Academic year/semester: 2025/26/2

ECTS Credits: 5

Available for: All OU students

Lecture hours: 3
Seminarium:2
Practice: 0
Laboratory: 0
Consultation: -

Prerequisites: Some prior knowledge of the subject is required.

Course Leader: Ágnes Záborszky

Faculty: John von Neumann Faculty of Informatics, 1034 Budapest, Bécsi út 96/b

Course Description:
Matrix arithmetic. Vector geometry, algebra of spatial vectors. Systems of linear equations. Propositional, predicate logic. Sets, relations, functions.

Competences:
Students are introduced to the basic concepts of linear algebra (vector geometry, matrix arithmetic, linear systems) as well as of propositional and predicate logic and sets, relations which are necessary for their posterior studies and for the common applications.

Topics:
1. Determinants, properties, evaluation. Solution of linear systems with Cramer’s rule.
2. Matrix arithmetic: concept of matrices, types, operations. Adjugate, inverse of quadratic
matrices.
3. Linear systems: representation with matrices, solution with Gaussian elimination
4. Vector geometry I.: concept of vectors, basic operations. Cartesian components, basis.
Operations of vectors given with their coordinates. Scalar product. Applications.
5. Vector geometry II.: Vector product. Applications. Triple scalar product. Applications.
6. Vector geometry III. Equations of a straight line. Equation of a plane.
7. 1st test. Propositional logic I.: basic concepts.
8. Propositional logic II.: Operations, properties. Formulae.
9.
Propositional logic III.: Evaluation of formulae: truth tables, Quine algorithm. Disjunctive
and conjunctive normal forms. Karnaugh-Veitch method. Arguments, logical implication,
formal proofs, natural deduction rules
10. Predicate calculus I.: Predicate as a propositional function, universal set, universal- and
existential quantifiers, bound and free variables.
11. Predicate calculus II.: Writing statements using the symbols of predicate calculus,
predicate language symbols, terms and formulae, rules for quantifiers.
12. Sets, operations, Venn-diagram. Power-set. Cartesian-product. Relations, basic concepts.
Binary relations, basic concepts, inverse relation, composition of relations.
13. 2nd test. Partial function, (total) function. Special properties of functions: injective,
surjective, bijective..
14. Test retake. Cardinality of sets. Countable and continuum cardinalities. Cardinality of
power sets

Assessment: examination

Exam Types:

Test Exam

Compulsory bibliography: Seymour Lipschutz, Marc Lipson: Discrete Mathematics, 2007 http://elearning.uni-obuda.hu/

Recommended bibliography: S. Axler: Linear Algebra Done Right. Springer, 1997 J.K. Truss (ed.): Discrete Mathematics for Computer Scientists. Addison-Wesley, 1991

Additional bibliography: -

Additional Information: -