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Limits and L'Hospital's rule
Ranšová, Kateřina ; Staněk, Jakub (advisor) ; Halas, Zdeněk (referee)
Title: Limits and l'Hospital's rule Author: Kateřina Ranšová Department: Department of Mathematics Education Supervisor: RNDr. Jakub Staněk, Ph.D., Department of Mathematics Education Abstract: The aim of this BA thesis is to introduce to the reader the concept of the limit of function and the means of its solution. The main impact of the thesis lies in a didactic approach and in the connection of a limit theory with its graphic representation and different methods of algebraic calculation. The text consists of eight chapters which can be divided into two parts according to their content. The first part explores the term "the limit of the function". Individual types of limits are then defined. To facilitate understanding, most of the definitions are accompanied by a particular example and a graphic representation . The first part is concluded by a unified definition which by means of the term "vicinity" summarizes all preceding types of limits. The other part deals with some basic methods of limits' calculation. Other topics include Taylor Series, l'Hospital's Rule and their applications to the limits. The core of the thesis is a comparison of calculation by means of l'Hospital's Rule and Taylor Series. The conclusion of the thesis presents some advantages and disadvantages of applying Taylor Series and...
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Web application for teaching of complex numbers
Kneblík, Radovan ; Robová, Jarmila (advisor) ; Staněk, Jakub (referee)
This thesis deals with complex numbers and teaching of them in high school mathematics. The thesis is a web page, it includes the definition of complex numbers in various forms (form of ordered pair, algebraic, polar and exponential form) and operations and also conversions between forms. The lecture is enhanced with interactive applets, which demonstrate given topic. Solved exercises, exercises leading to set of points satisfying a condition and an overall test are also parts of the thesis. Web page created within the thesis can be used by high school students as well as by teachers. 1
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Roulette and its strategies
Zadražil, Tomáš ; Staněk, Jakub (advisor) ; Slavík, Antonín (referee)
Objective of this thesis is to describe history of gambling, in a context of roulette to explain basic and advanced parts of probability theory which allow to the reader to decide about function of several popular roulette systems. There was mainly used expected value of discrete random variable, homogenous discrete-time Markov chain and simulations made in programming language R. Concrete output of the thesis are in precisely calculated expected values of a profit with fixed spins and with chosen limitation and corresponding estimations provided by simulation. On the basis of that it's possible to decide which systems are functional and which are not. Main contribution of this text is in didactical approach which helps to describe popular problematics of roulette systems by using basic and advanced areas of probability theory.
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The beginnings of probability theory
Marcinčín, Martin ; Staněk, Jakub (advisor) ; Halas, Zdeněk (referee)
The purpose of this thesis is to give a summary of historical development and explain fundamentals of the probability theory. Early systematic thoughts, emergence of classical Laplace, geometric and statistical definition of probability with development of theory, independence, conditional probability and Bayes theorem are shown. The thesis describes first mention of random values and the central limit theorem. The alternative, discrete uniform, binomial, Poisson, continuous uniform, normal and exponential distributions are discussed with historical background of their discoveries. The theory is supplemented with illustrative and contemporary examples. The thesis describes development in various fields of probability until publication of the Kolmogorov's probability theory in 1933. Powered by TCPDF (www.tcpdf.org)
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Poker and Probability
Jelínek, Roman ; Staněk, Jakub (advisor) ; Slavík, Antonín (referee)
Title: Poker and Probability Author: Roman Jelínek Department: Department of Mathematics Education Supervisor: RNDr. Jakub Staněk, Ph.D., Department of Mathematics Education Abstract: The aim of this Bachelor thesis is to create a historical introduction to the exciting card game and especially proximity of its mathematical aspects to the general public. The work consists of didactic way with many comments to the theory. The text is worded in a way that most people understand the situations, which are described without mathematical basics. For this reason there are no complicated formulas written and used are thoroughly described. The work focuses mainly on amateur poker players, but also on people, who knows anything about this card game. Keywords: history of poker, poker rules, poker hands, the probability of winning
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The beginnings of probability theory
Marcinčín, Martin ; Staněk, Jakub (advisor) ; Halas, Zdeněk (referee)
The purpose of this thesis is to give a summary of historical development and explain fundamentals of the probability theory. Early systematic thoughts, emergence of classical Laplace, geometric and statistical definition of probability with development of theory, independence, conditional probability and Bayes theorem are shown. The thesis describes first mentions of random values and the central limit theorem. The alternative, discrete uniform, binomial, Poisson, continuous uniform, normal and exponential distributions are discussed with historical background of their discoveries. The theory is supplemented with illustrative and contemporary examples. The thesis describes development in various fields of probability until publication of the Kolmogorov's probability theory in 1933. Powered by TCPDF (www.tcpdf.org)
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Stochastic modelling of epidemics
Drašnar, Jan ; Staněk, Jakub (advisor) ; Hlubinka, Daniel (referee)
This thesis uses a simple deterministic model represented by an ordinary di- fferential equation with two equilibrium points - depending on the initial state the illness either vanishes or persists forever. This model is expanded by adding some diffusion coefficients leading to different stochastic differential equations. They are analyzed to show how the choice of diffusion coefficients changes be- havior of the model in proximity of its equilibria and near the boundary of area with biological meaning. The theoretical results are than illustrated by computer simulations. 1
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Game Theory for Gifted Secondary School Students
Skálová, Alena ; Hykšová, Magdalena (advisor) ; Staněk, Jakub (referee)
The thesis contains a textbook for gifted secondary school students. Its aim is to give to these students (or to their teachers) a Czech-written text covering fundamental principles in the field of game theory. In the first part we introduce the combinatorial games and some elementary methods of their solution. The second part is devoted to the game of Nim, to the Sprague-Grundy function and to the sums of the combinatorial games. It also contains a necessary introduction to the binary numeral system. In the third part we present the concept of matrix and bimatrix games. There is a lot of exercises and examples in the textbook. At the end we bring solutions to the most of them, providing the active reader with the opportunity of checking their own solutions.
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Regression models and their teaching
Rybář, Marian ; Staněk, Jakub (referee) ; Kopa, Miloš (referee)
Title: "Regression models and their teaching" Author: Mgr. Marian Rybář Department: Department of Mathematics Education Abstract: Regression models and their outputs have a huge utilization not only in the field of medicine, science and managerial decision-making but also in many other fields. From the math didactics point of view is a question of intelligible explanation of regression models to non- math students very topical and exploitable theme. The main problem is an understandable explanation of this topic to statistics schooling members with minimal math application. These people aren't usually math or technical branch alumni, but they use regression models in their work. This work tries to suggest simply and clearly explanation of regression models on particular examples. Practical examples show the effects of the most common mistakes that are made by laymen in application of regression models. The main output of this work is a set of examples that could be used in regression models schooling. Keywords: regression models, regression analysis, didactics, teaching
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