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 (President Substitute)
The class will start according to the academic calendar.
The exam consists of a written test and an oral exam.