Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

Study Plan

A.A. 2024/2025 A.A. 2023/2024 A.A. 2022/2023 A.A. 2021/2022 A.A. 2020/2021 A.A. 2019/2020 A.A. 2018/2019 A.A. 2017/2018 A.A. 2016/2017 A.A. 2015/2016 A.A. 2014/2015 A.A. 2013/2014 A.A. 2012/2013 A.A. 2011/2012 A.A. 2010/2011 A.A. 2009/2010

This information is intended exclusively for students already enrolled in this course.
If you are a new student interested in enrolling, you can find information about the course of study on the course page:

Laurea in Matematica applicata - Enrollment from 2025/2026

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.

1° Year

ModulesCreditsTAFSSD
12
A
MAT/02 ,MAT/03
12
A
MAT/05
12
A
FIS/01
6
B
MAT/01
12
A
INF/01
6
E
-

2° Year  activated in the A.Y. 2012/2013

ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
6
B
MAT/03
6
B
MAT/06
6
B
MAT/07
Uno tra i seguenti due insegnamenti
6
C
SECS-P/01
6
C
FIS/01
Uno tra i seguenti due insegnamenti
6
C
MAT/07
6
C
SECS-P/01

3° Year  activated in the A.Y. 2013/2014

ModulesCreditsTAFSSD
6
C
MAT/06 ,SECS-P/05
6
B
MAT/08
6
C
MAT/09
6
B
MAT/06
Uno da 12 cfu o due da 6 cfu tra i seguenti tre insegnamenti
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
Prova finale
6
E
-
activated in the A.Y. 2012/2013
ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
6
B
MAT/03
6
B
MAT/06
6
B
MAT/07
Uno tra i seguenti due insegnamenti
6
C
SECS-P/01
6
C
FIS/01
Uno tra i seguenti due insegnamenti
6
C
MAT/07
6
C
SECS-P/01
activated in the A.Y. 2013/2014
ModulesCreditsTAFSSD
6
C
MAT/06 ,SECS-P/05
6
B
MAT/08
6
C
MAT/09
6
B
MAT/06
Uno da 12 cfu o due da 6 cfu tra i seguenti tre insegnamenti
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
Prova finale
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
Ulteriori conoscenze
6
F
-
Between the years: 1°- 2°- 3°
12
D
-

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Stochastic systems (2013/2014)

Teaching code

4S00254

Credits

6

Coordinator

Laura Maria Morato

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Seminars 0

The teaching is organized as follows:

Catene di Markov in tempo discreto

Credits

3

Period

I semestre

Academic staff

Laura Maria Morato

Analisi di serie temporali

Credits

2

Period

I semestre

Academic staff

Federico Di Palma

Esercitazioni

Credits

1

Period

I semestre

Academic staff

Marco Caliari

Learning outcomes

Module 1 ( Discrete time Markov Chains )

Basics of the theory of discrete time Markov chain with finite or countable state space and examples of application.


Module 2 (Practice session of Stochastic systems)

Approximation and computation of invariant probabilities, Metropolis algorithm, simulation of queues and renewal processes with the use of Matlab.

Module 3 Introduction to Time Series analysis: the lessons aims to provide to the student a general framework to analyze time series as the outcome of a discrete time model fed by a white noise and an exogenous input. The lesson are completed by the use of a dedicated software in order to apply the theoretical aspects.

Program

Module 1
Markov chains with finite space state:
Definitions, transition matrix, transition probability in n steps, Chapman -Kolmogorov equation, finite joint densities, Canonocal space and Kolmogorov theorem (without proof).
State classification, invariant probabilities, Markov-Kakutani theorem, example of gambler's ruin, regular chains, criterion, limit probabilities and Markov theorem, reversible chains, Metropolis algorithm and Simulated annealing, numerical generation of a discrete random variable and algorithm for generation an omogeneus Markov chains with finite state space.

Markov chains with countable space state:
Equivalent definitions of transient and recurrent state, positive recurrence, periodicity, solidarity property, canonical decomposition of the state space, invariant measures, existence theorem, example of the unlimited random walk. Ergodicity and limit theorems.

Elements of Martingales associated to discrete time Markov chains:
Natural filtration, stopping times, conditional expectation given a random variable, strong Markov property, martingales. Optional stopping Theorem, example of gambler's ruin.

Module 2 Approximation and computation of invariant probabilities, Metropolis algorithm, simulation of queues with the use of Matlab.

Module 3 Elements of time series analysis :
Main scope of time series analysis: modelling, prediction and simulation.
Identification problem main components: a priori Knowledge, experiment design, goodness criteria, model, filtering and validation.
Model: main variables and correspondent schema. (AR, ARX, ARMA, output-error).
Goodness Criteria: least square, Maximum Likelihood, Maximum a posteriori.
Filtering: Linear parameter model, frequency filtering.
Matlab : main purpose and examples.

Bibliography

Reference texts
Activity Author Title Publishing house Year ISBN Notes
Analisi di serie temporali LJung System Identification, Theory for the User (Edizione 2) Prentice Hall PTR 1999

Examination Methods

Module 1 Oral exam

Module 2 Discussion of the solution of given homeworks.

Module 3 Written exam

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE