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, 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 di laurea estiva | Jul 22, 2020 | Jul 22, 2020 |
Sessione di laurea autunnale | Oct 14, 2020 | Oct 14, 2020 |
Sessione di laurea invernale | 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
![Foto, June 23, 2016](https://docs.univr.it/documenti//Persona/foto/foto574302.jpg)
Rapa Alessandro
![foto, December 14, 2020](https://docs.univr.it/documenti//Persona/foto/foto367750.jpg)
Rubio Y Degrassi Lleonard
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.
1° Year
Modules | Credits | TAF | SSD |
---|
Modules | Credits | TAF | SSD |
---|
Modules | Credits | TAF | SSD |
---|
1 module between the following
1 module between the following
3 modules among the following
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.
Optimization (2020/2021)
Teaching code
4S001106
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Period
I semestre dal Oct 1, 2020 al Jan 29, 2021.
Learning outcomes
In this course we will provide an introduction to Convex Analysis in finite and infinite-dimensional spaces. We will show also some applications to problems of nonlinear optimizations and control theory arising from physics and economics. At the end of the course, the student should be able to: - understand the deep link between this and the previous courses (in particular, Functional Analysis); - use the main tools of convex analysis to solve convex optimization problems; - formalize and analyze simple control system coming from physical and economics models, in the framework of optimal control theory; - be autonomous in the use of the textbook suggested for the course.
Program
Table of contents
==============
- Review of weak topology on Banach spaces: convex sets, Minkowski functional, linear continuous operators, weak topology, separation of convex sets.
- Convex functions: general properties, lower semicontinuous convex functions, convex conjugate, subdifferential in the sense of Convex Analysis. Introduction to Calculus of Variations.
- Generalizations of convexity: differential calculus in Hilbert and Banach spaces, proximal and limiting subdifferential, the density theorem, sum rule, chain rule, generalized gradient in Banach space.
- Introduction to control theory: multifunctions and trajectories of differential inclusions, viability,
equilibria, invariance, stabilization, reachability, Pontryagin Maximum Principle, necessary conditions
for optimality.
- Application to optimization problems arising from physical or economic models.
The course is divided in two part: 5 ECTS (Theory, 40 hours) and 1 ECTS (Exercises, 12 hours). Both part will be held as in class lectures.
During the course some cases of study will be assigned to groups of 4-5 student and will be discussed.
Recommended Textbooks
=====================
Ivar Ekeland and Roger Témam, Convex Analysis and Variational Problems, Ed. SIAM (1987)
F.H. Clarke, Y.S. Ledyaev, Ronald J. Stern, P.R. Wolenski, Nonsmooth Analysis and Control Theory, Ed. Springer-Verlag New York Inc. (1998)
Frank H. Clarke, Optimization and Nonsmooth Analysis, Ed. SIAM (1990)
**************************************
WARNING: DUE TO SANITARY EMERGENCY, ALL THE LECTURES WILL BE RECORDED AND WILL BE AVAILABLE IN THE MOODLE PAGE OF THE COURSE. SOME LECTURES WILL BE HELD IN CLASS (CHECK THE SCHEDULE FOR FURTHER DETAILS).
Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|
Ralph Tyrrell Rockafellar | Convex Analysis | Princeston University Press | 1997 | 9780691015866 | |
Ivar Ekeland and Roger Témam | Convex Analysis and Variational Problems | SIAM | 1987 | 0-89871-450-8 | |
F.H. Clarke, Y.S. Ledyaev, Ronald J. Stern, P.R. Wolenski | Nonsmooth Analysis and Control Theory | Springer-Verlag New York Inc. | 1998 | 0387983368 | |
Frank H. Clarke | Optimization and Nonsmooth Analysis | SIAM | 1990 | 0-89871-256-4 |
Examination Methods
WARNING: THE ASSESSMENT PROCEDURES ARE SUBJECTED TO CHANGES FOLLOWING THE EVOLUTION OF THE COVID-19 EPIDEMY.
