B_DMa Discrete mathematics

University of Finance and Administration
Winter 2016
Extent and Intensity
2/1. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Ivan Havlíček, CSc. (seminar tutor)
Guaranteed by
RNDr. Ivan Havlíček, CSc.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Ing. Barbora Ptáčková
Timetable of Seminar Groups
B_DMa/cAPH: each even Wednesday 14:00–14:44 E129, each even Wednesday 14:45–15:30 E129, I. Havlíček
B_DMa/pAPH: Wed 12:15–12:59 E129, Wed 13:00–13:45 E129, except Wed 26. 10. ; and Wed 19. 10. 15:45–17:15 E228, I. Havlíček
Prerequisites
There are no prerequisites for this course
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of this course students will be able to: - Understand the proofs of logical formulae. - Apply the proofs of mathematical relations, especially proofs using contradiction and/or mathematical induction. - Understand binary relations: ordering and equivalence. Functions onto and one-toone. - Combinatorial counting, - Remember the definition of unoriented graph, basic terminology of graphs. - Search for the shortest paths using Dijkstra‘s algorithm, matching in graph and its change. - Apply the score of graph and its conversions, solve the Euler trail and the task of a Chinese Mailman. - Explain properties of the special class of graphs, i.e. trees. Utilize different algorithms of the lightest spanning tree of an evaluated graph. - Apply Kruscal, Jarník/Prim and Borůvka algorithms finding the lightest spanning trees and discuss their effectivity. - Draw plannar graphs, construct and describe dual graphs. Try to color maps, verticie and edges, the four-color problem. - Oriented graph and its symetrisation, acyclic graph, condensation of graph, De Bruijn sequences. - Search in a network for the maximum flow and the minimum cut.
Syllabus
  • 1. Introduction to mathematical logic. 2. Mathematical proofs, sets. 3. Binar relations and functions. 4. Combinatorial counting and discrete probability. 5. The definition and basic types of undirected graph. 6. The lightest path in graph (Dijstra algorithm) and matching in graph. 7. Euler graphs and connectivity of graphs. 8. Special class of graphs - trees. 9. The algorithms for finding the lightest spanning tree of a graph, plannar graphs. 10. Coloring of a map, the four color theorem. 11. The oriented graphs. 12. Flows in a network.
Literature
    required literature
  • Matoušek, J., Nešetřil, J.: Kapitoly z diskrétní matematiky. Nakladatelství Karolinum: Praha, 2002.
  • Havlíček, I.: Diskrétní matematika. Praha: VŠFS - Eupress, 2007.
  • Havlíček, I. Sbírka příkladů y diskrétní matematiky, VŠFS Praha 2017.
  • Demel, J., Grafy a jejich aplikace, ČVUT Praha 2015.
Teaching methods
Lectures and seminars in full-time study; tutorials in part-time study; compulsory seminar participation is 75% in full-time study, compulsory tutorial participation is 50% in part-time study
Assessment methods
Credit (75% participation in the exercise), written exam (50% correct answers) and oral examen.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
General note: pouze prezenční forma.
Information on the extent and intensity of the course: 10 hodin KS/semestr.
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2015, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
  • Enrolment Statistics (Winter 2016, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/winter2016/B_DMa