Università Roma Tre

Elements of set theory. Maps between sets: invective, surjective, bijective maps.
Elements of propositional logic, truth tables. Equivalence and order relations.
Combinatorics. Binomial coefficients and binomial theorem. Permutations. The Integers: divisibility, GCD and Euclidean algorithm, Bézout identity, linear congruences.
Baiscs of algebraic structures: permutation groups, abstract groups, polynomials and finite fields.
Elements of graph theory.Lattices and Boolean algebras

Giulia Maria Piacentini Cattaneo
Matematica discreta e applicazioni
Zanichelli 2008

Sets. Operations between sets. Applications between sets. Permutations. Relations. Equivalence relations. Order relations. Lattices. Algebraic structures. Group of permutations of n elements. Vector spaces. Linear dependence and independence of vectors. Basis. Dimension. Subspaces. Subspace sum. Subspace intersection. Grassmann’s relation. Matrices. Determinants. Inverse matrix. Reduction of a matrix into treads. The rank of a matrix. Linear systems. Theorem of Rouche-Capelli. Cramer's theorem. Method of Gaussian elimination.

F.J. Leon Trujillo, P. Mercuri. Elementi di Algebra Lineare, Ed. Efesto
F.J. Leon Trujillo, P. Mercuri. Elementi di Geometria Affine ed Euclidea, Ed. Efesto
F.J. Leon Trujillo. Esercizi di Algebra Lineare e Geometria, Ed. Efesto