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, 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 autunnale  Dicembre  Dec 9, 2021  Dec 9, 2021 
Sessione invernale di laurea  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 di Pasqua  Apr 2, 2021  Apr 6, 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.
Academic staff
Raffaele Alice
alice.raffaele@univr.itStudy 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 

2° Year activated in the A.Y. 2021/2022
Modules  Credits  TAF  SSD 

3° Year activated in the A.Y. 2022/2023
Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

Modules  Credits  TAF  SSD 

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.
Geometry (2021/2022)
Teaching code
4S00247
Academic staff
Coordinator
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/03  GEOMETRY
Period
Primo semestre dal Oct 4, 2021 al Jan 28, 2022.
Learning outcomes
The course aims to provide students with the basic concepts of the general topology and the basics of differential geometry of curves and surfaces embedded in an Euclidean space.
At the end of the course, the student has a general and complete vision of topological properties in a wider context than that of real Euclidean spaces. He/She be able to recognize and compute the main geometrical characteristics of a curve and of a surface (Frenet frames, curvatures, fundamental quadratic forms ...). He/She also be able to produce rigorous arguments and proofs on these topics and he/she can read papers and advanced texts on Topology and Differential Geometry.
Program
The entire course will be available online. There will also be 12 hours of tutoring (also online) that will focus in particular on the resolution of topology exercises.
General Topology.
Topological space, definition. Examples: trivial topology, discrete topology, discrete topology, cofinite topology. Comparison of topologies. Basis. Neighbourhoods. Closure. Contnuos applications. Homeomorphisms. Limit points and isolated points. Dense set. Topological subspace, induced topology. Product spaces.
Separation axioms. Hausdorff spaces, Normal spaces, Regular spaces.
Countability axioms. Quotient space. Open and closed applications.
Relevant examples: sphere, projective space, Moebius strip...
Compactness. HeineBorel Theorem. Tychonoff Theorem. BolzanoWeierstrass Theorem.
Connectivity, local connectivity. Path connectivity. Examples and counterexamples. Simply connected, homotopy and fundamental group. Jordan curve Theorem.
Differential geometry of curves.
Curves in the plane:
Examples. Regular points and singular points. Embedding and immersion. Vector fields along a curve. Tangent vector and line. Length of an arc. Parametrization by arclength. Inflection points. Curvature and radius of curvature. Center of curvature. FrenetSerret formula.
Curves in the space:
Tangent line. Normal plane. Inflection points. Osculator plane. Curvatures. Principal frame. FrenetSerret formula. Torsion. Fundamental Theorem.
Differential geometry of surfaces.
Definitions. Differentiable atlas. Oriented atlas, Tangent plane, Normal versor.
First fundamental quadratic form: metric and area. Tangential curvature and normal curvature of a curve on a surface. Curvatures, normal sections, Meusnier Theorem. Principal curvatures, Gaussian curvature and mean curvature: Theorem Egregium. Geodetics.
Bibliography
Examination Methods
To pass the exam, students must show that:
 they know and understand the fundamental concepts of general topology
 they know and understand the fundamental concepts of local theory of curves and surfaces
 they have analysis and abstraction abilities
 they can apply this knowledge in order to solve problems and exercises and they can rigorously support their arguments.
Written test (150 minutes).
The exam consists of four exercises (2 on topology, 1 on curve theory and 1 on surfaces theory) and two questions (1 on general definition / concepts and 1 with a proof of a theorem presented during the lectures).
Oral Test (Optional)
It is a discussion with the lecturer on definitions and proofs discussed during the lessons.
Type D and Type F activities
Le attività formative in ambito D o F comprendono gli insegnamenti impartiti presso l'Università di Verona o periodi di stage/tirocinio professionale.
Nella scelta delle attività di tipo D, gli studenti dovranno tener presente che in sede di approvazione si terrà conto della coerenza delle loro scelte con il progetto formativo del loro piano di studio e dell'adeguatezza delle motivazioni eventualmente fornite.
years  Modules  TAF  Teacher  

1° 2°  History and Didactics of Geology  D 
Guido Gonzato
(Coordinator)


1° 2° 3°  Algorithms  D 
Roberto Segala
(Coordinator)


1° 2° 3°  Scientific knowledge and active learning strategies  F 
Francesca Monti
(Coordinator)


1° 2° 3°  Genetics  D 
Massimo Delledonne
(Coordinator)

years  Modules  TAF  Teacher 

1° 2° 3°  Algorithms  D 
Roberto Segala
(Coordinator)

1° 2° 3°  Python programming language  D 
Vittoria Cozza
(Coordinator)

1° 2° 3°  Organization Studies  D 
Giuseppe Favretto
(Coordinator)

years  Modules  TAF  Teacher  

1°  Subject requirements: mathematics  D 
Rossana Capuani


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  
1° 2° 3°  Introduzione all'analisi non standard  F 
Sisto Baldo


1° 2° 3°  C Programming Language  D 
Pietro Sala
(Coordinator)


1° 2° 3°  LaTeX Language  D 
Enrico Gregorio
(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.
Graduation
Documents
Title  Info File 

1. Come scrivere una tesi  pdf, it, 31 KB, 29/07/21 
2. How to write a thesis  pdf, it, 31 KB, 29/07/21 
5. Regolamento tesi  pdf, it, 171 KB, 20/03/24 
List of thesis proposals
theses proposals  Research area 

Formule di rappresentazione per gradienti generalizzati  Mathematics  Analysis 
Formule di rappresentazione per gradienti generalizzati  Mathematics  Mathematics 
Proposte Tesi A. Gnoatto  Various topics 
Mathematics Bachelor and Master thesis titles  Various topics 
THESIS_1: Sensors and Actuators for Applications in MicroRobotics and Robotic Surgery  Various topics 
THESIS_2: Force Feedback and Haptics in the Da Vinci Robot: study, analysis, and future perspectives  Various topics 
THESIS_3: CableDriven Systems in the Da Vinci Robotic Tools: study, analysis and optimization  Various topics 
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 onsite.
Parttime enrolment is permitted. Find out more on the Parttime 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
Erasmus+ and other experiences abroad
Ongoing orientation for students
The committee has the task of guiding the students throughout their studies, guiding them in their choice of educational pathways, making them active participants in the educational process and helping to overcome any individual difficulties.
It is composed of professors Lidia Angeleri, Sisto Baldo, Marco Caliari, Paolo dai Pra, Francesca Mantese, and Nicola Sansonetto
To send an email to professors: name.surname@univr.it