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Symplectic spin geometry
Holíková, Marie ; Krýsl, Svatopluk (advisor) ; Eelbode, David (referee) ; Souček, Vladimír (referee)
The symplectic Dirac and the symplectic twistor operators are sym- plectic analogues of classical Dirac and twistor operators appearing in spin- Riemannian geometry. Our work concerns basic aspects of these two ope- rators. Namely, we determine the solution space of the symplectic twistor operator on the symplectic vector space of dimension 2n. It turns out that the solution space is a symplectic counterpart of the orthogonal situation. Moreover, we demonstrate on the example of 2n-dimensional tori the effect of dependence of the solution spaces of the symplectic Dirac and the symplectic twistor operators on the choice of the metaplectic structure. We construct a symplectic generalization of classical theta functions for the symplectic Dirac operator as well. We study several basic aspects of the symplectic version of Clifford analysis associated to the symplectic Dirac operator. Focusing mostly on the symplectic vector space of the real dimension 2, this amounts to the study of first order symmetry operators of the symplectic Dirac ope- rator, symplectic Clifford-Fourier transform and the reproducing kernel for the symplectic Fischer product including the construction of bases for the symplectic monogenics of the symplectic Dirac operator in real dimension 2 and their extension to symplectic spaces...
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Beneficial utilisation of GeoGebra software in geometric constructions at the lower secondary level of basic school
Krejčíčková, Klára ; Holíková, Marie (advisor) ; Jančařík, Antonín (referee)
Diplomová práce se zabývá využitím programu GeoGebra ve výuce ma- tematiky, konkrétně v tématu konstrukce trojúhelník·. Cílem práce bylo na- vrhnout přípravu na hodiny výuky konstrukce trojúhelník· s využitím pro- gramu GeoGebra a následně ověřit, zda využití softwaru dynamické geometrie mělo vliv na zvládnutí nového učiva. Teoretická část obsahuje použité pojmy z planimetrie. V dalších dvou kapitolách se čtenář seznámí s programem GeoGebra a GeoTest a některými výzkumy, které jsou zaměřené na použití program· dynamické geometrie ve výuce matematiky. Následuje kapitola se- znamující s úlohami, které jsou v experimentu využity, a popisuje přípravu jednotlivých hodin. Poslední část je věnovaná pr·běhu experimentu, srovnání výsledk· žák· pomocí test· s kontrolní třídou. Získaná data jsou zpracována na základě pozorování a test·. Výsledky pozorování a analýzy potvrzují, že GeoGebra je vhodným doplňkem výuky konstrukce trojúhelník·. 1
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Comparison of Euclid's and Hilbert's Axiomatic Systems of Geometry from the Didactic Viewpoint
Tavačová, Adela ; Kvasz, Ladislav (advisor) ; Holíková, Marie (referee)
Title: Comparison of Euclid's and Hilbert's Axiomatic Systems of Geometry from the Didactic Viewpoint Author: Adela Tavačová Supervisor: prof. RNDr. Ladislav Kvasz, Dr. The aim of this thesis is to describe the development of axiomatic systems of geometry and its applicability in didactics of mathematics. The thesis is composed of two parts, the first of which is focused on Euclid and his work The Elements, the second being aimed at David Hilbert and his work Grundlagen der Geometrie. The thesis contains a short historical context describing the gradual development of geometry and geometrical thinking, from the ancient times up to now. It will further cover the influence of The Elements upon mathematics as such, its teaching, and a spread across the countries of the world and the Czech Republic in particular. A detailed view is given to the characteristics of Euclid's axiomatic system and its possible difficulties caused predominantly by a vast temporal span and translations from Greek to other languages. I will continue with the analysis of the most considerable logical gaps in The Elements, thus paving the way for the introduction of a modern axiomatic system of geometry, represented by David Hilbert. Apart from the main features and the structure of David Hilbert's axiomatic system, the second...
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Návrh rekonstrukce doprovodné vegetace vodního toku
Holíková, Marie
This diploma thesis describes the project of watercourse bank vegetation restoration. It is also focused on the recreation potential of the watercourse. Introductory chapters are dealing with general issues of watercourses, bank vegetation, abrasion protection and related legislation. As a sample river for the purpose of the research was selected the small river "Lutoninka", flowing through the Zádveřice village, situated near Zlín. For this particular watercourse was worked out the project of vegetation factors reconstruction. The project is accompanied by a proposal that takes into account landscaped and recreational potential of the area.
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