This course provides the minimum mathematical requirements to study mathematical finance or more precisely the pricing of financial derivatives. Topics covered in the lectures include: basic probability, random variables, distribution function and independence, Chebyshev inequality, Borel-Cantelli lemma, law of large numbers and central limit theorem, conditional expectation, martingales, Brownian motion, stochastic integrals, Ito calculus, and stochastic differential equations. (from nptel.ac.in)