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Circle inverse and its utilization
Vach, Petr ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
The objective of this paper is to make reader acquainted with the depiction known as ring inversion. A definition of the depiction set forth in the introduction and a subsequent description including proofs of all characteristics of this depiction in two planes, namely a synthetic and an analytic plane with a complex variable, shall enable a reader to solve problems and tasks which are contained in the second part of this paper. The aim of this work is to familiarize a reader with the ring inversion in such a degree so that he will understand all of the characteristics and will be able to make use of this knowledge not only to solve theoretical problems but also in practice.
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Problem Posing
Šilhavá, Marie ; Vondrová, Naďa (advisor) ; Zhouf, Jaroslav (referee)
This diploma thesis concentrates on problem posing from the students' point of view. Problem posing can be either seen as a teaching method which can be used in the class, or it can be used as a tool for researchers or teachers to assess the level of students' understanding of the topic. In my research, I compare three classes, one mathematics specialist class and two generalist classes, in their ability of problem posing. As an assessment tool it seemed that mathemathics specialists were able to pose problems at a higher level of sophistication while the generalist class students could pose more questions but at a lower level of sophistication. Problem posing is an issue that requires further study in the Czech educational context.
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The construction of curves by Descartes
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Zhouf, Jaroslav (referee)
This work studies the construction of algebraic curves by means of mechanical plotting tools designed by René Descartes. The work includes a brief biography of Descartes, an outline of his scientific method and a description of Descartes' views on curves, their construction and use. By means of dynamic geometry several curves established by Descartes are constructed. These include curves constructed by means of a drawing instrument composed of several rulers; a drawing instrument designed for the hyperbola and its different variations, in which the guiding line is replaced by one of conics in a special position. In the final part we present the construction of four ovals, which are usable in catoptric and dioptric that Descartes constructed by a point wise construction. All drawings are made in Cabri Geometry II and are accompanied by a derivation of the equations of the resulting curves. In deriving these equations we used only elementary algebraic methods, which could be used by Descartes himself and which are comprehensible by secondary school students. Keywords: Descartes, ruler device, curve, conchoid, trident, oval
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Functions in examples and counterexamples
Janda, David ; Pilous, Derek (advisor) ; Zhouf, Jaroslav (referee)
The aim of my Bachelors thesis is to explicate students coming to the uni- versity the key problems in fundamentals of mathematical analysis. I focus on the most notable terms of continuity and limit, which these secondary students were acquainted with. However, majority of them just intuitively and informaly. I am trying to point out the fact, that the knowledge of many students is distortid and uncomplete. As a result it is necessary to practise and clarify this knowledge so that the intuitive imagination of these terms corresponds to the formal definition. I am trying to get this point by brea- king of intuitive imaginations of students by counterexamples. Important is a chapter named The Construction of Functions, which contains instructi- ons leading to the finding functions with specific features. Not only these features, described in this thesis, but also more complex such as derivation, primitive function or uniform convergence. It is a consequence of the fact, that the principle of examples to practise these terms is in many sights similar and repetitious. In chapters named Continuity and Limit, I am interpreting these terms using the special examples, which are in my opinion optimal for rehearsing. My intention is to help illustrate selected problematical sections of mathematical analysis.
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Interactive textbook of descriptive geometry
Krsová, Michaela ; Dvořák, Petr (advisor) ; Zhouf, Jaroslav (referee)
An aim of this diploma thesis is to create interactive descriptive geometry coursebook. As a basis for coursebook creation was used "Present State of Descriptive Geometry Education on High Schools Survey" which was proceeded via questionnaire. Before the creation of coursebook itself were made analyses of accessible textbooks, geometric softwares in use and possible environments for coursebook content presentation. A result is integrated part of subject matter taught on high schools complemented by solved examples and interactive applets created in software GeoGebra. The coursebook content is presented in a form of HTML sites on a public website http://www.sadsam.cz/dg/ and also as an off- line version on DVD disc enclosed.
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Selected objects in non-euclidian metrics
Bruna, Jiří ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
This bachelor thesis studies the shape of a circle, ellipse, hyperbola and parabola in the taxicab metric, using elementary mathematical methods. It thus constitutes a material suitable for the study of this topic without special requirements regarding knowledge in the field of mathematics on the part of the reader. There is a number of illustrations accompanying the text, most of them created using GeoGebra software. Major hypotheses concerning the shape of the above mentioned objects are supplied with a proof. With its scope and margin, the paper represents a unique work in mathematical literature written in the Czech language at the time of its creation. The secondary benefit of the development of an open mind is mentioned as well.
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Language recognition based on the frequency analysis
Čadek, Jan ; Jančařík, Antonín (advisor) ; Zhouf, Jaroslav (referee)
TITLE: Language recognition based on the frequency analysis SUMMARY: The aim of this bachelor thesis is to use the basic cryptoanalytic aid - frequency analysis - for the recognition of the language of a text (or of a cryptogram). The first chapter is devoted to the history of cryptology. Chapter 2 focuses on frequency analysis, its principle is explained on a simple example. In the third part, there is the description of three programs for language recognition. Last chapter compares the results, which I gained through my programs, with the affinity of European languages as described in linguistics. One of the conclusions of my work is that the real affinity of languages is well approximated using the program analysis. KEY WORDS: frequency analysis, cryptology, European languages, recognition, relationships of languages
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Four Topics for Secondary Mathematics Seminars
Nečasová, Marie ; Vondrová, Naďa (advisor) ; Zhouf, Jaroslav (referee)
The diploma thesis describes four less known mathematical topics, which could be part of mathematical seminars at the secondary schools or mathematical camps, 1 Hippocrates lunes, Golden section, tangram and Columbus egg. Each topic is elaborated into a didactic material, which should function as a source of information for teachers. Two of the topics were trialled with secondary school students, which is dealt with in one of the chapters. The main part of the thesis focuses on the preparation and description of worksheets, which consist of a set of solved and commented upon tasks. The thesis also contains the results of a questionnaire aimed at finding out the content of mathematical seminars at some secondary schools in the Czech Republic.
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Factors influencing the efficiency of learning in mathematics at lower secondary schools
Klímová, Hana ; Novotná, Jarmila (advisor) ; Zhouf, Jaroslav (referee)
Klímová Hana: Factors Influencing Effective Learning of Mathematics: with respect to lower-secondary education background The question of relevant factors that influence effective human learning has been a centre of attention to many scientists so far. This diploma thesis examines the impact of motivation on effective reception of text with mathematical content. The thesis consists of two parts, theoretical and practical. As for the theoretical part, four key terms, i.e. human learning; factors which influence human learning; meaningful learning; learning from text are to a great extent analysed, so that they can be viewed as a complex topic. The practical part of my thesis, first, discusses the pre-experiment that provided background data for the experiment. Secondly, the experimental part includes the description of the process of preparing specific test material based on involving as many positive motivation factors as possible, and the discussion over the results of the experiment that was carried out at a lower secondary school. Finally, relevant differences between the results of my experiment and the experiment of Helena Čechová are compared and discussed Some data used in pre-experiment and experiment are presented in the section of attachments.
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