Which is more important for buy side jobs? Stoch. Calculus or Trading?

[The Spartan Guy]

I am finishing Ph.D in Electrical and Communication engineering. My mathematics knowledge (stochastic calculus to Black-Scholes, Ito's integral, Differential equation etc.) is stronger than my programming or processor design, execution time analysis etc.

So the questions are

1. Do I have a chance of landing a job at the buy side, since they are the only ones that seem available?
2. Are those mathematical topics (stochastic calculus etc.) used exclusively on the sell side, investment banks? Or do they have some relevance for the prop trading firms etc. as well?
3. I am also learning on those things more in depth, I still have about a year before I can actually start a job. (Working on my thesis now.) So given this, when it comes to dividing the time, should I focus more on understanding trading (statistical arbitrage, execution systems, backtesting etc.) or should I sharpen the math side (again, on things like geomtric Brownian motion and differential equation)?

Of course suggesting an ideal time division is not possible, but which is hotter (or rather, less cold) in today's job market?

 

[Parallax]

Focus on applied statistics (time series analysis, econometrics, etc.) and trading.