Course detail

Mathematical Principles of Computer Science

FSI-VZI Acad. year: 2025/2026 Winter semester

Learning outcomes of the course unit

Prerequisites

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

Language of instruction

Czech

Aims

Specification of controlled education, way of implementation and compensation for absences

The study programmes with the given course

Programme N-AIŘ-P: Applied Computer Science and Control, Master's
branch ---: no specialisation, 6 credits, compulsory

Type of course unit

 

Lecture

39 hours, optionally

Syllabus

1. Introduction.
2. The list, queue, stack structures, designs of representation and implementation.
3. Breadth-first and depth-first search of graph, combined search; the use of queue and stack. AND/OR graphs.
4. Eulerian trails, Hamiltonian paths.
5. The shortest path, minimum spanning tree.
6. Network flows, graph colouring.
7. Voronoi diagrams and Delaunay triangulation.
8. Formal languages and grammars. Chomsky’s classification.
8. Regular grammars and finite automata.
9. Finite automata without stack, representation.
10. Context-free grammars and finite automata with stack.
11. Turing machine, enumeratibility, algorithm complexity.
12. Sorting algorithms
13. Recapitulation.

Computer-assisted exercise

26 hours, compulsory

Syllabus

1. Principles of code security improvement, separation of overhead and data classes.
2. Implementation of list.
3. Implementation of queue and stack.
4. Implementation of tree.
5. Implementation of general oriented graph, search in graph I.
6. Implementation of general oriented graph, search in graph II.
7. Approaches to implementation of graph evaluation.
8. Searching in special graph topologies; examples of use.
9. Solution designs of simple problems realized through search in oriented evaluated graph.
10. Object implementation of finite automaton without stack.
11. Object implementation of finite automaton with stack.
12. Linguistic variable implementation, if-then operation.
13. Accreditation.