# MATHEMATICAL AND STATISTICAL METHODS FOR APPLICATIONS 2

**Academic Year 2023/2024**- Teacher:

**Giulia PICCITTO**

## Expected Learning Outcomes

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.

In particular, the course aims to allow the student to acquire the following skills:

**knowledge and understanding: **knowledge of results
and fundamental methods in advanced statistics, stochastic processes
and Monte Carlo method. Skill of understanding problems and to extract
the major features. Skill of reading, understanding and analyzing a
subject in the related literature and present it in a clear and accurate
way.

**applying knowledge and understanding:** skill of
elaborating new example or solving novel theoretical exsercise, looking
for the most appopriate methods and applying them in an appropriate
way.

**making judgements:** To be able of devise proposals
suited to correctly interprete complex problems in advanced statistics,
stochastic processes and Monte Carlo simulation. To be able to
formulate autonomously adequate judgements on the applicablity of
simulation methods or statistical or stochastic models to theoretical or
real situations.

**communication skills**: skills of presenting
arguments, problems, ideas and solutions in mathematical terms with
clarity and accuracy and with procedures suited for the audience, both
in an oral and a written form. Skill of clearly motivating the choice of
the strategy, method and contents, along with the employed
computational tools.

**learning skills: **reading and analyzing a subject in
the literature involving applied mathematics. To tackle in an
autonomuous way the systematic study of arguments not previously
treated. To acquire a degree of autonomy such that the student can be
able to start with an autonomuos reserach activity.

## Course Structure

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

If restrictions will be introduced because the COVID pandemic, le lectures will be given in a mixed way or only online and some changes could be introduced to assure the accomplishiments foreseen for the course.

Learning assessment may also be carried out on line, should the conditions require it.

## Required Prerequisites

## Attendance of Lessons

## Detailed Course Content

## Textbook Information

Notes of the lecturer

V. Romano, *Metodi Matematici per i Corsi di Ingegneria*, CittàStudi

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*

*Applied statistics and probability for engineers*, J. Wil

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Metodo della massima verosimiglianza. Correlazione normale. Inferenza statistica Bayesiana. Metodo della massima entropia. Processi stocastici. Equazioni differenziali stocastiche. Metodi Monte Carlo. | Notes of the lecturer |

## Learning Assessment

### Learning Assessment Procedures

If necessary the exam will be online.