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.

Piacentini Cattaneo, Matematica discreta. Zanichelli.
Delizia-Longobardi-Maj-Nicotera, Matematica Discreta, McGraw Hill.
Procesi-Rota, Elementi di algebra e matematica discreta. Accademica.

Linear applications. Kernel. Image. Linear maps and linear dependence. Linear maps and matrices. Change of basis. Similar matrices. Diagonalization of an endomorphism. Eigenvalues. Eigenvectors. Eigenspaces. Characteristic polynomial. Scalar products. Euclidean vector spaces. Diagonalization of symmetric endomorphisms. Elements of affine and Euclidean geometry of the plane and space.

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

Matrices. Addition and scalar multiplication. diagonals, triangular matrices. Transpose. Symmetric, antisymmetric matrices. Matrix product, identity matrix. Elementary row operations, reduction. Gaussian elimination. Rank of a matrix as a number of pivot. Rouché-Capelli theorem.
Echelon form. Inverse of a square matrix, inversion algorithm. The vector space R^n. Linear combinations. Subspaces of R^n. The subspace Null(A). The subspace spanned by a set of vectors. Linear dependence and independence. Basis and dimension of a vector space. Linear maps. Kernel and image. Matrix associated to a linear map. Nullity + rank theorem.
Determinants, properties of determinants. Adjunct matrix.
Eigenvalues, eigenvectors, eigenspaces. diagonalization

K.W. Nicholson, Algebra lineare. McGraw Hill.
Flamini-Verra, Matrici e vettori. Carocci.
Procesi-Rota, Algebra lineare e geometria. Accademica.

Applicazioni lineari. Nucleo . Immagine. Applicazioni lineari e dipendenza lineare. Applicazioni lineari e matrici. Cambiamenti di base. Matrici simili. Diagonalizzazione di un endomorfismo. Autovalori. Autovettori. Autospazi. Polinomio caratteristico. Prodotti scalari. Spazi vettoriali euclidei. Diagonalizzazione degli endomorfismi simmetrici. Elementi di geometria affine ed euclidea del piano e dello spazio.

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