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Course detail
FP-dimPAcad. year: 2026/2027
Basic Theoretical Tools of Applied Informatics – Mathematical Logic, Relations, Graph Theory, and the Theory of Formal Languages and Automata.Mastering these methods enables students to gain deeper insight into their field and to use computing technology more effectively when solving specific problems.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
High School MathematicsMathematics 1
Rules for evaluation and completion of the course
Requirements for Course Credit:
Completion of control tests with a minimum score of 50%, or completion of a comprehensive written assignment with at least 50% of the total points. All tasks in the written part must include calculations, a described procedure, or a verbal justification of the result.
Course Completion for Students with Individual Study Plans:
Completion of a comprehensive control test with a minimum score of 50%. All tasks in the written part must include calculations, a described procedure, or a verbal justification of the result. The deadlines for completing the course are arranged individually according to the conditions approved in the ISP.
Attendance at exercises is monitored.
Aims
The aim of the course is to introduce the basic concepts and relationships of mathematical logic, relations, graph theory, and the principles of the theory of languages and automata, along with their potential applications in the field.
Study aids
See literature
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
Lecture
Teacher / Lecturer
Syllabus
1. Mathematical logic - laws of propositional logic, Boolean algebras, logic circuit.2. Relations - relations on a set, properties and types of relations.3. Graph Theory - basic types of graphs, fundamental concepts of undirected graphs.4. Graph Theory - directed graphs, weighted graphs, Dijkstra’s shortest path algorithm, Kruskal’s algorithm.5. Languages, grammars - the concept of language and grammar, Chomsky hierarchy.6. Automata - finite automaton, Kleene’s characterization.7. Summary
Exercise
1. Mathematical logic - laws of propositional logic.2. Mathematical logic - Boolean algebras, logic circuit.3. Relations - relations on a set.4. Relations - properties and types of relations.5. Graph Theory -basic types of graphs.6. Graph Theory - fundamental concepts of undirected graphs.7. Graph Theory - directed graphs, weighted graphs.8. Graph Theory - Dijkstra’s shortest path algorithm, Kruskal’s algorithm.9. Languages, grammars - the concept of language and grammar.10. Languages, grammars - Chomsky hierarchy.11 Automata - finite automaton.12. Automata - Kleene’s characterization.13. SummaryProfessional Knowledge:The student has a comprehensive knowledge of the fundamentals of mathematical logic, relations, and graph theory. They understand the principles of formal languages, grammars, finite automata, and their mutual relationships. They are familiar with basic graph algorithms and their theoretical background.
Professional Skills:The student is able to apply principles of mathematical logic and relations to solve formally defined problems. They can model problems using graphs and apply basic graph algorithms to solve them. They are able to work with formal languages, grammars, and finite automata in simple tasks.
General Competences:The student develops logical, abstract, and algorithmic thinking skills. They are able to independently analyze a problem and choose an appropriate formal model for its solution. The acquired knowledge serves as a theoretical foundation for further studies in computer science and related fields.
Self-study
Individual preparation for an ending of the course