Remote examination will be granted for all students requiring it in the academic year 2020/2021.
Assessment Procedure
===================
The exam is divided into a written and an oral test, the two tests must be passed in the same exam session. There are no difference between the assessment of attending or non-attending students.
There will be also two partial test, one at the mid of the semester (indicatively, end of November), and the other one at the end of the semester. The first part will concern the first part of the program (until the introduction to the Calculus of Variations included), and the second on the remaining part of the program. The students who will pass both the partial tests, can directly access to the oral part in the exam session of February.
After the oral part, the teacher will propose the final mark (on the Italian ranking system from 18 to 30).
Structure of the tests
==================
The written test is concerns three exercise, and each of them will have the same contribute to the final mark. The first two exercises (one on the first part and the other on the second part of the program) will require the solution of specific problems. The third will be composed of questions on the whole of the program or on the material given to the students, asking for short open answers.
Each of the partial test will concern the relative part of the program, and will be made of three exercise. The first two will require the solution of specific problems, and the third one will be composed of questions on the relative part of the program or on the material given to the students, asking for short open answers. It will be mandatory for the student to solve the third exercise and choose one between the first and the second.
The oral part will test the whole of the program of the course.
Targets of the assessment procedure
===============================
- Knowledge and understanding: a part of the written and the oral tests will be devoted to verify the effective knowledge and understanding of the course's contents (mainly, the third exercise of the written test and the oral test).
- Applying knowledge and understanding: both during the written and the oral tests, the student will be required to solve problems based on the course's contents.
- Making judgements: during the tests, the student can be asked to solve problems requiring a contribution basing on the material of the course assigned for personal study.
- Communication skills: during the written and the oral tests, the solutions expressed in a clear, complete and short way will be preferred.
- Learning skills: part of the course's contents will be based on textbook or scientific articles left to the students for personal study.
Type D and Type F activities
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° | Python programming language | D |
Maurizio Boscaini
(Coordinator)
|
1° 2° | SageMath | F |
Zsuzsanna Liptak
(Coordinator)
|
1° 2° | History of Modern Physics 2 | D |
Francesca Monti
(Coordinator)
|
1° 2° | History and Didactics of Geology | D |
Guido Gonzato
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° | Advanced topics in financial engineering | D |
Luca Di Persio
(Coordinator)
|
1° 2° | C Programming Language | D |
Sara Migliorini
(Coordinator)
|
1° 2° | C++ Programming Language | D |
Federico Busato
(Coordinator)
|
1° 2° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° | Axiomatic set theory for mathematical practice | F |
Peter Michael Schuster
(Coordinator)
|
1° 2° | Corso Europrogettazione | D | Not yet assigned |
1° 2° | Corso online ARPM bootcamp | F | Not yet assigned |
1° 2° | ECMI modelling week | F | Not yet assigned |
1° 2° | ESA Summer of code in space (SOCIS) | F | Not yet assigned |
1° 2° | Google summer of code (GSOC) | F | Not yet assigned |
1° 2° | Higher Categories - Seminar course | F |
Lidia Angeleri
(Coordinator)
|
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 also via the Univr app.
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
Title | Info File |
---|---|
![]() |
pdf, it, 167 KB, 27/08/21 |
![]() |
pdf, it, 97 KB, 29/07/24 |
![]() |
pdf, it, 113 KB, 30/08/21 |
Attendance modes and venues
As stated in the Teaching Regulations , 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.
Part-time enrolment is permitted. Find out more on the Part-time enrolment possibilities page.
The course's teaching activities take place in the Science and Engineering area, which consists of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma campus.
Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.
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 |
---|---|
![]() |
pdf, it, 31 KB, 02/11/22 |
![]() |
pdf, en, 31 KB, 02/11/22 |
![]() |
pdf, it, 171 KB, 20/03/24 |
List of thesis 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 |