1. The student should become aware of the limitations of pseudo-random numbers and of the different architectures of random number generators.
2. He must understand how Monte Carlo simulation works and how and when to apply it.
3. He should be able to simulate from a sample and to anticipate, through simulation, the response of a system.
4. He should also be able to model a physical process to predict and reproduce the outcome of a system

Monte Carlo method: Definition and implementation.
Random numbers ? requirements. Types of random number generators. Tests.
Probabilities: discrete, continuous and cumulative. Uniform distribuition. Non-uniform distributions: exponential and Gaussian.
Change of probability density: inversion and Box-Muller methods. Change of variables.
Monte Carlo integration.
Importance sampling
Finding the root of equations: successive substitutions, Newton-Cotes, half intervals and regula-falsi methods.
Interpolation methods: polynomial interpolation, Lagrange formula and piecewise interpolation.
Finding the roots of functions: Newton-Raphson, secant, bisection and regula-falsi
Integration methods: Newton-Cotes quadrature (open and closed), middle point, trapezoid and Simpson rules. Gaussian quadrature.
Integration of differential equations: Euler, Neuer and Runge-Kutta methods.
Random walks, Markov chains, Metropolis algorithm. Examples and applications.

Programming capabilities at an intermediate level.