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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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KAM-DIMATIA Series 2004-685 and ITI Series 2004-206. Two algorithms for general list matrix partitions
Sgall, Jiří ; Feder, T. ; Hell, P. ; Králď, D.
List matrix partitions are restricted binary list constraint satisfaction problems which generalize list homomorphisms and many graph partition problems arising, e.g., in the study of perfect graphs. Most of the existing algorithms apply to concrete small matrices, i.e., to partitions problems, provide algorithms for their solution, and discuss their implications.
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