B_DMa Discrete mathematics

University of Finance and Administration
Winter 2013
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: Dagmar Medová, DiS.
Timetable of Seminar Groups
B_DMa/cAPH: each even Wednesday 12:15–12:59 E123, each even Wednesday 13:00–13:45 E123, I. Havlíček
B_DMa/pAPH: Wed 10:30–11:14 E123, Wed 11:15–12:00 E123, 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 the student will be able to: - Understand the proofs of logical formulae, the proofs of mathematical relations,proofs using mathematical induction, the operations with sets, combinatorial counting, binary relations. - Search for shortest paths algorithm pairing, Dikstrův, matching in graph. - Apply the score of graph and its conversions, solve the Euler trail and the task of a Chinese Mailman. - Explain trees and algorithms of the lightest spanning tree of a graph. - Describe dual graphs, De Bruijn sequences, find the condensation of the graph. - Search in a network for maximum flow and minimum cut. - Understand the cyclical nature of mathematical modeling, the simplex method, the transportation problem.
Syllabus
  • 1. Mathematical logic, mathematical proofs, sets. 2. Binar relations nad functions. 3. Combinatorial counting and discrete probability. 4. The definition and different types of undirected graph. 5. The lightest path (Dijstra algorithm), matching in graph. 6. Euler graphs and graph´s connectivity. 7. Special class of graphs - trees. 8. The algorithms for finding the lightest spanning tree of a graph, plannar graphs. 9. Coloring of a map, the four color theorem. 10. The oriented graphs. The codensed graphs. 11. Flows in a network. 12. Mathematical modelling.
Literature
    required literature
  • Matoušek, J., Nešetřil, J.: Kapitoly z diskrétní matematiky. Nakladatelství Karolinum: Praha, 2002.
  • Havlíček, I.: Diskrétní matematika. Praha: VŠFS - Eupress, 2007.
  • Fábry, J.: Matematické modelování. Praha: VŠE, 2007.
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: Bb0, 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 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Winter 2024.
  • Enrolment Statistics (Winter 2013, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/winter2013/B_DMa