# GEOMETRY

OVERVIEW

The course provides an introduction to linear algebra and analytic geometry, with particular focus on matrix computations, on vector spaces and on solving linear systems and analitical geometry problems in 2 and 3 dimensions.

Prerequisites: elementary knowledge of arithmetic, algebra, trigonometry, set theory.

## AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide the basic concepts of linear algebra and analytic geometry , particularly with respect to the matrix calculus , the vector spaces , to the solution of linear systems and problems of analytic geometry in space .

AIMS AND LEARNING OUTCOMES

Computation of expressions with complex numbers. Roots of a complex number. Roots and factorization of polynomials. Calculations with matrices and linear maps. Solving systems of linear equations. Vector operations. Solving geometric problems by means of vectors, matrices, cartesian coordinates, and algebraic equations. Identification and canonical form of conics.

Teaching methods

Frontal Lectures (52 hours)

SYLLABUS/CONTENT

Sets and maps. Complex numbers and polynomials. Linear systems and gaussian elimination. Matrices, determinants, rank. Vector spaces. Vectors in geometry. Subspaces, bases, dimension. Linear maps. Matrices related to a linear map. Eigenvalues, eigenvectors. The diagonal form of a matrix. Quadratic forms. Systems of cartesian coordinates, linear changes of coordinates. Points, lines and planes: cartesian and parametric equations, parallelism, angles, distances, orthogonal projections. Circumferences and spheres. Conics.

RECOMMENDED READING/BIBLIOGRAPHY

- Lecture notes (Perelli-Catalisano) (see http://www.diptem.unige.it/catalisano/ )
- E.Carlini, M.V.Catalisano, F.Odetti, A.Oneto, M.E.Serpico, GEOMETRIA PER INGEGNERIA - Una raccolta di temi d'esame risolti, ProgettoLeonardo - Editore Esculapio (Bologna), 2011.
- S.Greco, P.Valabrega, Algebra lineare, Levrotto & Bella, 2009.
- S.Greco, P.Valabrega, Geometria analitica, Levrotto & Bella, 2009.
- Odetti-Raimondo – Elementi di algebra lineare e geometria analitica – ECIG, 2002.
- Web Resources: http://www.diptem.unige.it/catalisano/default.htm

## TEACHERS AND EXAM BOARD

**Ricevimento:** By appointment

Exam Board

DANILO PERCIVALE (President)

VALENTINA BERTELLA

MARIA VIRGINIA CATALISANO (President Substitute)

## LESSONS

Teaching methods

Frontal Lectures (52 hours)

LESSONS START

The third week of September

## EXAMS

Exam description

The examination consists of a written part and an oral discussion. The written part is made up of 10 questions that cover all the material of the course.

The use of notes, books, or electronic devices is forbidden.

Assessment methods

The questions of the written part will verify both the operational skills through problem solving and the learning of the theory, such as definitions and theorems. During the oral test there will be a discussion about the written part and two to three additional questions.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

09/06/2021 | 09:00 | LA SPEZIA | Scritto + Orale | |

09/06/2021 | 09:00 | LA SPEZIA | Scritto | |

30/06/2021 | 09:00 | LA SPEZIA | Scritto + Orale | |

09/07/2021 | 09:00 | LA SPEZIA | Scritto | |

08/09/2021 | 09:00 | GENOVA | Scritto | |

16/09/2021 | 09:00 | LA SPEZIA | Scritto + Orale |

## FURTHER INFORMATION

Pre-requisites :

Elementary notions of arithmetic, algebra, trigonometry, set theory,