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.
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, 2013 | Jan 31, 2014 |
| II semestre | Mar 3, 2014 | Jun 13, 2014 |
| Session | From | To |
|---|---|---|
| Sessione straordinaria | Feb 3, 2014 | Feb 28, 2014 |
| Sessione estiva | Jun 16, 2014 | Jul 31, 2014 |
| Sessione autunnale | Sep 1, 2014 | Sep 30, 2014 |
| Session | From | To |
|---|---|---|
| Sessione autunnale | Oct 15, 2013 | Oct 15, 2013 |
| Sessione straordinaria | Dec 9, 2013 | Dec 9, 2013 |
| Sessione invernale | Mar 18, 2014 | Mar 18, 2014 |
| Sessione estiva | Jul 21, 2014 | Jul 21, 2014 |
| Period | From | To |
|---|---|---|
| Vacanze Natalizie | Dec 22, 2013 | Jan 6, 2014 |
| Vacanze di Pasqua | Apr 17, 2014 | Apr 22, 2014 |
| Festa del S. Patrono S. Zeno | May 21, 2014 | May 21, 2014 |
| Vacanze Estive | Aug 11, 2014 | Aug 15, 2014 |
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
Squassina Marco
marco.squassina@univr.it +39 045 802 7913
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 |
|---|
1° 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.
Functional analysis (2013/2014)
Teaching code
4S001101
Credits
12
Language
English
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
The teaching is organized as follows:
Parte 1
Parte 2
Parte 3
Credits
3
Period
I semestre
Academic staff
Marco Squassina
Learning outcomes
The course introduces to the basic concepts of measure theory (Lebesgue and abstract) and of modern functional analysis, with particular emphasis on Banach and Hilbert spaces. Whenever possible, abstract results will be presented together with applications to concrete function spaces and problems: the aim is to show how these techniques are useful in the different fields of pure and applied mathematics.
Program
Lebesgue measure and integral. Outer measures, abstract integration, integral convergence theorems. Banach spaces and their duals. Theorems of Hahn-Banach, of the closed graph, of the open mapping, of Banach-Steinhaus. Reflexive spaces. Spaces of sequences. Lp and W1,p spaces: functional properties and density/compactness results. Hilbert spaces, Hilbert bases, abstract Fourier series. Weak convergence and weak compactness. Spectral theory for self adjoint, compact operators. Basic notions from the theory of distributions.
Bibliography
| Activity | Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|---|
| Parte 1 | Brezis, Haïm | Analisi funzionale. Teoria e applicazioni | Liguori | 1986 | 8820715015 | |
| Parte 1 | A.N. Kolmogorov, S.V. Fomin | Elementi di teoria delle funzioni e di analisi funzionale (Edizione 4) | MIR | 1980 | xxxx | |
| Parte 1 | Kolmogorov, A.; Fomin, S. | Elements of the Theory of Functions and Functional Analysis | Dover Publications | 1999 | 0486406830 | |
| Parte 1 | Haim Brezis | Functional Analysis, Sobolev Spaces and Partial Differential Equations | Springer | 2011 | 0387709134 |
Examination Methods
Written and oral test.
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Teaching materials
-
Lecture Notes (28/11/2013)
(en, 750 KB, 28/11/13)
-
Mid terms test of the past Academic Year 2012-2013
(it, 602 KB, 13/11/13)
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course diary - part 2
(it, 154 KB, 23/01/14)
-
Some exercise of functional analysis, N.1
(it, 26 KB, 20/10/13)
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Some exercise of functional analysis, N.2
(it, 28 KB, 20/10/13)
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Some exercise of functional analysis, N.3
(it, 28 KB, 20/10/13)
-
Some exercise of functional analysis, N.4
(it, 35 KB, 15/11/13)
-
Some exercise of functional analysis, N.5
(it, 34 KB, 15/11/13)
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.
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.
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)
|
171 KB, 17/02/22 |
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 |
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.
The latest Call for applications for Double/Joint Degrees at the University of Verona is available now!
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.Attachments
| Title | Info File |
|---|---|
|
1. Convenzione | Learning Agreement UNITN - UNIVR
|
167 KB, 27/08/21 |
|
2. Sostituzione insegnamenti a UNITN - Courses replacement at UNITN
|
44 KB, 30/08/21 |
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3. Sostituzione insegnamenti a UNIVR - Courses replacement at UNIVR
|
113 KB, 30/08/21 |
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 on-site.Please refer to the Crisis Unit's latest updates for the mode of teaching.
