Spatial vision is not obvious for everyone; thus, solving stereometric problems can be difficult for some secondary school students. This thesis on "Creation of Interactive Aids for Teaching Stereometry at Secondary Schools" focuses on one part of stereometry - sections of solids&#...

Many different mathematical models exist to describe market penetration after a new product is launched on a market. They usually assume an infinite continuous population and continuous time. These premises might be at odds with the real world, as the population is probably much&#x...

Thesis deals with semidefinite programming in combinatorial optimization. The first part is summarizes the theory needed to work in this field. In the second section we are dealing with Shannon capacity of the graph, Lovasz $\vartheta$ function, and with MAX CUT problem. The m...

The main purpose of this thesis is to propose changes and improvements of the Elo rating system for a prediction of the NBA games results and compare the prediction outcomes with a model of selected bookmaker and with the FiveThirtyEight model based on the Elo rating....

The work is devoted to the study of the appearance of arbitrage opportunity in betting on sports results, in particular football. This analysis treats of betting reality and conditions of arbitrage opportunities. The work displays conditions for the bookmaker to choose the&...

This thesis deals with an S-packing coloring of graphs. This thesis focuses on a general S-packing coloring and its some special variations, specifically on a packing coloring and a distance coloring. The thesis sumarizes known results on a distance coloring, a packing coloring&#x...

This dissertation deals with partial differential equations with differential inclusions which are closely connected with the term 'multi-valued mapping'. Mainly, this text is focused on numerical methods for solving real physical problems which are usually simulated by the systems of par...

This master thesis is focused on study of problems for travelling waves in partial differential equations. At first, we explain the notions of travelling wave and soliton. After that, we describe problems containing these notions. Next, we deal with suspension bridge model with aty...

The subject of this diploma thesis is the special class of undirected graphs known as distance graphs. We first summarize known results on vertex colouring of distance graphs, their hamiltonian properties and other types of graph colourings with stricter requirements for vertex distance...

This diploma thesis describes the theory behind the discontinuous Galerkin finite element method (DG FEM) and subsequently the implementation of the method into numerical software package SfePy (Simple finite elements in Python). SfePy uses the term based representation ...

We use numerical simulations to study reaction-diffusion problems with diffusion driven by fractional Laplacian. Fractional Laplacian appears, e.g., in mathematical models of population dynamics where the dispersion of individuals is due to the so called Levy flights rather than due to Brown...

In this thesis we investigate applications of the Lovász local lemma and its related methods. We are going to describe the gradual development of these methods and show the specific examples of its use in the field of research on independent transversals and hypergraphs.

This thesis is focused on option pricing in stochastic volatility models using neural networks. First, option prices in the Heston model are generated using the Heston-Lewis formula. A neural network is then trained using these prices to first estimate the parameters of the Heston&...

This paper deals with a BVP for a system which consists of two ordinary differential equations of the second order with concave and convex nonlinearities and Dirichlet boundary conditions. One of the equations contains a positive parameter $\lambda$. The aim of this work is&#x...

Nowadays, the majority of financial markets are order-driven. An order book is a record of all buy and sell orders for a particular financial instrument. A limit order is an instruction given by a trader to buy or sell a financial instrument at a specified price or&#...

This thesis focuses on planning and optimization of an industrial paint shop production process. It aims to provide a comprehensive view of the paint shop planning issues and to propose an optimized model that can be effectively used to improve the production process. The pape...

The thesis demonstrates a possible implementation of project-based teaching of mathematics at a secondary school. Two fully developed projects have undergone a pilot implementation at a grammar school, including student preparation, specific assignments and evaluations, supplemented with student outputs.&#...

This work deals with the teaching process of complex numbers and fractals in high schools. The complex numbers from a historical point of view were presented in the introduction. Subsequently, research was carried out on the teaching process of this subject at the level of...

The aim of this thesis is to contribute to the study of the constitutive laws of groundwater flow in porous media of the fractured rock type. In this work, the constitutive laws are obtained from a series of numerical simulations of water flow in a small section ...

In this thesis we investigate the boundary value problem consisting of a second order differencial equation, Sturm-Liouville condition and integral type condition. We are going to describe eigenvalues of corresponding linear problem. We introduce an implicit description of the Fučík spectrum ...