LEARNING OUTCOMES

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.

TEACHING METHODS

In presence

SYLLABUS/CONTENT

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.