1. Conditional expectation, Brownian motion, diffusions, and martingales. 2. Ito’s stochastic integral, Ito's formula, and stochastic calculus. 3. Stochastic differential equations and their applications.

CILO-1: Formulate and solve basic problems in stochastic calculus, such as Ito's derivative and Ito's integration. CILO-2: Apply basic concepts of stochastic calculus and Ito's formula to solve problems in mathematical finance. CILO-3: Explain and apply the Markov processes and Brownian motion in probability.