Teachings

Select Academic Year:     2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022
Professor
MARIA PAOLA PIU (Tit.)
Period
First Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/65]  MATHEMATICS [65/40 - Ord. 2020]  MATEMATICA PURA 6 48
[60/65]  MATHEMATICS [65/50 - Ord. 2020]  MATEMATICA PER LA DIDATTICA E LA DIVULGAZIONE 6 48

Objectives

KNOWLEDGE AND UNDERSTANDING ABILITIES
The purpose of the course is to enable students to understand the language, techniques and contents of projective geometry and related topics.
The preferred teaching tool for achieving these goals are the frontal lessons, where the various topics of the course will be developed, by introducing fundamental concepts and developing a series of theorems with the respective proofs, alongside significant examples, exercises and applications

CAPACITY OF APPLICATION: the student must be able to apply all the general knowledge necessary for the understanding of projective geometry.

JUDGEMENT: The course aims to stimulate objective teaching evaluation constantly offering students a comparison between the theoretical contents proposed while they were lessons front and obtain them through self-study using the recommended texts and course material provided.

COMMUNICATION SKILLS: ability to express with the appropriate mathematical terminology the basic concepts of projective geometry

Prerequisites

The contents of first degree in Mathematics.

Contents

Projective Geometry

Motivation. Projective spaces. Examples. Dependence and subspaces. Reference frames. Projectivities. Perspectivities. Duality. Connection affine-projective space. Improper points. Hyperquadrics. Polarity. Hyperquadrics in the affine and Euclidean spaces. Pencils of conics.
Determination of projective subspaces and of projectivities. Detection of improper points. Computation of pole, polar, vertex, center, principal hyperplanes.

Teaching Methods

Compatibly with the teaching methods provided for in the in the Manifesto Accademico 2021-22, as a consequence of the COVID-19 emergency, the tools used for the frontal lessons will mainly be the blackboard with, possibly, a synchronous streaming system via internet using the Microsoft Teams platform.
For the student's preparation at home, the teacher has a web-site dedicated to students (https://people.unica.it/mariapaolapiu/didattica/) where they can find teacher notes, the lesson register.

oral examination

Texts

J. Richter-Gebert, Perspectives on projective geometry. A guided tour through real and complex geometry. Springer, Heidelberg, 2011

C. Gagliardi, L. Grasselli, Algebra lineare e geometria, vol. 1-3, coll. Leonardo, ed. Esculapio, 1993

M.R. Casali, C. Gagliardi, L.Grasselli, Geometria, Progetto Leonardo, Bologna, 2002