## 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, 2018 | Jan 31, 2019 |

II semestre | Mar 4, 2019 | Jun 14, 2019 |

Session | From | To |
---|---|---|

Sessione invernale d'esame | Feb 1, 2019 | Feb 28, 2019 |

Sessione estiva d'esame | Jun 17, 2019 | Jul 31, 2019 |

Sessione autunnale d'esame | Sep 2, 2019 | Sep 30, 2019 |

Session | From | To |
---|---|---|

Sessione di laurea estiva | Jul 22, 2019 | Jul 22, 2019 |

Sessione di laurea autunnale | Oct 15, 2019 | Oct 15, 2019 |

Sessione di laurea invernale | Mar 19, 2020 | Mar 19, 2020 |

Period | From | To |
---|---|---|

Sospensione attività didattica | Nov 2, 2018 | Nov 3, 2018 |

Vacanze di Natale | Dec 24, 2018 | Jan 6, 2019 |

Vacanze di Pasqua | Apr 19, 2019 | Apr 28, 2019 |

Vacanze estive | Aug 5, 2019 | Aug 18, 2019 |

## 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 |
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#### 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 (2018/2019)

Teaching code

4S003197

Teacher

Coordinatore

Credits

6

Language

English

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

II semestre dal Mar 4, 2019 al Jun 14, 2019.

## 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, Erdos-Szekeres Theorem.

-Intersection patterns of Convex Sets, the fractional Helly Theorem, the colorful Caratheodory theorem.

-Embedding Finite Metric Space into Normed Spaces, the Johnson-Lindenstrauss Flattening Lemma

-Discrete surfaces and discrete curvatures.

COMPUTATIONAL GEOMETRY

-General overview: reporting vs counting, fixed-radius near neighbourhood problem.

-Convex-hull 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

**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 |

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.