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Combinatorics of filters on the natural numbers
Chládek, Alexandr ; Verner, Jonathan (advisor) ; Grebík, Jan (referee)
The work is intended to combinatorial properties of filters on natural numbers as an introduction and motivation to the problematics between definability of the filters and its combinatorics. Basic filter types: P-filter, Q-filter, Rapid filter; orders: Rudin-Kiesler, Rudin-Blass, Katětov and Tukey; filter kon- structions; basic definitions related to combinatorics on ω; introduction to basic descriptive set theory and topology and some specific results. 1
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Czech and Serbian phraseology: comparison, aspects and structure of the Czech-Serbian phraseological dictionary
Linda Popović, Snežana ; Čermák, František (advisor) ; Jirásek, Karel (referee) ; Krejčí, Pavel (referee)
Title: Czech and Serbian phraseology: comparison, aspects and structure of the Czech-Serbian phraseological dictionary Author: Mgr. Snežana Linda Popović Department: Department of South Slavonic and Balkan Studies Supervisor: prof. PhDr. František Čermák, DrSc. Abstract Despite the fact that phraseology is present-day and appealing theme in linguistic, that many linguists gain from, which is due to fact that our language is made up of many steady and idiomatic structures that foreign students have to learn, this scientific discipline is still an area where the linguists have not yet agreed on the definition of its basic unit and field of research. Besides that, there is evident variance in the number of works within phraseology and phraseography in Czech and Serbian linguistics. The main objective of this dissertation is to analyse the Czech and Serbian phraseological theory, classification of phrasemes and phraseography, including the theoretical background to create a bilingual phraseological dictionary. The analysis was based on field of definition of phrasemes, its formal distribution, equivalents on all combinatorial levels and design of dictionary entry in monolingual and bilingual phraseological dictionaries. The findings have confirmed that there are areas in context of phraseology that did...
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Computational complexity of combinatorial problems in specific graph classes
Masařík, Tomáš ; Fiala, Jiří (advisor)
The topic of this diploma thesis is the edge distance labeling problem with specified parametres p, q and λ. We found a dychotomy for p = 2 and q = 1. So the problem is polynomial if λ ≤ 4 and it is NP-complete for λ > 4. The boundary is shifted by one prior to the vertex distance labeling problem, which has already been solved. Polynomial cases are characterized as some special paths and cycles with a few additional vertices. To show NP-completeness we use a well-known NP-complete problem of Monotone not all equal 3-SAT. That section has four parts: One for odd λ, one for even λ and two more reductions for λ = 5 and λ = 6. 1
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Tests of knowledge and skills on websites and their use in combinatorics
Hamáček, Jan ; Robová, Jarmila (advisor) ; Slavík, Antonín (referee)
The goal of this thesis is creation of testing system that works on web pages. Created test system with test excercises serves as instrument to self education of students. Another goal is creating combinatorics tests. This thesis contains summary of basic concepts of didactic tests and properties of created tests. It contains also detailed instructions on how to create test using testing system and short description of possibilities to extend testing system. Last part contains examples of generated combinatorics tests and results of trying the system with students of high school. 1
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Computational complexity of combinatorial problems in specific graph classes
Masařík, Tomáš ; Fiala, Jiří (advisor) ; Dvořák, Zdeněk (referee)
The topic of this diploma thesis is the edge distance labeling problem with specified parametres p, q and λ. We found a dychotomy for p = 2 and q = 1. So the problem is polynomial if λ ≤ 4 and it is NP-complete for λ > 4. The boundary is shifted by one prior to the vertex distance labeling problem, which has already been solved. Polynomial cases are characterized as some special paths and cycles with a few additional vertices. To show NP-completeness we use a well-known NP-complete problem of Monotone not all equal 3-SAT. That section has four parts: One for odd λ, one for even λ and two more reductions for λ = 5 and λ = 6. 1
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Combinatorics in mathematics competitions
Kadeřábek, Václav ; Jančařík, Antonín (advisor) ; Zhouf, Jaroslav (referee)
This work analyzes the possibilities of division of combinatorial problems that occur in mathematical competitions. It contains presentation of Combinatorics taught at secondary schools. It shows the differences between solving problems in schools and math competitions. Using graphs and tables, it demonstrates an unbalanced distribution of combinatorial problems. In conclusion, it offers some types of examples that are missing in competitions, or are there in insufficient numbers.
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Mathematics on the chess board
Šperl, Jiří ; Jančařík, Antonín (advisor) ; Pilous, Derek (referee)
TITTLE: Mathematics on the chessboard AUTHOR: Jiří Šperl DEPARTMENT: The Department of mathematics and the teaching of mathematics SUPERVISOR: RNDr. Antonín Jančařík, Ph.D. ABSTRACT: The main subject of my thesis is mathematical problems on the chessboard using chess pieces. The work aims to demonstrate how a secondary school student would approach and solve several typical mathematical tasks of this nature. Consequently, it outlines ways to incorporate chessboard mathematical problems and exercises in mathematical classes. Moreover, the thesis includes a compact collection of solved problems on the chessboard that can serve as an inspiring source of unconventional mathematical tasks in conventional mathematical education. My own mathematical research forms a major part of the thesis. The research was conducted as a series of tests in three school classes. In order to achieve a high de- gree of objectivity classes of students with different specializations were selected to take part in the tests. The participating classes were also of different age groups. The theoretical part of the thesis takes a look at the past of the subject and presents several interesting historical problems concerning the mathematics on the chess- board. Last but not least, the thesis contains a discussion of solutions of the...
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The use of logic in IT security
Švarný, Petr ; Řepa, Václav (advisor) ; Mařík, Vladimír (referee)
This thesis studies the use of dynamic epistemic logics for the sake of information privacy. The core of the work is the synthesis of three approaches: security logics from A. Hommersom, plausibility frames and communication logic from A. Baltag and S. Smets, and studies concerning the so called Russian cards protocol. Thereafter we present a program, made in the NetLogo environment, in order to demonstrate the workings of the basic ideas.
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