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.

Academic calendar

The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.

Academic calendar

Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Definition of lesson periods
Period From To
I semestre Oct 1, 2018 Jan 31, 2019
II semestre Mar 4, 2019 Jun 14, 2019
Exam sessions
Session From To
Sessione invernale d'esame Feb 1, 2019 Feb 28, 2019
Sessione estiva d'esame Jun 17, 2019 Jul 31, 2019
Sessione autunnale d'esame Sep 2, 2019 Sep 30, 2019
Degree sessions
Session From To
Sessione di laurea estiva Jul 22, 2019 Jul 22, 2019
Sessione di laurea autunnale Oct 15, 2019 Oct 15, 2019
Sessione di laurea autunnale straordinaria Nov 21, 2019 Nov 21, 2019
Sessione di laurea invernale Mar 19, 2020 Mar 19, 2020
Period From To
Sospensione attività didattica Nov 2, 2018 Nov 3, 2018
Vacanze di Natale Dec 24, 2018 Jan 6, 2019
Vacanze di Pasqua Apr 19, 2019 Apr 28, 2019
Vacanze estive Aug 5, 2019 Aug 18, 2019

Exam calendar

Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.

Exam calendar

Should you have any doubts or questions, please check the Enrolment FAQs

Academic staff


Albi Giacomo

symbol email symbol phone-number +39 045 802 7913

Baldo Sisto

symbol email symbol phone-number 045 802 7935

Bos Leonard Peter

symbol email symbol phone-number +39 045 802 7987

Caliari Marco

symbol email symbol phone-number +39 045 802 7904

Canevari Giacomo

symbol email symbol phone-number +39 045 8027979

Capuani Rossana

symbol email

Chignola Roberto

symbol email symbol phone-number 045 802 7953

Cozza Vittoria

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Cubico Serena

symbol email symbol phone-number 045 802 8132

Daffara Claudia

symbol email symbol phone-number +39 045 802 7942

Dai Pra Paolo

symbol email symbol phone-number +39 0458027093

Daldosso Nicola

symbol email symbol phone-number +39 045 8027076 - 7828 (laboratorio)

Delledonne Massimo

symbol email symbol phone-number 045 802 7962; Lab: 045 802 7058

De Sinopoli Francesco

symbol email symbol phone-number 045 842 5450

Di Persio Luca

symbol email symbol phone-number +39 045 802 7968

Favretto Giuseppe

symbol email symbol phone-number +39 045 802 8749 - 8748

Fioroni Tamara

symbol email symbol phone-number 0458028489

Gnoatto Alessandro

symbol email symbol phone-number 045 802 8537

Gonzato Guido

symbol email symbol phone-number 045 802 8303

Gregorio Enrico

symbol email symbol phone-number 045 802 7937

Imperio Michele

Mantese Francesca

symbol email symbol phone-number +39 045 802 7978

Marigonda Antonio

symbol email symbol phone-number +39 045 802 7809

Mattiolo Davide

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Mazzuoccolo Giuseppe

symbol email symbol phone-number +39 0458027838

Monti Francesca

symbol email symbol phone-number 045 802 7910

Nardon Chiara

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Orlandi Giandomenico

symbol email giandomenico.orlandi at symbol phone-number 045 802 7986

Patacca Marco

symbol email symbol phone-number 0458028788

Rizzi Romeo

symbol email symbol phone-number +39 045 8027088

Sala Pietro

symbol email symbol phone-number 0458027850

Sansonetto Nicola

symbol email symbol phone-number 049-8027932

Schuster Peter Michael

symbol email symbol phone-number +39 045 802 7029

Segala Roberto

symbol email symbol phone-number 045 802 7997

Solitro Ugo

symbol email symbol phone-number +39 045 802 7977

Vincenzi Elia

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Zuccher Simone

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Study Plan

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 enrolment year.

Modules Credits TAF SSD
Between the years: 1°- 2°- 3°
Between the years: 1°- 2°- 3°
Other activities

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.

S Placements in companies, public or private institutions and professional associations

Teaching code



Paolo Dai Pra





Scientific Disciplinary Sector (SSD)



I semestre dal Oct 1, 2020 al Jan 29, 2021.

