## 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, 2015 | Jan 29, 2016 |

II semestre | Mar 1, 2016 | Jun 10, 2016 |

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

Sessione straordinaria Appelli d'esame | Feb 1, 2016 | Feb 29, 2016 |

Sessione estiva Appelli d'esame | Jun 13, 2016 | Jul 29, 2016 |

Sessione autunnale Appelli d'esame | Sep 1, 2016 | Sep 30, 2016 |

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

Sess. autun. App. di Laurea | Oct 12, 2015 | Oct 12, 2015 |

Sess. autun. App. di Laurea | Nov 26, 2015 | Nov 26, 2015 |

Sess. invern. App. di Laurea | Mar 15, 2016 | Mar 15, 2016 |

Sess. estiva App. di Laurea | Jul 19, 2016 | Jul 19, 2016 |

Sess. autun. 2016 App. di Laurea | Oct 11, 2016 | Oct 11, 2016 |

Sess. autun 2016 App. di Laurea | Nov 30, 2016 | Nov 30, 2016 |

Sess. invern. 2017 App. di Laurea | Mar 16, 2017 | Mar 16, 2017 |

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

Festività dell'Immacolata Concezione | Dec 8, 2015 | Dec 8, 2015 |

Vacanze di Natale | Dec 23, 2015 | Jan 6, 2016 |

Vacanze Pasquali | Mar 24, 2016 | Mar 29, 2016 |

Anniversario della Liberazione | Apr 25, 2016 | Apr 25, 2016 |

Festa del S. Patrono S. Zeno | May 21, 2016 | May 21, 2016 |

Festa della Repubblica | Jun 2, 2016 | Jun 2, 2016 |

Vacanze estive | Aug 8, 2016 | Aug 15, 2016 |

## 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

Rinaldi Davide

davide.rinaldi@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 enrolment year.

Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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1° Year

Modules | Credits | TAF | SSD |
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2° Year

Modules | Credits | TAF | SSD |
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3° Year

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 (2016/2017)

Teaching code

4S00247

Teacher

Coordinatore

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

II sem. dal Mar 1, 2017 al Jun 9, 2017.

## 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.

## 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 |
---|---|

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 |

## 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.