Programma d'esame
Modulo di Matematica discreta
Induction. Sequences and linear recurrences.
Divisibility, prime numbers, greatest common divisor, Bézout identity, congruences and modular arithmetic, inverses modulo n, Chinese Remainder theorem, Fermat's little theorem, Euler's phi function, RSA encryption algorithm.
Binomial coefficients, Newton's binomial formula, elementary combinatorics, inclusion-exclusion principle.
Polynomials. Euclidean division of polynomials. Polynomial factorization. Complex roots. Irreducible polynomials over the real numbers.
Modulo di Algebra Lineare
Linear Systems. Matrices. Gauss elimination. Echelon form. Matrix multiplication. Elementary matrices. Inverse matrix.
Vector spaces, linear dependence, dimension and basis. Subspaces. Sum and intersection of subspaces.
Linear applications and associated matrices. Kernel and image of a linear map. Rank. Determinants. Eigenvalues and eigenvectors. Characteristic polynomial of an endomorphism. Diagonalizability.
Orthogonality. Gram-Schmidt orthogonalization.