Learning outcomes

The Stochastic Systems course aims at giving an introduction to the basic concepts underlying the rigorous mathematical description of the temporal dynamics for random quantities. The course prerequisites are those of a standard course in Probability, for Mathematics / Physics. It is supposed that students are familiar with the basics Probability calculus, in the Kolmogorov assiomatisation setting, in particular with respect to the concepts of density function, probability distribution, conditional probability, conditional expectation for random variables, measure theory (basic ), characteristic functions of random variables, convrgence theorems (in measure, almost everywhere, etc.), central limit theorem and its (basic) applications, etc. The Stochastic Systems course aims, in particular, to provide the basic concepts of: Filtered probability space, martingale processes, stopping times, Doob theorems, theory of Markov chains in discrete and continuous time (classification of states, invariant and limit,measures, ergodic theorems, etc.), basics on queues theory and an introduction to Brownian motion. A part of the course is devoted to the computer implementation of operational concepts underlying the discussion of stochastic systems of the Markov chain type, both in discrete and continuous time. A part of the course is dedicated to the introduction and the operational study, via computer simulations, to univariate time series. It is important to emphasize how the Stochastic Systems course is organized in such a way that students can concretely complete and further develop their own: capacity of analysis, synthesis and abstraction; specific computational and computer skills; ability to understand texts, even advanced, of Mathematics in general and Applied Mathematics in particular; ability to develop mathematical models for physical and natural sciences, while being able to analyze its limits and actual applicability, even from a computational point of view; skills concerning how to develop mathematical and statistical models for the economy and financial markets; capacity to extract qualitative information from quantitative data; knowledge of programming languages or specific software.


The entire course will be available online. In addition, a number of the lessons/all the lessons (see the course
schedule) will be held in-class.

1. Discrete-time Markov chains. Markov properties and transition probability. Irreducibility, aperiodicity. Stationary distributions. Reversible distributions.

2. Hitting times. Convergence to the stationary distribution. Law of large numbers for Markov chains. MCMC: Metropolis algorithm and Gibbs sampler.

3. Reducible Markov chains. Transient and recurring states. Probability of absorption.

4 .. Markov chains with countable states. Recurrence and transience of the random walk on Z ^ d. Positive recurrent states and stationary distributions. Convergence theorem for irreducible Markov chains with countable states.

5. Continuous-time Markov chains. The Poisson process and its properties. Continuous-time Markov property. Semigroup associated with a Markov chain: continuity and differentiability; generator. Kolmogorov equations. Stationary distributions. Dynkin's formula. Probabilistic construction of a continuous-time Markov chain.

6. Erdos-Renyi random graphs. Model definition. Connected components.

7. Conditional Expectation and Conditional Distribution. Martingale. Stopping theorem and convergence theorem.

Reference texts
Author Title Publishing house Year ISBN Notes
Levin, David A., and Yuval Peres Markov chains and mixing times American Mathematical Society 2017

Examination Methods

Written exam, with exercises and theoretical questions.

The assessment methods could change according to the academic rules


Type D and Type F activities

Modules not yet included

Career prospects

Module/Programme news

News for students

There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details.


For schedules, administrative requirements and notices on graduation sessions, please refer to the Graduation Sessions - Science and Engineering service.


Title Info File
Doc_Univr_pdf 1. Come scrivere una tesi 31 KB, 29/07/21 
Doc_Univr_pdf 2. How to write a thesis 31 KB, 29/07/21 
Doc_Univr_pdf 5. Regolamento tesi (valido da luglio 2022) 171 KB, 17/02/22 

List of theses and work experience proposals

theses proposals Research area
Formule di rappresentazione per gradienti generalizzati Mathematics - Analysis
Formule di rappresentazione per gradienti generalizzati Mathematics - Mathematics
Proposte Tesi A. Gnoatto Various topics
Mathematics Bachelor and Master thesis titles Various topics
Stage Research area
Internship proposals for students in mathematics Various topics


As stated in point 25 of the Teaching Regulations for the A.Y. 2021/2022, except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.
Please refer to the Crisis Unit's latest updates for the mode of teaching.

Career management

Area riservata studenti