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## GEOMETRY

CODE 98169 2022/2023 6 cfu during the 1st year of 10716 INGEGNERIA GESTIONALE (L-9) - GENOVA MAT/03 Italian GENOVA 2° Semester AULAWEB

## OVERVIEW

The course will provide the basic notions in linear algebra and analytic geometry necessary to any STEM student.

## AIMS AND CONTENT

### AIMS AND LEARNING OUTCOMES

At the end of the course the student will be able to:

- give correct definitions of the objects and properties studied, using the appropriate mathematical formalism;

- recognize in concrete examples the geometrical objects and the algebraic properties studied;

- describe the set of solutions of systems of linear equations;

- solve exercises of plane and space geometry involving points, lines, planes, angles, distances, scalar products, orthogonal projections, conics, quadrics;

- give explicit examples of objects that satisfy the geometrical or algebraic properties studied;

- apply the notions and procedures studied in order to solve problems, also of new types and of an abstract nature.

### PREREQUISITES

Basic arithmetic skills in computations and manipulations of algebriac formulas. Trigonometry.

### TEACHING METHODS

Frontal lessons in class. Some exercises will be posted on Aulaweb. Attendance is strongly recommended.

### SYLLABUS/CONTENT

Complex numbers: algebraic and trigonometric form. Solutions to z^n=a. Fundamental theorem of algebra.

Polynomials: roots and multiple roots. Ruffini’s theorem. Factorization of polynomials in R[X].

Algebraic operations on matrices. Invertibility of matrices.

Gaussian elimination

Determinant and rank of a matrix. Laplace expansion, Cramer theorem, Rouché-Capelli’s theorem.

Vector spaces and linear maps.

Diagonalization of endomorphisms. Eigenvalues and eigenvectors. Characteristic polynomial.

Vector algebra in the plane and the space.

Real symmetric matrices

The following notes will be posted on Aulaweb:
1. Appunti di Geometria e Calcolo numerico (A. Perelli e M.V. Catalisano)
2. Appunti di Algebra Lineare (M.E. Rossi).
3. Appunti di Geometria (G. Niesi)
Recommended book:  Algebra Lineare a Geometria Analitica (F. Odetti, M. Raimondo), ECIG Universitas.

## TEACHERS AND EXAM BOARD

### Exam Board

FRANCESCO VENEZIANO (President)

## LESSONS

### LESSONS START

https://corsi.unige.it/10716/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### Exam schedule

Date Time Location Type Notes
01/06/2023 09:00 GENOVA Scritto
06/06/2023 09:00 GENOVA Orale
29/06/2023 09:00 GENOVA Scritto
03/07/2023 09:00 GENOVA Orale
11/09/2023 09:00 GENOVA Scritto
13/09/2023 09:00 GENOVA Orale