Discrete Mathematics
A.Y. 2018/2019
Learning objectives
Fornire allo studente parte del linguaggio algebrico di base e familiarità con alcune tra le più comuni tecniche matematiche.
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
Milan
Responsible
Lesson period
Second semester
ATTENDING STUDENTS
Course syllabus
NON-ATTENDING STUDENTS
1) Basic algebraic tools and algorithms
Integers: induction; division; Euclidean algorithm; prime numbers; integer factorization.
Polynomials with real coefficients. Roots. Irreducible polynomials. Factorization of polynomials.
Linear systems; Gauss-Jordan method.
Matrices and their algebra.
2) An outline of abstract algebra
Sets and relations: equivalence relations, partial orderings,maps. Congruence: the integers mod n.
Algebraic structures and their homomorphisms: groups, rings (fields and polynomial rings).
3) Linear Algebra
Vector spaces. Bases. Linear maps and matrices; the rank of a matrix. Determinants of square matrices. Inverse matrices: existence and computing. Cramer and Rouché-Capelli theorems. Eigenvalues and eigenvectors.
The course will be supported by practical exercises to improve comprehension of the several subjects discussed during lectures.
Integers: induction; division; Euclidean algorithm; prime numbers; integer factorization.
Polynomials with real coefficients. Roots. Irreducible polynomials. Factorization of polynomials.
Linear systems; Gauss-Jordan method.
Matrices and their algebra.
2) An outline of abstract algebra
Sets and relations: equivalence relations, partial orderings,maps. Congruence: the integers mod n.
Algebraic structures and their homomorphisms: groups, rings (fields and polynomial rings).
3) Linear Algebra
Vector spaces. Bases. Linear maps and matrices; the rank of a matrix. Determinants of square matrices. Inverse matrices: existence and computing. Cramer and Rouché-Capelli theorems. Eigenvalues and eigenvectors.
The course will be supported by practical exercises to improve comprehension of the several subjects discussed during lectures.
Course syllabus
1) Basic algebraic tools and algorithms
Integers: induction; division; Euclidean algorithm; prime numbers; integer factorization.
Polynomials with real coefficients. Roots. Irreducible polynomials. Factorization of polynomials.
Linear systems; Gauss-Jordan method.
Matrices and their algebra.
2) An outline of abstract algebra
Sets and relations: equivalence relations, partial orderings,maps. Congruence: the integers mod n.
Algebraic structures and their homomorphisms: groups, rings (fields and polynomial rings).
3) Linear Algebra
Vector spaces. Bases. Linear maps and matrices; the rank of a matrix. Determinants of square matrices. Inverse matrices: existence and computing. Cramer and Rouché-Capelli theorems. Eigenvalues and eigenvectors.
The course will be supported by practical exercises to improve comprehension of the several subjects discussed during lectures.
Integers: induction; division; Euclidean algorithm; prime numbers; integer factorization.
Polynomials with real coefficients. Roots. Irreducible polynomials. Factorization of polynomials.
Linear systems; Gauss-Jordan method.
Matrices and their algebra.
2) An outline of abstract algebra
Sets and relations: equivalence relations, partial orderings,maps. Congruence: the integers mod n.
Algebraic structures and their homomorphisms: groups, rings (fields and polynomial rings).
3) Linear Algebra
Vector spaces. Bases. Linear maps and matrices; the rank of a matrix. Determinants of square matrices. Inverse matrices: existence and computing. Cramer and Rouché-Capelli theorems. Eigenvalues and eigenvectors.
The course will be supported by practical exercises to improve comprehension of the several subjects discussed during 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
Practicals: 24 hours
Lessons: 32 hours
Lessons: 32 hours
Professors:
Bertolini Marina, Turrini Cristina
Professor(s)
Reception:
by appointment (by e-mail)
Math. Dept. - via C. Saldini 50 - Milano