math and biology students. Of the two, those with a strong mathematical background tended to perform better, in spite of their unfamiliarity with the underlying biology.
I've also had the opportunity to do some work in bioinformatics with coworkers and supervisors from very diverse academic backgrounds. People tended to learn enough to get their work done, and had a general understanding of what everyone else was doing. Nearly no one had a complete grasp of everything, though.
So my advice would be: don't set the bar too high. You don't need the equivalent of a university degree in biology to be able to work in the field. You can learn enough to get started by attending seminars, taking a few undergraduate courses, reading papers/textbooks, etc. That said, until you become familiar with the biology, I imagine you'd probably have to stick to the more math-heavy areas of the field.
