- 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.