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Introduction of Negative Numbers in the History of Algebra
Daněk, Jaroslav ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
I have divided this work in four chapters, according to the most important places of development of mathematics and his symbolism and I have described some specific historical period of progress of mathematics, which was in the global comparison the most attractive or developed. In the first chapter I occupy with Chinese mathematics, which keep the oldest mathematical knowledge already since the second millennium, therefore immediately on the first place of my work. The second chapter deal with the Indian mathematics, which leaves us knowledge of Indian mathematician Brahmagupta from the 7th century AD, who probably continues in Chinese mathematics. After that it follows mathematics of the Arab world, which had the biggest influence on the European mathematics, where the minus sign was definitively established and stabilized from the earlier rhetorical markings. The central figure, as this chapter, so the whole work, is the German mathematician Michael Stifel and his piece of work the Arithmetica integra. KEYWORDS negative numbers, equations, coefficient, solutions
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Equation editor for Android
Marek, Jiří ; Kučera, Petr (advisor) ; Jančík, Pavel (referee)
Title: Equation editor for Android Author: Jiří Marek Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: RNDr. Petr Kučera, Ph.D. Abstract: The goal of this project is to implement an application for the mobile operating system Android, which allows user to interactively create mathematical expressions and typeset them in LATEX. The application is also capable of saving and sharing its output in various file formats. The application contains a general editor and compiler of LaTeX documents. It is possible to use the equation editor to create a formula, place it into a full LaTeX document and to edit it later in the equation editor again. The application is designed in such a way that even a user, who doesn't know LATEX, is capable of creating complex mathematical expressions. It is also possible to seamlessly switch between an interactive type of input and direct editing of a LATEX code. Keywords: Equation, Editor, LaTeX, Android
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Real-life problems solved by quadratic equations
Hanzal, Petr ; Zhouf, Jaroslav (advisor) ; Pilous, Derek (referee)
This thesis contains a set of real-life problems solved using quadratic equations. The aim is to gather avaiable practical problems, with which students of all ages can meet at school or in everyday life and create additional model problems that could be used in teaching or mathematical competitions. Part of this work are pictures for a better understanding of some tasks. Images were created in Geogebra.
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Elementary mathematics from an advanced standpoint
Kučera, Jiří ; Bečvář, Jindřich (advisor) ; Staněk, Jakub (referee)
Mine thesis is written for self-study of secondary school graduates students which prepare for the mathematically oriented high schools. It clarifies theoretical approach to mathematics. It was chosen topics exponents, square roots, logarithms and equations that contain these objects for this purpose. For this reason students are given the opportunity to gain stance to university mathematics knowledge that should be known from high school. In addition, his work allows him to enlarge knowledge of those topics and learn heavier and unusual examples.
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File of educational materials to support the teaching of mathematics
Hanzal, Petr ; Battistová, Eva (advisor) ; Štípek, Jiří (referee)
The aim of this bachelor thesis is to suggest and create the collection of solved exercises from mathematic on a theme quadratic, absolute-value equations and equations involving square roots. It is intended for the students of the fifth grade of the eight-year grammar school and for the students of the first grade of the four-year grammar school or secondary school. Thanks to the solved exercises it is possible for students to get to know the methods for solving given types of quadratics more deeply.
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Development of equation understanding at primary school
Koudelková, Věra ; Jirotková, Darina (advisor) ; Hejný, Milan (referee)
This master thesis concerns progress of junior school pupils in understanding of equations. It describes benchmark problems and mathematical environments in which equations and equation systems occur. Occurrences of such exercises in text books for primary schools are also mapped here. The main part of this thesis is focused on comprehension of pupils' intellectual actions during solving the equations. Thanks to several experiments, it includes description of pupils' solutions of exercises. The result of the phenomenal analysis of pupils' solving processes is an overview of phenomena, which appeared during solving exercises.
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Economic Curves
Hrubešová, Gabriela ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
The topic of this bachelor's thesis is to study some economic curves, a description of their attributes and a determining the mathematical expression. In the first part, it is explained the issues of general plane curves. Next part focuses on the characteristics of the most important economic curves and their use. The mathematical properties of the individual curves are described below. The last part is a software implementation in the program Wolfram Mathematica.
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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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Self-study support multimedia materials for basic school mathematics
BRADÁČOVÁ, Hana
The main focus of my thesis piece of work is the creation of multimedia tools for pupils´ self-study Math. This tool is an interactive software, specifically it is a Web page that work without connecting to the internet. Especially it is useful for children's home preparation and practising of pupils' knowledge. It can be used during lessons at school too. The main topic of this thesis is solution of equations. A part of the thesis is practical verification of primary school pupils. Their results are compared with the results of pupils who haven´t practised Math on this practical CD.
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A digest of word problems solved through equations
PEJCHAL, Michal
My bachelor´s thesis is a digest of word problems solved through equations. Word problems are on level of 8th a 9th classes of elementary school. The work is divided into two main parts, which are divided into another parts. Main parts contain theory, elaborate examples and examples with solutions. Some examples include pictures, which help to understand situations.
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