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!