Mathematical Methods for Digital Communication
A.Y. 2018/2019
Learning objectives
Fornire agli studenti le basi del linguaggio algebrico/geometrico con alcuni concetti e tecniche di frequente uso in matematica e nelle applicazioni.
Expected learning outcomes
Undefined
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
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.
The course will be supported by practical exercises to improve the comprehension of the subjects discussed throughout lectures.
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.
The course will be supported by practical exercises to improve the comprehension of the subjects discussed throughout lectures.
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
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
Professors:
Bertolini Marina, Lanteri Antonio
Professor(s)