MATHEMATICAL AND STATISTIC METHODS FOR APPLICATIONS

The aim of the course is to give the main tools for statistical investigations along with the study of advanced subjects for tackling problems of interest in mathematical physics, economics, industry and in general for applications arising from applied sciences. In particular, the course furnishes the background for mathematical analysis in economics and therefore suitable for student in the program of finance.

Some aspects treated in the course are in any case relevant for those who want to teach Mathematics at the high schools.

Mainly frontal lectures. Moreover, the theoretical acquired competencies will be applied in a laboratory where study cases will be tackled in a MATLAB enviroment.

1. Recalls and complements of probability. Estimators. Non parametrical estimators. Maximum likelihood method. Normal correlation. Bayesian statistical inference. Maximum entropy method. Stochastic processes. Stochastic differential equations. Monte Carlo method.

2.  

3.  

4.  

P. Baldi Calcolo delle probabilità e statistica, McGraw-Hill
R. Scozzafava Incertezza e probabilità, Zanichelli
A. Rotondi, P. Pedroni, A. Pievatolo Probabilità Statistica e Simulazione, Springer
L. C. Evans, An introduction to stochastic differential equations, AMS
D. C. Montgomery, G. C. Runger Applied statistics and probability for engineers, J. Wiley