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. 2013/2014

ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
6
B
MAT/03
6
B
MAT/07
6
B
MAT/06
One course chosen from the following two
6
C
SECS-P/01
6
C
FIS/01
One course chosen from the following two
6
C
MAT/07
6
C
SECS-P/01

3° Year  activated in the A.Y. 2014/2015

ModulesCreditsTAFSSD
One course of 12 ECTS or two courses of 6 ECTS chosen from the following three
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
6
C
MAT/06 ,SECS-P/05
6
C
SECS-S/06
6
B
MAT/06
6
B
MAT/08
Prova finale
6
E
-
activated in the A.Y. 2013/2014
ModulesCreditsTAFSSD
6
A
MAT/02
12
B
MAT/05
12
B
MAT/08
6
B
MAT/03
6
B
MAT/07
6
B
MAT/06
One course chosen from the following two
6
C
SECS-P/01
6
C
FIS/01
One course chosen from the following two
6
C
MAT/07
6
C
SECS-P/01
activated in the A.Y. 2014/2015
ModulesCreditsTAFSSD
One course of 12 ECTS or two courses of 6 ECTS chosen from the following three
12
C
SECS-S/06
6
C
MAT/07
6
C
MAT/05
6
C
MAT/06 ,SECS-P/05
6
C
SECS-S/06
6
B
MAT/06
6
B
MAT/08
Prova finale
6
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
Other activities
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 (2014/2015)

Teaching code

4S00254

Credits

6

Coordinator

Marco Caliari

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 sem.

Academic staff

Paolo Dai Pra

Analisi di serie temporali

Credits

2

Period

I sem.

Academic staff

Federico Di Palma

Esercitazioni

Credits

1

Period

I sem.

Academic staff

Marco Caliari

Learning outcomes

The course is split into three parts.

Module 1 (Discrete-time Markov Chains, Prof. Dai Pra)

The course provides an introduction to discrete-time Markov chain, with finite or countable state space

Module 2 (Practice of Stochastic Systems, Dott. Caliari)

Exercises and practice on Module 1, see web page.

Module 3 (Temporal series analysis, Dott. Di Palma)

Theory for the analysis of discrete time temporal series.

Program

Module 1

  • Introduction to finite-state Markov chain: irreducibility, periodicity, stationary distributions, classification of states. Examples.
  • Markov chain Monte Carlo. Perfect simulation.
  • Convergence to equilibrium of Markov chains. Mixing time. Ergodic Theorem. Coupling methods. Strong stationary times.
  • Martingales: optional stoppini theorem, harmonic functions.
  • Markov chains with countable state space: recurrence and transience.
Module 2
  • Approximation of invatiant measures.
  • Metropolis' algorithm
  • Queue simulation

Examination Methods

Module 1: written examination.
Module 2: oral discussion about homeworks.
Module 3: oral discussion of a given project.

The final mark is the weighted average of the three.

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

Teaching materials e documents