Basic numerical methods, (floating-point arithmetic, numerical linear algebra, solutions of non-linear equations, interpolation, curve fitting, splines, differentiation, integration, Monte-Carlo methods, ordinary differential equations) numerical solutions of PDEs (finite-difference methods for parabolic PDEs, stability, convergence, applications to Black-Scholes equations, free boundary problems, applications to pricing American options) and probabilistic methods (random variables, generation, Monte-Carlo simulation, binomial tree models, stochastic differential equations).