The course aims to: (a) the importation of students both in theoretical construction and study of numerical methods, and the implementation of the corresponding computer algorithms for solving specific problems and (b) to make students able to study key issues of statistical analysis (linear regression - correlation, non-parametric hypothesis testing) and understand basic principles and methods so they can exploit them in solving math problems and analyzing statistical data.
Numerical Analysis: Introduction - Errors. Approximate methods: solving nonlinear equations, interpolation, approximation, numerical integration, solution of differential equations.
Probability - Statistics: Potential and possibilities. Conditional probability. Theorem of total probability and random variables. Probability distributions. Basic distributions (binomial, exponential, C, F, x2, Poisson, Sudent). Mean and variance of random variables. Multivariate distributions. Distribution function of random variables. Statistical inference and sampling principles. Parameter estimation. Simple linear regression. Multiple linear regression. Analysis of variance in model selection.