Discrete Mathematics I. lec. (informatikus angol)

Tanszék: Algebra és Számelmélet Tanszék

Tematika:
The rudiments of propositional calculus: operations (logical connectives), formulas, disjunctive normal forms, tautologies. Examples from predicate calculus: atomic formulas, quantifiers, formulas, and negation in a constructive way. Mathematical induction and recursive definition. Standard operations for sets, functions, and relations. Finite, countabily infinite, and uncountable sets. Properties of relations. The transitive hull and the reflexive and transitive hull of a relation. Directed graphs, partial orderings, equivalence relations, and quotient sets. Complex numbers, trigonometric form, roots of complex numbers. Polynomials and their factorized forms. Interpolation with polynomials. Matrix operations. Determinants of matrices and their elementary properties; expansions using minors. The determinant of the product of two square matrices. The inverse of a matrix. Systems of linear equations, Gauss elimination, Cramer’s rule. Vector space, basis, finite dimensional vector spaces, coordinates. Eigenvalue and eigenvector.

Előfeltétel: nincs.

Helyettesítő tárgyak: nincsenek.

Előadás:
Kurzuskód: DMAngEa Kredit: 2 Óraszám: 2 hetente