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, 2020 | Jan 29, 2021 |
| II semestre | Mar 1, 2021 | Jun 11, 2021 |
| Session | From | To |
|---|---|---|
| Sessione invernale d'esame | Feb 1, 2021 | Feb 26, 2021 |
| Sessione estiva d'esame | Jun 14, 2021 | Jul 30, 2021 |
| Sessione autunnale d'esame | Sep 1, 2021 | Sep 30, 2021 |
| Session | From | To |
|---|---|---|
| Sessione di laurea estiva | Jul 22, 2021 | Jul 22, 2021 |
| Sessione di laurea autunnale | Oct 14, 2021 | Oct 14, 2021 |
| Sessione di laurea invernale | Mar 16, 2022 | Mar 16, 2022 |
| Period | From | To |
|---|---|---|
| Festa dell'Immacolata | Dec 8, 2020 | Dec 8, 2020 |
| Vacanze Natalizie | Dec 24, 2020 | Jan 3, 2021 |
| Vacanze Pasquali | Apr 2, 2021 | Apr 5, 2021 |
| Festa del Santo Patrono | May 21, 2021 | May 21, 2021 |
| Festa della Repubblica | Jun 2, 2021 | Jun 2, 2021 |
| Vacanze estive | Aug 9, 2021 | Aug 15, 2021 |
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 Enrollment FAQs
Academic staff
+39 045 802 7913
andrea.albiero@univr.it
leonardpeter.bos@univr.it
vittoria.cozza@univr.it
federicoluigi.dipasquale@univr.it
matteo.garbelli@univr.it
davide.mattiolo@univr.it
Rapa Alessandro
alessandro.rapa@univr.it
Rubio Y Degrassi Lleonard
lleonard.rubioydegrassi@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.
1° Year
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
1 module between the following1 module between the following 3 modules among the followingLegend | 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.
Differential geometry (2020/2021)
Teaching code
4S003196
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
Period
I semestre dal Oct 1, 2020 al Jan 29, 2021.
Learning outcomes
The course aims to provide students with the basic concepts on Differential Geometry of manifolds. At the end of the course the student will know the main terminology and definitions about manifolds and Riemannian manifolds, and some of the main results. He/she will be able to produce rigorous arguments and proofs on these topics and he/she will be able to read articles and texts of Differential Geometry.
Program
All the lectures will be held in-class and the entire course will be available also online.
In addition, notes for each lecture will be provided.
-REVIEW GENERAL TOPOLOGY
-SURFACES EMBEDDED IN THE EUCLIDEAN 3-SPACE:
• Differentiable Atlas
• Orientable Atlas
• Tangent plane
• Normal versor
• First Fundamental Form: lengths and area
• Geodesic curvature and normal curvature
• Normal sections and Meusnier Theorem
• Principal Curvatures, Gaussian curvature, Mean curvature: minimal surfaces
• Theorema Egregium
• Geodetics
- TENSOR CALCULUS
• Free vector space
• Tensor product of two vector spaces
• Tensor product of n vector spaces
• Tensor Algebra
• Transformation of the componenents of a tensoriale
• Mixed tensors
• Symmetric tensors
• Antysimmetric (alternating) tensors
• Exterior Algebra
• Determinant
• Area and Volume
-DIFFERENTIAL MANIFOLDS
• Definition and examples
• Classification of 1-manifolds
• Classification of simply-connected 2-manifolds
• Product and quotient spaces
• Differentiable maps
• Tangent space and tangent bundle
• Vector field on a manifold
• Tensor field
• Exterior Algebra on manifolds
• Riemannian Manifolds
• Metric Tensor
• Orientations
• Volume
• Exterior derivative
• De Rham Cohomology
• Homotopy
-AFFINE CONNECTION AND CURVATURE TENSOR
• Affine connection
• Parallel transport
• Levi-Civita connection
• Geodetics
• Riemann curvature tensor
• Bianchi identities
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| Do Carmo | Differential Geometry of Curves and Surfaces (Edizione 2) | 2016 | |||
| Do Carmo | Riemannian Geometry | 1992 | |||
| Jürgen Jost | Riemannian Geometry and Geometric Analysis (Edizione 5) | Springer | 2008 |
Examination Methods
During the exam, students must show that:
- they know and understand the fundamental concepts of differential geometry
- they have analytical and abstraction abilities
- they support their argumentation with mathematical rigor.
The exam consists of a written test in which the student will have to choose one of two essays in which they provide a broad discussion of one of the topics presented during the lectures (answer approximately 2/3 pages ) and two of three short questions (answer approximately 10 rows).
Type D and Type F activities
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Algorithms | D |
Roberto Segala
(Coordinator)
|
| 1° 2° | Scientific knowledge and active learning strategies | F |
Francesca Monti
(Coordinator)
|
| 1° 2° | Genetics | D |
Massimo Delledonne
(Coordinator)
|
| 1° 2° | History and Didactics of Geology | D |
Guido Gonzato
(Coordinator)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 1° 2° | Advanced topics in financial engineering | F |
Luca Di Persio
(Coordinator)
|
| 1° 2° | Algorithms | D |
Roberto Segala
(Coordinator)
|
| 1° 2° | Python programming language | D |
Vittoria Cozza
(Coordinator)
|
| 1° 2° | Organization Studies | D |
Giuseppe Favretto
(Coordinator)
|
| years | Modules | TAF | Teacher |
|---|---|---|---|
| 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° | Introduzione all'analisi non standard | F |
Sisto Baldo
|
| 1° 2° | C Programming Language | D |
Pietro Sala
(Coordinator)
|
| 1° 2° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
| 1° 2° | Mathematics mini courses | F |
Marco Caliari
(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 |
|---|---|
1. Convenzione | Learning Agreement UNITN - UNIVR
|
pdf, it, 167 KB, 27/08/21 |
|
2. Sostituzione insegnamenti a UNITN - Courses replacement at UNITN
|
pdf, it, 97 KB, 29/07/24 |
|
3. Sostituzione insegnamenti a UNIVR - Courses replacement at UNIVR
|
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 |
|---|---|
|
1. Come scrivere una tesi
|
pdf, it, 31 KB, 02/11/22 |
|
2. How to write a thesis
|
pdf, en, 31 KB, 02/11/22 |
|
5. Regolamento tesi
|
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 |
