9 credits during the 1st year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA
Provide basic mathematical language. Introduction to abstract algebraic notions by studying the algebra of integers, polynomials in a rational, real, complex or finite coefficient variable and their quotients. Theoretical notions of groups.
Introduction to the basic notions: sets, maps, surjectiive, , injective and bijective.
- Binary operation and their properties. Equivalence relations and induced quotients.
- Cardinality: countsble and uncountable sets. Permutations. Induction. Newton binomial formula.
- The integers: Euclidean algorithm and its applications. Prime numbers and unique factorization. The integers mod n.
- Complex numbers.
- Polinomials: with rational, real or complex coefficients. Unique factorization property for polynomials. Irreducibility criteria. Quotients and their properties: zero-divisors, nilpotents and invertible elements.
- Introduction to algebraic structures. Abelian groups. Subgroups, homomorphisms and quotients.
MARIA EVELINA ROSSI (President)
ALESSANDRO DE STEFANI
The class will start according to the academic calendar.
The exam consists of a written test and an oral exam.