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The mathematical theory of juggling
Búzik, Michal ; Slavík, Antonín (advisor) ; Karger, Adolf (referee)
Title: The mathematical theory of juggling Author: Michal Búzik Department: Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D. Abstract: This bachelor thesis is concerned with methods of mathematical descrip- tion of juggling. The main part deals with notation of simulation of throwing balls using integer sequences, so-called siteswaps. It indicates generating, mutual relations and ways of graphic interpretation of these sequences in diagrams. Summarized re- sults with generalization of all possible calculations of juggling sequences according to restrictive aspects are provided in this thesis. Beside usage of combinatorics and graph theory, there are also relations between juggling and braid theory, and change ringing interpreted. Keywords: juggling, sequence, siteswap
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The mathematical theory of juggling
Zamboj, Michal ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
Title: The mathematical theory of juggling Author: Bc. Michal Zamboj Department: Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D. Abstract: This diploma thesis extends the bachelor thesis of the same name. It deals with the graphic representation of juggling sequences by the cyclic diagram. Using the Burnside theorem and cyclic diagrams, we calculate the number of all genera- tors of juggling sequences. The relation between juggling and the theory of braids is described as well. The mathematical model of inside and outside throws is made from an empirical observation of trajectories of balls. Braids of juggling sequences and their attributes are provided using a real model of ladder. A sketch of the proof of the theorem that any braid is juggleable is given as well.
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Fairy tale as a space for artistic reinterpretation
Švajková, Monika ; Velíšek, Martin (advisor) ; Kafková, Helena (referee)
Fairy tale as a space for an art reinterpretation Bc. Monika Švajková Abstract The thesis introduces authors view on the evolution of fairy tales in Europe and its transformation since 19th century in literature, visual arts and related field of knowledge. Its purpose was to create an art project that would connect cultures of Czech Republic and Finland through fairy tales and fine art. Resulting didactical tasks develop fairy tales of one country through contemporary art of the other. The tasks apply to several conceptions of teaching as the implementation took place at the primary art school, high school and lappish art gallery. The art project closes with authors art etudes that expand theme of the forest as an area for updating of fairy tales and simultaneously captures the authors view on the theme of fairy tales. The outcomes and benefits of the thesis were verification of the didactical tasks that would in contemporary art update the classic children literature in context of these two countries.
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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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Determination of Objects Similarity Based on Image Information
Rajnoha, Martin ; Kamencay,, Patrik (referee) ; Beneš, Radek (referee) ; Burget, Radim (advisor)
Monitoring of public areas and their automatic real-time processing became increasingly significant due to the changing security situation in the world. However, the problem is an analysis of low-quality records, where even the state-of-the-art methods fail in some cases. This work investigates an important area of image similarity – biometric identification based on face image. The work deals primarily with the face super-resolution from a sequence of low-resolution images and it compares this approach to the single-frame methods, that are still considered as the most accurate. A new dataset was created for this purpose, which is directly designed for the multi-frame face super-resolution methods from the low-resolution input sequence, and it is of comparable size with the leading world datasets. The results were evaluated by both a survey of human perception and defined objective metrics. A hypothesis that multi-frame methods achieve better results than single-frame methods was proved by a comparison of both methods. Architectures, source code and the dataset were released. That caused a creation of the basis for future research in this field.
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Reeducating university students' mechanical knowledge in mathematical analysis
Šmídová, Kristýna ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The topic of this thesis is the didactics of mathematical analysis. The thesis describes selected observations from the reeducation in an individual tutoring environment of for- mal knowledge of university students in the field of calculus. The aim of the thesis is to describe what formal knowledge appeared, to describe and evaluate selected reeducation interventions and on this basis formulate appropriate methodological recommendation. In the first chapter we deal with the contradiction between definition and concept concept of students, we outline how to convey to students the purpose of definitions and we suggest how to teach students to work with definitions properly, including understanding quan- tified propositions. In the second chapter we present the theory of process and concept together with the generic model theory. In the third chapter we explain the methods of work with students and the methods of the analysis of videos from tutoring. In the fourth chapter we analyze cognitive processes of the concept of sequence limits. KEYWORDS reeducation, individual tutoring, mechanical knowledge, calculus, definitions, quantified proposition, infinity, sequence, limit 1
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Teaching geometric series through CLIL method with using of German language
Korcová, Aneta ; Moravcová, Vlasta (advisor) ; Hromadová, Jana (referee)
The core of the thesis is the realization of three lessons of mathematics conducted in accordance with the CLIL method, which integrates the teaching a non-linguistic subject with foreign language teaching. The topic of the lessons was non-finite geometric series and the chosen foreign language was German. The first part of the thesis introduces key definitions and theorems concerning sequences and geometric series. Comparisons are drawn between approaches of the Czech Republic and two German-speaking countries, Austria and Germany, in relationship to the teaching non-finite geometric series. Furthermore, available teaching materials of the selected countries are compared and applied visualized problems which appear in them are analysed. In the second part, the CLIL teaching method is presented together with the methodology according to which the lessons were prepared, realized and subsequently assessed. To conclude, the thesis presents a detailed analysis of the preparation and progress of the lessons, including the reflection. The appendix comprises of the utilized teaching materials as well as a range of the solved problems.
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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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