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.
Should you have any doubts or questions, please check the Enrolment FAQs
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
Modules  Credits  TAF  SSD 

3° Year
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 (2019/2020)
Teaching code
4S00254
Academic staff
Coordinatore
Credits
6
Scientific Disciplinary Sector (SSD)
MAT/06  PROBABILITY AND STATISTICS
Language
Italian
Period
I semestre dal Oct 1, 2019 al Jan 31, 2020.
Learning outcomes
Stochastic Systems [ Applied Mathematics ]
AA 2018/2019
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
Stochastic Systems [ Applied Mathematics ]
AA 2018/2019 Syllabus
1) Markov chains with discrete time and finite state space: irreducibility and aperiodicity, stationary distributions, classification of states, MCMC.
2) Markov chains with countable state space: recurrence, positivity.
3) The Poisson process and other counting processes. Introduction to queuing theory.
4) Markov chains with finite state space and continuous time: associated semigroup, generator, stationary distributions, Kolmogorov equations, rate of convergence to equilibrium and functional inequalities,
Bibliografia
Author  Title  Publishing house  Year  ISBN  Notes 

Levin, David A., and Yuval Peres  Markov chains and mixing times  American Mathematical Society  2017  Scaricabile alla pagina https://s3.amazonaws.com/academia.edu.documents/30694248/recent.pdf?responsecontentdisposition=inline%3B%20filename%3DMarkov_chains_and_mixing_times.pdf&XAmzAlgorithm=AWS4HMACSHA256&XAmzCredential=AKIAIWOWYYGZ2Y53UL3A%2F20191005%2Fuseast1%2Fs3%2Faws4_request&XAmzDate=20191005T133241Z&XAmzExpires=3600&XAmzSignedHeaders=host&XAmzSignature=3c046ef319a0d4eaa4a83f4138d7950cb982f2f0c351b6f2e135234f11790559 
Examination Methods
Stochastic Systems [ Applied Mathematics ]
AA 2018/2019
The course is diveded into the following three parts
1) Theory of stochastic systems
2) Introduction to timeseries analysis
3) Computer exercises ( mainly based on the theory of Markov Chains, in discrete as well in continuous time )
Part (2) will be mainly performed in laboratory mode, using computer equipped classrooms, with the possibility, for each student to use a computer in order to implement , real time, the models proposed during the lesson. This activity will be supported by a tutor for a total amount of 24 (frontal) hours.
Part (3) will be taught by Prof. Caliari in a computer equipped laboratory.
The exam will be subdivided into the following three parts
* a written exam concerning point (1)
* a project presented in agreement with the programme developed with prof. Marco Caliari (point 3)
* exercises and a project concerning point (2)
The programme concerning the written exam, with respect to point (1), is the one reported in the Program section.
The project to be presented with prof. Caliari has to be decided with him.
The project to be presented with respect to point (2), will be chosen, by each student, within the the following list
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@Projects
@
@Warning: Since the list of projects may vary during the year, Students are warmly invited to directly contact prof. Di @Persio in order to choose the right project to develop, within the list of arguments that will be actually developed @during laboratory hours
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
1Compare the following methods of estimate and/or elimination of time series trends
*First order differences study
*Smoothing with moving average filter
*Fourier transform
*Exponential Smoothing
*Polynomial Data fitting
2 Describe and provide a numerical implementation of the onestep predictor for the following models
FIR(4)
ARX(3,1)
OE(3,1)
ARMA(2,3)
ARMAX(2,1,2)
BoxJenkins(nb,nc,nd,nf)
3 Compare the Prediction Error Minimization (PEM) and the Maximum Likelihood (ML) approach for the identification of the model parameters (it requires a personal effort in the homes ML)
4 Provide a concrete implementation for the kfold crossvalidation, e.g. using Matlab/Octave, following the exampletest that has been given during the lessons
5Detailed explanation of (at least) one of the following test
*ShapiroWilk
*KolmogorovSmirnov
*Lilliefors
Practical implementation of the project chosen by the student can be realized exploiting one of the following software frameworks : R, Python, Matlab, Gnu Octave, Excel
The final grade, expressed in thirtieths, will result from the following formula
Rating = (5/6) * T + (1/6) * E + P
where
T is the mark out of 30 on the part of Theory (written exam with prof. Di Persio)
It is the mark out of 30 on the part of Exercises (oral exam with prof. Caliari)
P is a score within the range [0,2]
It is important to emphasize how the objectives of the exam are also centered on assessing the individual student's ability to:
° carry out technical tasks defined in the modelmathematical settings;
° extract qualitative information from quantitative data with particular reference to the analysis of historical series, the study and the realization of predictive models, the development of automatic processes in the analysis of random phenomena;
° use computer/software tools such as R, Matlab, Gnu Octave, etc. , to realize models analyzed in the course and / or implemented in laboratory hours.
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.
Attendance
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 onsite.Please refer to the Crisis Unit's latest updates for the mode of teaching.
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 
4. Regolamento tesi (valido da luglio 2020)  259 KB, 29/07/21 
5. Regolamento tesi (valido da luglio 2022)  256 KB, 29/07/21 
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 
Mathematics Bachelor and Master thesis titles  Various topics 
Stage  Research area 

Internship proposals for students in mathematics  Various topics 
Gestione carriere
Further services
I servizi e le attività di orientamento sono pensati per fornire alle future matricole gli strumenti e le informazioni che consentano loro di compiere una scelta consapevole del corso di studi universitario.