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 sem. Oct 2, 2017 Jan 31, 2018
II sem. Mar 1, 2018 Jun 15, 2018
Exam sessions
Session From To
Sessione invernale d'esami Feb 1, 2018 Feb 28, 2018
Sessione estiva d'esame Jun 18, 2018 Jul 31, 2018
Sessione autunnale d'esame Sep 3, 2018 Sep 28, 2018
Degree sessions
Session From To
Sessione di laurea estiva Jul 23, 2018 Jul 23, 2018
Sessione di laurea autunnale Oct 17, 2018 Oct 17, 2018
Sessione di laurea invernale Mar 22, 2019 Mar 22, 2019
Holidays
Period From To
Christmas break Dec 22, 2017 Jan 7, 2018
Easter break Mar 30, 2018 Apr 3, 2018
Patron Saint Day May 21, 2018 May 21, 2018
VACANZE ESTIVE Aug 6, 2018 Aug 19, 2018

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 Enrollment FAQs

Academic staff

A B C D G M O R S Y

Agostiniani Virginia

symbol email virginia.agostiniani@univr.it symbol phone-number +39 045 802 7979

Albi Giacomo

symbol email giacomo.albi@univr.it symbol phone-number +39 045 802 7913

Baldo Sisto

symbol email sisto.baldo@univr.it symbol phone-number 0458027935

Bos Leonard Peter

symbol email leonardpeter.bos@univr.it symbol phone-number +39 045 802 7987

Caliari Marco

symbol email marco.caliari@univr.it symbol phone-number +39 045 802 7904

Daldosso Nicola

symbol email nicola.daldosso@univr.it symbol phone-number +39 045 8027076 - 7828 (laboratorio)

Di Persio Luca

symbol email luca.dipersio@univr.it symbol phone-number +39 045 802 7968

Gregorio Enrico

symbol email Enrico.Gregorio@univr.it symbol phone-number 045 802 7937

Mantese Francesca

symbol email francesca.mantese@univr.it symbol phone-number +39 0458027978

Marigonda Antonio

symbol email antonio.marigonda@univr.it symbol phone-number +39 045 802 7809
Foto,  October 5, 2015

Mazzuoccolo Giuseppe

symbol email giuseppe.mazzuoccolo@univr.it symbol phone-number +39 0458027838

Monti Francesca

symbol email francesca.monti@univr.it symbol phone-number 045 802 7910

Orlandi Giandomenico

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

Rizzi Romeo

symbol email romeo.rizzi@univr.it symbol phone-number +39 045 8027088

Sansonetto Nicola

symbol email nicola.sansonetto@univr.it symbol phone-number 045-8027976

Schuster Peter Michael

symbol email peter.schuster@univr.it symbol phone-number +39 045 802 7029

Solitro Ugo

symbol email ugo.solitro@univr.it symbol phone-number +39 045 802 7977

Yengui Ihsen

symbol email ihsen.yengui@univr.it

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 enrollment year.

CURRICULUM TIPO:

2° Year   activated in the A.Y. 2018/2019

ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
activated in the A.Y. 2018/2019
ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°To be chosen between
Between the years: 1°- 2°
Between the years: 1°- 2°
Other activitites
4
F
-

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

4S001444

Coordinator

Luca Di Persio

Credits

6

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Period

II sem. dal Mar 1, 2018 al Jun 15, 2018.

Learning outcomes

This course will provide an introduction to the theory of Stochastic Differential Equations (SDEs), mainly based on the Brownian motion type of noise

The purpose of this course is to introduce and analyse probability models that capture
the stochastic features of the system under study to predict the short and long term
effects that this randomness will have on the systems under consideration. The study
of probability models for continuous-time stochastic processes involves a broad range of mathematical and computational tools. This course will strike a balance between the mathematics and the applications. The main applications will be mathematical finance, biology and populations evolution, also with respect to their descriptions in terms of the associated SDEs.
Topics include: construction of Brownian motion; martingales in continuous time; stochastic integral; Ito calculus; stochastic differential equations; Girsanov theorem; martingale representation; the Feynman-Kac formula and Lévy processes.

Some references
• Introduction to Stochastic Calculus Applied to Finance by D. Lamberton and B. Lapeyre
• Diffusions, Markov Processes and Martingales by L. Rogers and D. Williams, vol 2.
• Stochastic Differential Equations and Diffusion Processes by N. Ikeda and S. Watanabe
• Stochastic differential equations, by B. Øksendal.
• Brownian motion and stochastic calculus, by I. Karatzas and S. Shreve.
• Continuous martingales and Brownian motion, by D. Revuz and M. Yor.
• Stochastic integration and differential equations, by P. Protter.
• Probability with martingales, by D. Williams.

Program

Course Plan

I) BACKGROUND: sigma-algebras, filtrations, conditional expectation, martingale property, variations of a function, quadratic variation.

II) RANDOM WALK: random walk, rescaled random walk, martingale property.

III) BROWNIAN MOTION: definition of Brownian motion, function of a Brownian motion, martingale property, exponential martingale, applications in biology and finance, examples and exercises.

IIIa) SHORT INTRODUCTION TO JUMP PROCESSES: motivation, Poisson processes, properties, discrete time case, introduction to Galton Watson model.

III) WIENER INTEGRAL: motivation, case of step function, definition of Wiener integral, properties, law, martingale, quadratic variation, applications in biology and finance, examples and exercises.

IV) STOCHASTIC INTEGRALS: motivation, case of step function, definition of stochastic integral, properties, martingale, quadratic variation, variance, finite variation processes, Ito processes, applications in biology and finance, examples and exercises.

