## 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 autunnale straordinaria | Nov 21, 2019 | Nov 21, 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 Enrollment FAQs

## Academic staff

Magazzini Laura

laura.magazzini@univr.it 045 8028525Mazzuoccolo Giuseppe

giuseppe.mazzuoccolo@univr.it +39 0458027838## 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. 2019/2020

Modules | Credits | TAF | SSD |
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3° Year activated in the A.Y. 2020/2021

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 (2019/2020)

Teaching code

4S00247

Teacher

Coordinator

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

I semestre dal Oct 1, 2019 al Jan 31, 2020.

## 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 soon 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 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 |

Proposte Tesi A. Gnoatto | Various topics |

Mathematics Bachelor and Master thesis titles | Various topics |

THESIS_1: Sensors and Actuators for Applications in Micro-Robotics 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: Cable-Driven Systems in the Da Vinci Robotic Tools: study, analysis and optimization | Various topics |

Stage | Research area |
---|---|

Internship proposals for students in mathematics | Various topics |

## Attendance

As stated in the Teaching Regulations for the A.Y. 2022/2023, 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.

## Career management

## Student login and resources

## Erasmus+ and other experiences abroad

## Commissione tutor

La commissione ha il compito di guidare le studentesse e gli studenti durante l'intero percorso di studi, di orientarli nella scelta dei percorsi formativi, di renderli attivamente partecipi del processo formativo e di contribuire al superamento di eventuali difficoltà individuali.

E' composta dai proff. Sisto Baldo, Marco Caliari, Francesca Mantese, Giandomenico Orlandi e Nicola Sansonetto