Mathematical methods for digital communication

A.Y. 2020/2021
Overall hours
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
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

Lesson period
Second semester
The lectures will be by video (not live), and they will be put on "Ariel" shortly before the scheduled lectures. Occasionally there will be meetings on Skype or Zoom or Teams for further information and to discuss any questions the students may have.
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 knowledge 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 - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Lessons: 48 hours