- Docente: Calogero Tinaglia
- Credits: 6
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Information Technology (cod. 0099)
Learning outcomes
The student will learn the basics of Discrete Mathematics
Course contents
Natural numbers and elementary operations.Algebraic structures, order. Division, divisibility, euclidean algorithm. Integers numbers, groups and rings. Congruence and equivalente. Fields Q, R, Zn (n prime). Vector spaces and subspaces. Affine subspaces. Linear combinations. Finitely generated vector spaces, basis, dimension. Matrices. Matrix reduction, determinant. Proprieties of determinant, the group GL(n, K).Linear systems of equations, Cramer's sistems. Solving linear sistems. Representing affine subspaces, parallel affine subspaces. The affine subspace intersecting and the affine space joining two affine subspace. Lines, planes and real space. Linear maps and their caracterizations. Fundamental theorem of linear maps and their consequences. Isomorphic vector spaces.
LiReadings/Bibliography
C. TINAGLIA, Matematica discreta per informatici, Pitagora (Bologna). M. BARNABEI e F. BONETTI, Matematica discreta elementare, Pitagora (Bologna). M. BARNABEI e F. BONETTI, Sistemi lineari e Matrici, Pitagora (Bologna).
Teaching methods
In class,we will discuss the theory and solve noumerous exercises
Assessment methods
Written and oral exams
Office hours
See the website of Calogero Tinaglia