COMPUTER TECHNOLOGIES ENGINEERING

Professor: Andrea CATTANEO
Academic discipline: Geometria (MAT/03)
Field: Matematica, informatica e statistica
Type of training activity: Basic

72 hours
of face-to-face activities

9 credits

hub: PARMA

course unit
in ITALIAN

lectures timetable unavailable

exam calls

Learning objectives

The course not only aims to give to the student the basic tools of linear algebra and geometry, but also aims to transmit to the student the methods and the language of mathematics, which can be used also in other fields.

Prerequisites

- - -

Course unit content

The course is an introduction to Linear Algebra. In particular, it will cover the following topics: vectors and vector spaces, matrices, linear systems and linear maps; analytic gempetry in the three-dimensional space, lines, planes and their mutual positions.

Full programme

VECTORS IN THREE-DIMENSIONAL SPACE
* Vectors, coordinates and componentwise operations
* Scalar product, length, distance and orthogonality, the Cauchy--Schwartz inequality and angles
* Vector product

PLANES AND LINES
* Planes, lines and their equations
* Mutual positions

THE N-DIMENSIONAL SPACE
* Operations with vectors, scalar product and orthogonality, length and distance, angle between two vectors

MATRICES
* Definition and operations with matrices (sum and product)
* Invertible matrices
* Transpose of a matrix
* Determinant and rank of a matrix

LINEAR SYSTEMS AND MATRICES
* Elementary operations
* Solutions of a system
* Gauss algorithm
* Cramer rule
* Rank and solutions of a linear system

COMPLEX NUMBERS
* Cartesian and exponential form of complex numbers
* Operations with complex numbers (sum, product, power, conjugate)
* Norm of a complex number

VECTOR SPACES
* Definition of vector space and subspaces
* Linear combinations
* Linear dependence and independence
* Bases and coordinates
* Sum, direct sum and Grassmann formula

LINEAR MAPS
* Definition
* Kernel and image of a linear map
* Isomorphisms
* Matrices and linear maps

DIAGONALIZATION OF MAPS AND MATRICES
* Eigenvalues and eigenvectors
* The characteristic polynomial
* Diagonalizable matrices
* Algebraic and geometric multiplicities
* Criteria for diagonalizability

Bibliography

* L. Alessandrini, L. Nicolodi; "GEOMETRIA A"; Uni.Nova (Parma, 2002).
* L. Alessandrini, L. Nicolodi; "GEOMETRIA E ALGEBRA LINEARE, con esercizi svolti"; Uni.Nova (Parma 2012).

Teaching methods

Mainly lessons in classroom. Together with the theory, some significative examples will be diecussed, and there will be also some exercises.

Assessment methods and criteria

The examination consists in a written exam and in an ora lest. During the course there will be two intermediate tests: passing both of them is equivalent to have passed the written exam.

Other information

- - -

2030 agenda goals for sustainable development

- - -

Contacts

Toll-free number

800 904 084

Student registry office

E. segreteria.ingarc@unipr.it

Quality assurance office

Quality Assurance Manager:
Elena Roncai
T.+39 0521 903663
E. office dia.didattica@unipr.it
E. manager elena.roncai@unipr.it

GEOMETRY AND ALGEBRA cod. 1003714

Learning objectives

Prerequisites

Course unit content

Full programme

Bibliography

Teaching methods

Assessment methods and criteria

Other information

2030 agenda goals for sustainable development

Contacts

Toll-free number

Student registry office

Quality assurance office

Course President

Faculty advisor

Carrier guidance delegate

Tutor Professors

Erasmus delegates

Quality assurance manager

Tutor students

GEOMETRY AND ALGEBRA
cod. 1003714