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.

AIMS AND CONTENT

LEARNING OUTCOMES

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.

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. Elements of analytic geometry.

PREREQUISITES

Elementary knowledge of arithmetic, algebra, trigonometry, and set theory.

TEACHING METHODS

Frontal lectures.

SYLLABUS/CONTENT

1. Sets and functions
2. Complex numbers
3. Polynomials and factorization in R[x].
4. Matrices. Gauss’ method  solving linear systems
5. Determinant and rank of matrices
6. Vector spaces and homomorphisms
7. Diagonalizability. Eigenvalues and Eigenvectors. Symmetric real matrices.
8. Geometry in two-dimensional and three-dimensional spaces (lines, planes, circles, spheres). 

RECOMMENDED READING/BIBLIOGRAPHY

1. Appunti di Geometria e Calcolo numerico (A. Perelli and M.V. Catalisano)
2. Appunti di Algebra Lineare (M.E. Rossi).
3. Appunti di Geometria (G. Niesi)
4. Algebra Lineare e Geometria (C. Baldovino and V. Lanza)

TEACHERS AND EXAM BOARD

Exam Board

RICCARDO CAMERLO (President)

CHIARA CAMERE

GRETA CORAGLIA

MICHELA LAVAGGI

MARIA EVELINA ROSSI

ALESSANDRO DE STEFANI (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8719/p/studenti-orario

Class schedule

GEOMETRY

EXAMS

EXAM DESCRIPTION

Written exam and possibility of oral exam upon request.

ASSESSMENT METHODS

Solve basic exercises concerning the main topics of the program showing knowledge of the theory.

Exam schedule