Theory: 50 %

Practice: 50 %

Recommended semester: 1

Study mode: full-time

Prerequisites: -

Evaluation type: term mark

Course category: compulsory

Language: english

Responsible instructor: Dobjánné Dr. Antal Elvira Mercédesz

Responsible department: Department of Basic Sciences

Instructor(s): Dobjánné Dr. Antal Elvira Mercédesz, Dr. Végh Attila, - nincs

Course objectives:
Introduction to the basic concepts, terminology, theorems and connections of mathematical logic, set theory, combinatorics, and graph theory.

Course content - lectures:

1. Fundamentals of logic I.: propositions, equivalence. 2. Fundamentals of logic II.:predicates and quantifiers. 3. Rules of inference and proofs. 4. Sets, cartesian product of sets, set operations. 5. Correspondences, relations, functions. 6. Relations: Equivalence relations and partitions. 7. Permutations. 8. Combinatorics of finite sets. 9. Binomial theorem and multinomial theorem. 10. Mathematical induction. 11. Graphs, trees, graph coloring. 12. Basic graph algorithms.

Course content - seminars:

Problem solving relating to the lecture syllabus.

Acquired competences:
Knowledge:

- Knowledge of the principles and methods of natural sciences (mathematics, physics, other natural sciences) relevant to the field of IT.

Skills:

- He/she uses the principles and methods of natural sciences (mathematics, physics, other natural sciences) relevant to the field of information technology in his/her engineering work for the design of information systems.

Attitude:

- He/she makes decisions with full respect for the law and ethical standards in decision-making situations requiring a complex approach. - He/she makes an effort to work efficiently and to high standards.

Autonomy and responsibilities:

Additional professional competences:

- Efficient use of digital technology, knowledge of digital solutions to fulfill educational objectives

Requirements, evaluation, grading:
Mid-term study requirements:
Visiting lectures and seminars, taking notes, active participation in problem solving. Two 50-point written tests at times announced at the first lecture. Extra points can be earned at seminars based on class activity. Tests may be made up or substituted at the last lecture. Assessment of student performance, based on a five-grade scale: - excellent (5) if the performance is 86-100%, - good (4) if the performance is 76-85%, - satisfactory (3) if the performance is 61-75%, - pass (2) if the performance is 50-60%, - fail (1) if the performance is below 50%.
Exam requirements:

-

Generative AI usage:

1st position: The use of GAI tools is not permitted when solving tasks. This means that GAI tools cannot be used when creating or solving formative or summative assessment elements, and the use of generative AI constitutes academic misconduct. The use of AI tools for language and spelling checking is not subject to the complete ban under the 1st position.

Study aids, laboratory background:

Lecture slides and concept checks will be posted for each lectures.

Compulsory readings:

Recommended readings:

[1] Ralph P. Grimaldi: Discrete and Combinatorial Mathematics: Pearson New International Edition. Pearson, 5th edition (2013) ISBN: 978-1292035994 [2] Kenneth H. Rosen: Discrete Mathematics and Its Applications: International Student Edition. McGraw Hill, 9th edition (2025) ISBN: 978-1266191541 [3] Susanna S. Epp: Discrete Mathematics with Applications, Metric Edition. Cengage Learning, 5th edition (2019) ISBN: 978-0357114087