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Combinatorics and probability in problems from mathematical competition
MÍKA, Vojtěch
This bachelor thesis deals with solving problems from Czech and foreign mathematical competitions, which are focused on the topic of combinatorics and probability. The work is to serve as a supplementary study material for students with an increased interest in mathematics, as well as for teachers. The work includes pictures and diagrams needed to solve specific tasks.
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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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Combinatorics in didactic games at primary school
Majorová, Jana
The graduation thesis deals with problematics of combinatorics at primary school. It is focused on creation of a set of didactic games, which develope logical-combinatorial thinking and are based on pupils' own cognitive activity and on their active participation in teaching. These didactic games are implemented in teaching mathematics at primary school within an experimental survey and their effectiveness is evaluated based on test application detailed case studies of selected pupils and a questionnaire survey. Key words: didactic game, combinatorics, combinatorial and logical thought, effective and interesting mathematics, a pupil of primary school
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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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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Combinatorics in didactic games at primary school
Majorová, Jana
The graduation thesis deals with problematics of combinatorics at primary school. It is focused on creation of a set of didactic games, which develope logical-combinatorial thinking and are based on pupils' own cognitive activity and on their active participation in teaching. These didactic games are implemented in teaching mathematics at primary school within an experimental survey and their effectiveness is evaluated based on test application detailed case studies of selected pupils and a questionnaire survey. Key words: didactic game, combinatorics, combinatorial and logical thought, effective and interesting mathematics, a pupil of primary school
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Minimal coverings of pairs by triples
Hladíková, Veronika ; Krump, Lukáš (advisor) ; Kazda, Alexandr (referee)
In this thesis we deal with solving a combinatorics problem of finding the minimal covering of pairs by triples for a fixed finite set. We will show what is the minimal size of these coverings and more ways how to construct them. Second part of the thesis is a description of the attached program, which generates a minimal covering for a given set. 1
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Analysis of solving processes of combinatorial problems at primary school (grade 1 - 3)
Tomešová, Lenka ; Slezáková, Jana (advisor) ; Jirotková, Darina (referee)
This diploma thesis deals with combinatorics in primary school teaching methods. The theoretical part is focused on characterisation of mathematical field of combinatorics, briefly describes it's historical evolution and basic types of combinatorial problems. This theoretical knowledge is further supplemented by an analysis of utilization rate of combinatorics in curiculative documents, selected textbooks and mathematical contests for primary school pupils. An essential part of the theoretical part of the work are chapters dealing with solving combinatorial problems. The practical part is based on research of solving combinatorial proceses on tasks for primary school pupils. KEYWORDS Combinatorics, combinatorial problem, typology of combinatorial problems, primary school pupil, solving peoceses, analysis of pupils'solving processes, number of solutions
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Combinatorial sequences and divisibility
Michalik, Jindřich ; Slavík, Antonín (advisor)
This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1
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Practical didactic tests for preparation for the math matriculation examination
PIVOŇKA, Jiří
This bachelor thesis deals with the practical didactic tests for the math matriculation examination. It is divided into two parts. The first part is divided into 7 chapters. Each chapter deals with a specific thematic subjects for the math matriculation examination. The second part includes 3 didactic tests. For each didactic test is assigned solution. The aim of this bachelor thesis is to help students perform math matriculation examination.
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