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Funkcionální rovnice a jejich využití v úlohách matematické olympiády
LOUDOVÁ, Hana
The diploma thesis focuses on solving functional equations that appeared in the problems of Mathematical Olympiads. The thesis provides an overview of the best known and the most commonly used methods to solve these mathematics problems. Specifically, it is the substitution method, the variable symmetry method, the Cauchy method, and the fixed-point method. The contribution of the diploma thesis are the summary Mathematical tasks concerning the functional equations found from available years of both the Czech Mathematical Olympiad and the Middle European Mathematical Olympiad, the European Girls' Mathematical Olympiads, and the International Mathematical Olympiads. In addition, the summary of Mathematical tasks from the Czech Mathematical Olympiad provides a detailed written procedure of their solutions. Also, some of the several tasks of functional equations are solved in detail in each method. The work also brings a chart, which compares the success of the Czech representatives with other countries in problems containing functional equations in the above types of Mathematical Olympiads.
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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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Analysis of selected solutions of Mathematical Olympiad category Z - Arithmetic
ŘIČICOVÁ, Jana
The aim of the bachelor thesis is a detailed collection of solutions of selected twenty tasks of the Mathematical Olympiad category Z5-Z9. It is intended for pupils in the 5th to 9th grade and the corresponding classes of eight-year and six-year grammar school preparing for the Mathematical Olympiad or another similar competition. It is as well intended for teachers who help them with preparation. Some of the tasks can be used in a standard Mathematics class as diversification of teaching. The thesis also includes some basic information about the Mathematical Olympiad.
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The equations and systems of equations in problems from Mathematical Olympiad categories A, B and C
ŠIMÁNKOVÁ, Zuzana
The diploma thesis included of informations of a Mathematical Olympiad, equations and systems of equations. The theoretical part contains a historical development and its organization, next it contains informations about equations and their teaching as it is given in the National Curriculum. The practical part consists of a collection of exercises on the topic of equations and systems of equations, which were included in the competition Mathematical Olympiad. Examples in the collection are divided into categories vhich appeard, and ranked by difficulty. Further practical part includes evaluation works heets completed by students of Pedagogicial faculty, University of South Bohemia. This thesis may serve as preparation pupils on Mathematical Olympiad or as a collection of examples for talented pupils
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Teaching talented students in mathematics.
LOJÍKOVÁ, Barbora
The aim of this thesis is to elaborate a set of tasks that will have increasing difficulty and will lead pupils to the skill of solving problems designed for gifted students. The action research will focus on the student's work with the proposed tasks. In the theoretical part, attention will be paid to the available literature on the teaching of mathematics to exceptionally gifted pupils.
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Percentage tasks in a mathematical olympiad, in corresponding seminars, and in PISA and TIMSS tests.
TOMANOVÁ, Denisa
Diploma thesis includes information about percentages, mathematical olympiad, mathematical corresponding seminars and PISA ant TIMSS tests. The first, theoretical part describes historical development of mathematical olympiad and its organization, the history of mathematical corresponding seminars and list of current seminars for primary school students. The second part of the diploma thesis consists of the collection of tasks examples with percentages that appear in mathematical olympiad, mathematical corresponding seminars and PISA and TIMSS tests.
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Inequalities in problems MO (1951 - 1975 )
CHVÁL, Jan
The diploma thesis concerns the elaboration of excercises of inequality which were placed in mathematics olympics in 1951-1975, the clasification of inequality in agreement with the method of solution and showing other ways of solution. The thesis should serve as an addiltiolal study material for students interesed in mathematics.
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