60/61/113 - DISCRETE MATHEMATICS
Academic Year 2021/2022
Free text for the University
BENEDETTO MANCA (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/61] COMPUTER SCIENCE||[61/00 - Ord. 2016] PERCORSO COMUNE||9||72|
The goal is to provide the basic algebraic tools used in Mathematics with particular attention to those necessary to address the arithmetics problems.
Familiarity with basic algebraic operations such as addition, product and exponentiation.
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.)
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.
- Notes available on the website
Notes and exercises available on the website.