### Teachings

Select Academic Year:     2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022
Professor
BENEDETTO MANCA (Tit.)
Period
Second Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/61]  COMPUTER SCIENCE [61/00 - Ord. 2016]  PERCORSO COMUNE 9 72

### Objectives

The goal is to provide the basic algebraic tools used in Mathematics with particular attention to those necessary to address the arithmetics problems.

### Prerequisites

Familiarity with basic algebraic operations such as addition, product and exponentiation.

### Contents

1 - Basic notions of set theory, logic connectors, truth tables(6 ore lez.)

2 - Relations, equivalence classes, order and graphs; functions, bijections, cardinality, induction(6 ore lez.)

3 - combinatorics: permutations, factorial, combinations; odd and even permutations, the set of permutations as example of group structure(7 ore lez.)

4 - the integer numbers: divisors, prime numbers, b-adic representation, division algorithm, modular arithmetic, applications to crytography (12 ore lez.)

5 - vectors in ordinary plane and space, coordinates, n-tuples, lines and planes(8 ore lez.)

6 - systems of linear equations: row reduction algorithm, rank, applications to geometry (10 ore lez.)

7 - geometrics transformations and matrices, product and inverse of a matrix, determinant (14 ore lez.)

8 - eigenvalues and eigenvectors and applications (9 ore lez.)

### Teaching Methods

72 hours of lecture.
“According to the “Manifesto degli Studi” for the year 21-22, and if compatible with the pandemic, teaching will take place in person, integrated with online tools in order to guarantee its availability to all students in an innovative fashion.”

### Verification of learning

The exam consists on a written part, with the possibility of requesting an oral exam. The written exam is 3 hours long and consists in exercises on the different parts of the program. For each exercise, a certain number of points is assigned. Students who obtain a mark greater or equal than 16 in the written exam may request one (and only one) oral exam. For those requesting the oral exam, the final mark is a pondered average: 75% written, 25% oral. To pass the course the student must obtain a final mark greater or equal than 18.

### Texts

- Notes available on the website