Unit GEOMETRY II
- Course
- Mathematics
- Study-unit Code
- GP006039
- Curriculum
- In all curricula
- Teacher
- Massimo Giulietti
- Teachers
-
- Massimo Giulietti
- Marco Mamone Capria (Codocenza)
- Hours
- 68 ore - Massimo Giulietti
- 10 ore (Codocenza) - Marco Mamone Capria
- CFU
- 9
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Learning activities
- Base
- Area
- Formazione matematica di base
- Academic discipline
- MAT/03
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Eigenvalues and eigenvectors. Diagonalization. Bilinear forms. Quadratic forms. Euclidean vector spaces. Euclidean affine spaces. Orthogonal operators, symmetric operators and the spectral theorem. Classification of conics. Topological and metric spaces. Continuous functions. Connected and compact spaces. Product spaces and quotient spaces.
- Reference texts
- Marco Abate, Geometria, McGraw-Hill
Edoardo Sernesi, Geometria I, Bollati-Boringhieri
Marco Abate e Chiara De Fabritiis, Esercizi di Geometria, McGraw-Hill
Gianluca Occhetta, Note di Topologia Generale e primi elementi di Topologia Algebrica (online) - Educational objectives
- Knowledge and ability on bilinear and quadratic forms, euclidean spaces and basic elements of Topology.
- Prerequisites
- In order to be able to understand and reach the objectives of the course of Geometria II, it is important that the students have successfully passed the exam of Geometria I.In particular basic topics, such as : vector spaces, linear maps and matrices, affine spaces, parametric and cartesian equations of affine subspaces, are required.
- Teaching methods
- The course is organized as follows: face-to-face lessons on all the topics of the course and practical training usueful to prepare the students for the written test.
It is planned a tutor teaching activity. - Other information
- Attendance:Optional but advised
- Learning verification modality
- The exam consists of a written test (or two progress assessments) and a final oral exam.
The written exam requires the solution of three/four problems (eigenvectors and diagonalization of matrices, reduction to canonical form of quadratic forms,
Euclidean affine spaces, topology) and it has a duration of 3 hours. Its objectives are to evaluate the resolutive capacity of the problems and the proper use of acquired knowledge.
The oral exam consists of a talk of about 30 minutes.
It is aimed at testing the degree of comprehension the students have reached, expositive skills and capacity of finding connections between the topics studied. If it is required, the exam can be taken in English. - Extended program
- Eigenvalues and eigenvectors. Diagonalization. Bilinear forms. Quadratic forms. Euclidean vector spaces. Orthogonal operators, symmetric operators and the spectral theorem. Canonical forms of quadratic forms and conics. Topological and metric spaces. Continuous functions. Connected and compact spaces. Product spaces and quotient spaces.