Salta ai contenuti. | Salta alla navigazione

Strumenti personali


Academic year and teacher
If you can't find the course description that you're looking for in the above list, please see the following instructions >>
Versione italiana
Academic year
Green economy and sustainability
Didactic period
Primo Semestre

Training objectives

Mathematical module.
The aim of the course is the study of differential calculus in euclidean spaces, the critical analysis of games theory, with special emphasis on Nash equilibrium, and finally the use of the main functions of the Matlab software.

At the end of the course, the student will be able to:
- carry out optimization of two-variables functions;
- analyze real contexts in the framework of game theory;
- employ the basic functions in Matlab environment.

Statistical module
The aim of the course is to learn statistical techniques for processing data in the presence of complex datasets (multivariate problems), to support decision making processes in economics and business.

At the end of the course the student is able:
- to know the theoretical foundations and properties of the main statistical methods of multivariate analysis
- to apply these methods to real problems
- to implement their use by means of the R software environment


Mathematical module.
Basic notions related to the following topics are required:
-differential calculus for one-variable mappings; variable;
-linear algebra.

Statistical module.
Basic notions related to the following topics are required:
-descriptive statistics
-probability and main probability distributions
-inferential statistics (test of hypothesis, parameters estimation, random sampling, simple linear regression)

Course programme

Mathematical module
First part (9 hours): Fundamentals of linear algebra. Unconstrained optimization of two-variables functions.

Second part (9 hours): Basic notions of game theory: representation in strategic form, dominance, Nash equilibrium in pure and mixed strategies.

Third part (6 hours): problem solving in linear algebra and graphical representation of two-variables functions in Matlab environment

Fourth part (8 hours): Introduction to discrete dynamic models. Simulations in Matlab environment.

Statistical module
1.Basic notions on matrix algebra and on the R software environment (4 hours):
theory, methods and applications
2.Multiple linear regression (8 hours):
theory, methods and applications; use of R codes
3.Factor analysis and Principal component analysis (8 hours):
theory, methods and applications; use of R codes
4.Computation of composite indicators (4 hours):
theory, methods and applications; use of R codes
5.Cluster analysis (8 hours):
theory, methods and applications; use of R codes

Didactic methods

Theoretical lectures and guided practice exercises in computer lab.

Learning assessment procedures

Mathematical module
Written examination.

The written exam consists of two open-ended questions aimed at verification of all the course contents. The resolution of the problems is based upon both theoretical way and Matlab software aid.
The final score is given by the sum of the scores assigned to the single questions.
The test will be passed if and only if the minimum score is 18.

Statistical module
Written examination
Optional practice examination

The aim of the examination is to assess the level of achievement of the mentioned educational goals. The written test consists of a list of multiple choice questions.
The questions focus on the assessment of the knowledge of the theory, of the ability of reasoning and interpreting the results, of the use of the R commands for the application of the methods .
The practical examination is optional and consists of preparing a report documenting the application of statistical methods to a real problem and a real dataset agreed with the professor

The final grade is given by the arithmetic average of the marks of both the modules. The exam will be passed if and only if the minimum grade is 18.

Reference texts

Mathematical module
C.P.Simon, L.Blume “Mathematics for Econonists” Edited in 1994 or later
M.Osborne “An introduction to game theory”
Edited in 2004 or later
H.Peters “Game Theory: a multi-leveled approach” Edited in 2008 or later
D.Kreps “Game Theory and Economic modelling”
Edited in 1990 or later
R.Gibbons “Teoria dei giochi”
Edited in 1994 or later
Pocci et al. "Matlab for applications in Economics and Finance" APOGEO Education -Maggioli editore Edited in 2017

Statistical module
Mardia K.V., Kent J.T., Bibby J.M., «Multivariate Analysis», Academic Press, London,
Edited in 2000 or later
Anderson T.W., «An introduction to Multivariate Statistical Analysis», Wiley,
Edited in 2003 or later

Further material is available at the course web site: