I'm not quite sure what kinds of Brownian motion models I'll be using, but I think its safe to say they will have little to do with bacteria. However, the rest of your response actually seems quite relevant. My research will be directed by a faculty member and I think derivatives were mentioned...
Next semester I'll be doing some independent research in the mathematics of trading. Specifically I'm looking for a text that will teach me to grapple with Markov Chains, Brownian motion models, mean reversion models, and models with regime switching.