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 technicaladministrative 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.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period  From  To 

I semestre  Oct 1, 2019  Jan 31, 2020 
II semestre  Mar 2, 2020  Jun 12, 2020 
Session  From  To 

Sessione invernale d'esame  Feb 3, 2020  Feb 28, 2020 
Sessione estiva d'esame  Jun 15, 2020  Jul 31, 2020 
Sessione autunnale d'esame  Sep 1, 2020  Sep 30, 2020 
Session  From  To 

Sessione estiva di laurea  Jul 22, 2020  Jul 22, 2020 
Sessione autunnale di laurea  Oct 14, 2020  Oct 14, 2020 
Sessione autunnale di laurea solo triennale  Dec 10, 2020  Dec 10, 2020 
Sessione invernale di laurea  Mar 16, 2021  Mar 16, 2021 
Period  From  To 

Festa di Ognissanti  Nov 1, 2019  Nov 1, 2019 
Festa dell'Immacolata  Dec 8, 2019  Dec 8, 2019 
Vacanze di Natale  Dec 23, 2019  Jan 6, 2020 
Vacanze di Pasqua  Apr 10, 2020  Apr 14, 2020 
Festa della Liberazione  Apr 25, 2020  Apr 25, 2020 
Festa del lavoro  May 1, 2020  May 1, 2020 
Festa del Santo Patrono  May 21, 2020  May 21, 2020 
Festa della Repubblica  Jun 2, 2020  Jun 2, 2020 
Vacanze estive  Aug 10, 2020  Aug 23, 2020 
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.
Academic staff
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 

Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

1° Year
Modules  Credits  TAF  SSD 

2° Year activated in the A.Y. 2020/2021
Modules  Credits  TAF  SSD 

3° Year activated in the A.Y. 2021/2022
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

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.
Stochastic systems (2021/2022)
Teaching code
4S00254
Academic staff
Coordinatore
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/06  PROBABILITY AND STATISTICS
Period
Primo semestre dal Oct 4, 2021 al Jan 28, 2022.
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.
Program
The entire course will be available online. In addition, a number of the lessons/all the lessons (see the course
schedule) will be held inclass.
1. Conditional Expectation and Conditional Distribution. Martingale. Stopping theorem and convergence theorem.
2. Discretetime Markov chains. Markov properties and transition probability. Irreducibility, aperiodicity. Stationary distributions. Reversible distributions.
3. Hitting times. One step analysis. Convergence to the stationary distribution. Law of large numbers for Markov chains. MCMC: Metropolis algorithm and Gibbs sampler.
4. Reducible Markov chains. Transient and recurring states. Probability of absorption.
5. Continuoustime Markov chains. The Poisson process and its properties. Continuoustime Markov property. Semigroup associated with a Markov chain: continuity and differentiability; generator. Kolmogorov equations. Stationary distributions. Dynkin's formula. Probabilistic construction of a continuoustime Markov chain.
Bibliography
Examination Methods
To pass the exam, students must show:
 to have understood the theoretical notions, showing detailed knowledge of definitions and statements, as well as of some proofs;
 to be able to apply theory to problem solving.
The exam consists of a 180minute written test which includes a theoretical part, with at least one proof required, and a part of exercises.
The assessment methods could change according to the academic rules
Type D and Type F activities
years  Modules  TAF  Teacher 

1° 2° 3°  Python programming language  D 
Maurizio Boscaini
(Coordinatore)

1° 2° 3°  SageMath  F 
Zsuzsanna Liptak
(Coordinatore)

1° 2° 3°  History of Modern Physics 2  D 
Francesca Monti
(Coordinatore)

1° 2° 3°  History and Didactics of Geology  D 
Guido Gonzato
(Coordinatore)

years  Modules  TAF  Teacher 

1° 2° 3°  C Programming Language  D 
Sara Migliorini
(Coordinatore)

1° 2° 3°  C++ Programming Language  D 
Federico Busato
(Coordinatore)

1° 2° 3°  LaTeX Language  D 
Enrico Gregorio
(Coordinatore)

years  Modules  TAF  Teacher 

1° 2° 3°  Corso Europrogettazione  D  Not yet assigned 
1° 2° 3°  Corso online ARPM bootcamp  F  Not yet assigned 
1° 2° 3°  ECMI modelling week  F  Not yet assigned 
1° 2° 3°  ESA Summer of code in space (SOCIS)  F  Not yet assigned 
1° 2° 3°  Google summer of code (GSOC)  F  Not yet assigned 
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: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and soon also via the Univr app.
Graduation
Attachments
Title  Info File 

1. Come scrivere una tesi  31 KB, 29/07/21 
2. How to write a thesis  31 KB, 29/07/21 
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 
Erasmus+ and other experiences abroad
Attendance
As stated in the Teaching Regulations for the A.Y. 2022/2023, 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 onsite.
Please refer to the Crisis Unit's latest updates for the mode of teaching.