Mathematical methods for digital communication

A.Y. 2019/2020
6
Max ECTS
48
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
The aim of this course is to introduce the algebraic language and the basic notions of vector spaces and linear applications. These theoretical arguments are applied to the problem of solving linear systems of equations (even from an algorithm point of view).
Expected learning outcomes
The student should be able to understand and to utilize the formal language of abstract algebra, vector spaces and linear applications. Moreover, he should be able to work with matrices, to associate them to linear systems and to use them to discuss their solutions.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
1) Basic algebraic structures
Sets. Relations: equivalence relations, partial orderings. Maps and product of maps. Integers: division;
prime numbers; factorization. The integers mod n.
Algebraic structures: groups, rings, fields: definitions and examples. The symmetric group. The polynomial ring. Roots of a polynomial and their multiplicities. Irreducible polynomials. Factorization of polynomials.
2) Linear Algebra
Linear systems: the Gauss-Jordan method. Matrices and their algebra. Vector spaces: definitions and examples. Bases. Determinants. The rank of a matrix, matrices and linear maps, Cramer and Rouché-Capelli theorems. Eigenvalues and eigenspaces.
Prerequisites for admission
Mathematic knowledges at high school level.
Teaching methods
Lessons and exercises.
Teaching Resources
M. Bianchi, A. Gillio - Introduzione alla matematica discreta - McGraw-Hill (2005)
Assessment methods and Criteria
The final examination consists of a written exam.
During the written exam, the student must solve some exercises in the format of open-ended questions, with the aim of assessing the student's ability to solve problems about the arguments of the course and answer to some theorical questions. The duration of the written exam will be proportional to the number of exercises assigned and of the questions, also taking into account the nature and complexity of the exercises and questions themselves (however, the duration will not exceed three hours). In place of a single written exam given during the first examination session, the student may choose instead to take two midterm exams. The outcomes of these tests (marks given using the numerical range 0-30) will be available in the SIFA service through the UNIMIA portal.
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Lessons: 48 hours