## 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 sem. | Oct 3, 2016 | Jan 31, 2017 |

II sem. | Mar 1, 2017 | Jun 9, 2017 |

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

Sessione invernale Appelli d'esame | Feb 1, 2017 | Feb 28, 2017 |

Sessione estiva Appelli d'esame | Jun 12, 2017 | Jul 31, 2017 |

Sessione autunnale Appelli d'esame | Sep 1, 2017 | Sep 29, 2017 |

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

Sessione estiva Appelli di Laurea | Jul 20, 2017 | Jul 20, 2017 |

Sessione autunnale Appelli di laurea | Nov 23, 2017 | Nov 23, 2017 |

Sessione invernale Appelli di laurea | Mar 22, 2018 | Mar 22, 2018 |

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

Festa di Ognissanti | Nov 1, 2016 | Nov 1, 2016 |

Festa dell'Immacolata Concezione | Dec 8, 2016 | Dec 8, 2016 |

Vacanze di Natale | Dec 23, 2016 | Jan 8, 2017 |

Vacanze di Pasqua | Apr 14, 2017 | Apr 18, 2017 |

Anniversario della Liberazione | Apr 25, 2017 | Apr 25, 2017 |

Festa del Lavoro | May 1, 2017 | May 1, 2017 |

Festa della Repubblica | Jun 2, 2017 | Jun 2, 2017 |

Vacanze estive | Aug 8, 2017 | Aug 20, 2017 |

## 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

Cordoni Francesco Giuseppe

francescogiuseppe.cordoni@univr.itMagazzini Laura

laura.magazzini@univr.it 045 8028525Rossi Francesco

Zini Giovanni

## 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 |
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2° Year activated in the A.Y. 2017/2018

Modules | Credits | TAF | SSD |
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3° Year activated in the A.Y. 2018/2019

Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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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.

### Geometry (2017/2018)

Teaching code

4S00247

Teacher

Coordinator

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

II sem. dal Mar 1, 2018 al Jun 15, 2018.

## 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 course includes lectures, exercises sessions, and an exam. There will also be 12 hours of tutoring 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. Heine-Borel Theorem. Tychonoff Theorem. Bolzano-Weierstrass 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 arc-length. Inflection points. Curvature and radius of curvature. Center of curvature. Frenet-Serret formula.

Curves in the space:

Tangent line. Normal plane. Inflection points. Osculator plane. Curvatures. Principal frame. Frenet-Serret 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.

Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|

Abate, Tovena | Curve e Superfici (Edizione 1) | Springer | 2006 | ||

Kosniowski | Introduzione alla topologia algebrica (Edizione 1) | Zanichelli | 1988 |

## 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 (2 hours).

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.

**Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE**

## 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: 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 |

## 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

## 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