This summer, I've got an undergraduate research bursary at our university's Systems Biology centre, which is wierd as I always viewed myself of more of a pure mathematician, but is absolutely fascinating.
I have jumped in at the deep end, however (my supervisor seems to think I know a lot more than I really do and maybe hasn't realised I haven't done any serious integration/differentiation or ODEs stuff since the first year...).
What I'm actually doing is looking at the response of Neurons to different types of presynaptic noise, which I am slowly learning more about. In particular, noise is random (well, duh) and so all of the models I end up with have Stochastic Differential Equations, which are typically quite unpleasant. For those interested, the toy models I'm playing with end up with Brownian motion in a harmonic potential.
So the book I'm recommending is:
Paul and Baschnagel, "Stochastic Processes, From Physics to Finance"
Don't let the reference to finance put you off - I've found it absolutely fantastic for explaining the basics of Wiener processes, brownian motion and so on. In particular, it is written for the scientist rather than the mathematician and so everything's done in the real numbers, rather than over wierd and wonderful probability spaces. I really believe that even if you want to learn stochastic integration properly as a mathematician, this is a worthwhile read, because you end up for a real feel for what's going on.
The book's published by Springer and is on Amazon here at the terrifying price of about £50 used, so you might want to try a university library!
Now back to work!
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