Gurantor department | Department of Applied Mathematics | Credits | 10 |

Subject guarantor | doc. Mgr. Petr Kovář, Ph.D. | Subject version guarantor | doc. Mgr. Petr Kovář, Ph.D. |

Study level | postgraduate | Requirement | Choice-compulsory |

Year | Semester | winter + summer | |

Study language | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FEI, USP | Intended for study types | Doctoral |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

KOV16 | doc. Mgr. Petr Kovář, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Examination | 28+0 |

Part-time | Examination | 28+0 |

Each student is supposed to
- analyze real life problems
- express them using discrete mathematics formulation
- solve the problem using methods of discrete mathematics
- give an interpretation of the theoretical results in the terms of the original problems
At the same time he should decide what are the limits of an ideal theoretical solution in contrast to the real situation.

Lectures

Individual consultations

Tutorials

Project work

The scope of the course are selected topics of Discrete mathematics (combinatorics, graph theory and Combinatorial Designs. Applications vary from real life problems to application of one field in other branch of discrete mathematics (such as coding theory and error correcting codes).

D. B. West, Introduction to graph theory - 2nd ed., Prentice-Hall, Upper Saddle River NJ, (2001).
Hill: A First Course in Coding Theory, Clarendon Press, Oxford, reprinted 2009.
C.C. Lindner, C.A. Rodger, Design Theory second edition, CRC Press, Boca Raton FL, (2009)

Rosen K.: Discrete Mathematics and Its Applications - 6th ed., McGraw-Hill NY, 2007, 0-07-288008-2
Norman L. Biggs: Diskrete Mathematics Revised Edition, Oxford University Press, 1994, ISBN 019-853427-2

Active participation during lectures. Project - progress consulting. The exam has a written and oral part.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures (chosen among the following topics)
1) Sets, relations and functions. Algorithms and their complexity. Mathematical induction. Permutations and k-permutations, binomial coefficients and combinatorial identities. Inclusion and exclusion principle.
2) Recurrence relations. Applications, constructions and solving recurrence relations. Generating functions.
3) Pigeon-hole principle and its applications.
4) graphs and introduction to graph theory.
5) Communication networks, shortest/widest path, network flows, bipartite graphs, trees and spanning trees. Searching trees, algorithms. Bridges and articulations, Vertex and Edge-connectivit, blocks.
Oriented and weighted graphs, networks and flows, cuts and max-flown min-cut theorem.
6) Planar and non planar graphs.
7) Main coding theory problem. Equivalence of codes, necessary and sufficient conditions of the existence of (n, M, d) - codes, Hamming bound, perfect codes.
8) Finite fields and vector spaces Orthogonal Latin squares, projective planes.
9) Codes and Latin squares. Latin squares and mutually orthogonal Latin squares.
10) Introduction to combinatorial designs. Symmetric designs, Application in coding theory.
11) Steiner triple systems. Constructions and relation to graph decompositions.
During the semester each student prepares one or two projects.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Examination | Examination |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2019/2020 | (P0613D140006) Computer Science | P | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0541D170006) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0541D170006) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0613D140006) Computer Science | K | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P2658) Computational Sciences | (2612V078) Computational Sciences | P | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P2658) Computational Sciences | (2612V078) Computational Sciences | K | English | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P0613D140021) Computational Science | P | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2019/2020 | (P0613D140021) Computational Science | K | English | Ostrava | Choice-compulsory type B | study plan | ||||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P2658) Computational Sciences | (2612V078) Computational Sciences | P | English | Ostrava | Choice-compulsory | study plan | |||||

2018/2019 | (P2658) Computational Sciences | (2612V078) Computational Sciences | K | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P2658) Computational Sciences | (2612V078) Computational Sciences | P | English | Ostrava | Choice-compulsory | study plan | |||||

2017/2018 | (P2658) Computational Sciences | (2612V078) Computational Sciences | K | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P2658) Computational Sciences | (2612V078) Computational Sciences | P | English | Ostrava | Choice-compulsory | study plan | |||||

2016/2017 | (P2658) Computational Sciences | (2612V078) Computational Sciences | K | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1103V036) Computational and Applied Mathematics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | P | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P1807) Computer Science, Communication Technology and Applied Mathematics | (1801V001) Informatics | K | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P2658) Computational Sciences | (2612V078) Computational Sciences | P | English | Ostrava | Choice-compulsory | study plan | |||||

2015/2016 | (P2658) Computational Sciences | (2612V078) Computational Sciences | K | English | Ostrava | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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