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, 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.
Should you have any doubts or questions, please check the Enrolment FAQs
Academic staff
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.
Advanced geometry (2019/2020)
Teaching code
4S003197
Teacher
Coordinatore
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/03  GEOMETRY
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.
Learning outcomes
This course provides students with the basic concepts of Graph Theory and the basics of Discrete and Computational Geometry. At the end of the course, the student will know the main classical theorems of graph theory, in particular about structural properties, colorings, matchings, embeddings and flow problems. He/she will also be familiar with basic Discrete Geometry results and with some classical algorithms of Computational Geometry. He/she will have the perception of links with some problems in non mathematical contexts. he/she will be able to produce rigorous proofs on all these topics and he/she will be able to read articles and texts of Graph Theory and Discrete Geometry.
Program
GRAPH THEORY
Definitions and basic properties.
Matching in bipartite graphs: Konig Theorem and Hall Theorem. Matching in general graphs: Tutte Theorem. Petersen Theorem.
Connectivity: Menger's theorems.
Planar Graphs: Euler's Formula, Kuratowski's Theorem.
Colorings Maps: Four Colours Theorem, Five Colours Theorem, Brooks Theorem, Vizing Theorem.
DISCRETE GEOMETRY
Convexity, convex sets convex combinations, separation. Radon's lemma. Helly's Theorem.
Lattices, Minkowski's Theorem, General Lattices.
Convex independent subsets, ErdosSzekeres Theorem.
Intersection patterns of Convex Sets, the fractional Helly Theorem, the colorful Caratheodory theorem.
Embedding Finite Metric Space into Normed Spaces, the JohnsonLindenstrauss Flattening Lemma
Discrete surfaces and discrete curvatures.
COMPUTATIONAL GEOMETRY
General overview: reporting vs counting, fixedradius near neighbourhood problem.
Convexhull problem: Graham's scan and other algorithms.
Polygons and Art Gallery problem. Art Gallery Theorem, polygon triangulation.
 Voronoi diagram and Fortune's algorithm.
 Delaunay triangulation properties and Minimum spanning tree.
Author  Title  Publishing house  Year  ISBN  Notes 

Diestel  Graph Theory (Edizione 5)  Springer  2016  
Matousek  Lectures on Discrete Geometry (Edizione 1)  Springer  2002 
Examination Methods
To pass the exam, students must show that:
 they know and understand the fundamental concepts of graph theory
 they know and understand the fundamental concepts of Discrete and Computational Geometry
 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 (2 hours).
The written exam on Graph Theory consists of three/four exercises and two questions (1 on general definition / concepts and 1 with a proof of a theorem presented during the lectures).
Oral Test (Mandatory)
It is a discussion with the lecturer on definitions and proofs discussed during the lectures about Discrete and Computational Geometry.
Bibliography
Type D and Type F activities
years  Modules  TAF  Teacher 

1° 2°  Python programming language  D 
Maurizio Boscaini
(Coordinatore)

1° 2°  SageMath  F 
Zsuzsanna Liptak
(Coordinatore)

1° 2°  History of Modern Physics 2  D 
Francesca Monti
(Coordinatore)

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

years  Modules  TAF  Teacher 

1° 2°  Advanced topics in financial engineering  D 
Luca Di Persio
(Coordinatore)

1° 2°  C Programming Language  D 
Sara Migliorini
(Coordinatore)

1° 2°  C++ Programming Language  D 
Federico Busato
(Coordinatore)

1° 2°  LaTeX Language  D 
Enrico Gregorio
(Coordinatore)

years  Modules  TAF  Teacher 

1° 2°  Axiomatic set theory for mathematical practice  F 
Peter Michael Schuster
(Coordinatore)

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
(Coordinatore)

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  HamiltonJacobi 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 
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 onsite.Please refer to the Crisis Unit's latest updates for the mode of teaching.