V) ITO CALCULUS: motivation, Itō-Doeblin formula for Brownian motion, Itō-Doeblin formula for function depending on time,Itō-Doeblin formula for Ito processes, applications in biology and finance, examples and exercises.

VI) SDEs: motivations, definition, existence and uniqueness result, applications in biology and finance, examples and exercises.

VII) MULTI-DIMENSIONAL CASE: multi-dim Brownian motion, correlation, multi-dim Ito-formula,
SDE, applications in biology and finance, examples and exercises.

VIII) CHANGE OF PROBABILITY: motivations, Cameron-Martin theorem, Girsanov theorem, representation of martingale theorem, applications in biology and finance, examples and exercises.

IX) FEYNMAN KAC FORMULA: motivation, Feynman Kac formula, link PDE/SDE, Monte-Carlo methods.

X) JUMPS PROCESSES: Levy processes, characterization and properties.

Reference texts
Author Title Publishing house Year ISBN Notes
I. Karatzas and S. Shreve Brownian motion and stochastic calculus  
D. Revuz and M. Yor Continuous martingales and Brownian motion  
L. Rogers and D. Williams Diffusions, Markov Processes and Martingales (Vol 2.)  
D. Lamberton and B. Lapeyre Introduction to Stochastic Calculus Applied to Finance  
D. Williams Probability with martingales  
S. E. Shreve Stochastic Calculus for Finance II: Continuous-Time Models Springer, New York 2004
B. Øksendal Stochastic Differential Equations  
N. Ikeda and S. Watanabe Stochastic Differential Equations and Diffusion Processes  
P. Protter Stochastic integration and differential equations  

Examination Methods

Wrriten exam. An intermediate (mid-term) exam is forecasted. Then, will be a final exam focusing on the
whole course.

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

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: 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.

Double degree

The University of Verona, through a network of agreements with foreign universities, offers international courses that enable students to gain a Double/Joint degree at the time of graduation. Indeed, students enrolled in a Double/Joint degree programme will be able to obtain both the degree of the University of Verona and the degree issued by the Partner University abroad - where they are expected to attend part of the programme -, in the time it normally takes to gain a common Master’s degree. The institutions concerned shall ensure that both degrees are recognised in the two countries.

Places on these programmes are limited, and admissions and any applicable grants are subject to applicants being selected in a specific Call for applications.

It's online Erasmus + - double joint degree a.y. 2024/2025

The latest Call for applications for Double/Joint Degrees at the University of Verona is available now!

For the presentation of the LA and subsequent recognition of CFUs, please refer to the International Mobility Regulations.

 

Documents


Alternative learning activities

In order to make the study path more flexible, it is possible to request the substitution of some modules with others of the same course of study in Mathematics at the University of Verona (if the educational objectives of the modules to be substituted have already been achieved in the previous career), or with others of the course of study in Mathematics at the University of Trento.

Documents


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 on-site.
 


Career management


Student login and resources


Graduation

Deadlines and administrative fulfilments

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

Need to activate a thesis internship

For thesis-related internships, it is not always necessary to activate an internship through the Internship Office. For further information, please consult the dedicated document, which can be found in the 'Documents' section of the Internships and work orientation - Science e Engineering service.

Final examination regulations

Upon completion of the Master’s degree dissertation students are awarded 32 CFU. The final examination consists of a written dissertation on a specific topic agreed with a supervising professor and presented to a commission (Dissertation Committee).

The dissertation can be high-level theoretical or experimental (in the latter case, it may focus on either basic or applied research), it can deal with a theoretical topic or propose the resolution of a specific problem, or description of a work project, and may be carried out at universities, research institutions, schools, laboratories and companies in the framework of internships, traineeships, study stays in Italy and abroad. The dissertation must be original and written by the student under the guidance of a Supervisor. At the request of the student, the dissertation may be written and presented in Italian.

Professors belonging to the Mathematics Teaching Committee, the Department of Computer Science, and any associated departments may be appointed as Supervisors, as well as any professors from the University of Verona whose area of interest (SSD - Scientific-disciplinary Sector) is included in the teaching regulations of the degree programme.

Students may take the final exam only if meeting all requirements set by the School of Sciences and Engineering.

The Master's degree in Mathematics is obtained by successfully passing the final examination and thus earning the 120 CFU included in the study plan.

The material submitted by the student for the final examination will be examined by the Dissertation Committee, which comprises three professors, possibly including the Supervisor, and appointed by the President of the Teaching Committee. The final examination will be assessed based on the following criteria: the student’s performance during the entire study programme, the knowledge acquired during the dissertation work, their understanding of the topic and autonomy of judgment, their ability to apply such knowledge, and communicate effectively and fully all the outcomes of the work and the main results obtained.

The final examination and the degree ceremony will be carried out, in one of the four graduation sessions throughout the academic year, by the Final Examination Committee appointed by the President of the Teaching Committee, and made up of a president and at least four members chosen from among the professors of the University.

For further information, please refer to the Final examination regulations.

Documents

Title Info File
File pdf 1. Come scrivere una tesi pdf, it, 31 KB, 02/11/22
File pdf 2. How to write a thesis pdf, en, 31 KB, 02/11/22
File pdf 5. Regolamento tesi pdf, it, 171 KB, 20/03/24

List of theses and work experience proposals

theses proposals Research area
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Hamilton-Jacobi theories, including dynamic programming
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Manifolds
Controllo di sistemi multiagente Calculus of variations and optimal control; optimization - Optimality conditions
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

Erasmus+ and other experiences abroad