
Possibilities of using Wolfram Mathematica program in Mathematics Teaching
Krejčíčková, Klára ; Jančařík, Antonín (advisor) ; Kvasz, Ladislav (referee)
The aim of the thesis is analyzing of possibilities in application of program Wolfram Mathematica in education of Math. All analysed options are supported by applets created in investigated program. The text is focused on introduction of background of the program and web support including instructions and all prepared materials. The thesis mainly emphasizes on creation of demonstrations in program Wolfram Mathematica. Particular parts of the text are also focused on programs such as Wolfram Alpha, Wolfram Demonstration Project a Wolfram Problem Generator. 1


Nonlinear models for financial time series and software tools for their analysis
Fučík, Jan ; Zichová, Jitka (advisor) ; Hendrych, Radek (referee)
This thesis deals with some time series models applicable in finance. First, the basic concepts are introduced and the linear AR models are presented. Afterwards, the reader becomes familiar with the nonlinear ARCH volatility models including their properties and the modelbuilding. The generalized GARCH models are briefly mentioned. Another part of the thesis shows the usage of these models to real data in two available software products  R and Mathematica. The programs are compared from the point of the obtained results and the usability for the analysis of financial time series via the explained models. The description of the procedures and the attached CD with the outputs of the programs allow the reader to apply the models on his or her own data.


Level Sets of Multivariate Density Functions and their Estimates
Kubetta, Adam ; Hlubinka, Daniel (advisor) ; Zichová, Jitka (referee)
A level set of a function is defined as the region, where the function gets over the specified level. A level set of the probability density function can be considered an alternative to the traditional confidence region because on certain conditions the level set covers the region with minimal volume over all regions with a given confidence level. The benefits of using level sets arise in situations where, for example, the given random variables are multimodal or the given random vectors have strongly correlated components. This thesis describes estimates of the level set by means of a so called plugin method, which first estimates density from the data set and then specifies the level set from the estimated density. In addition, explicit direct methods are also studied, such as algorithms based on support vectors or dyadic decision trees. Special attention is paid to the nonparametric probability density estimates, which form an essential tool for plugin estimates. Namely, the second chapter describes histograms, averaged shifted histograms, kernel density estimates and its generalization. A new technique transforming kernel supports is proposed to avoid the so called boundary effect in multidimensional data domains. Ultimately, all methods are implemented in Mathematica and compared on financial data sets.


Financial functions in Mathematica
Stacho, Michal ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
The Mathematica software contains a fully integrated environment for a large number of instruments used in classical and modern finance. One of it`s basic capabilities is an advanced evaluation of the time value of money, then pricing of financial instruments such as bonds or financial derivatives and finally financial mapping with advanced library of technical indicators. Mathematica also provides immediate access to a large field of financial and economic data through external servers and offers financial tools for working with external data. This thesis deals with descriptions of the functions implemented in Mathematica, explaining the principle of their operation and application to real data.


Solving systems of equations over commutative rings
Seidl, Jan ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The object of this work is to offer algorithm how can be solved systems of linear equations Ax=b over principal ideal rings. We prove that for every nonzero matrix over principal ideal rings there exists its Smith form. Using Smith form we transform the system of equations to simple diagonal form and we show how we can obtain the solution of the original system from its diagonal form. Whole procedure we demonstrate by the examples over Z, Zm and Q[x]. Thereafter we show how is possible to implement the algorithm for these rings by using software Mathematica. The work should provide procedure according to which shold not be difficult to modify algorithm to gain solution over another rings. 1


Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.


Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.


Optimalizace portfolia cenných papírů pomocí strukturovaných produktů
Ondřej, Petr ; Žamberský, Pavel (advisor)
Diplomová práce popisuje vlastnosti a rizika investování do strukturovaných produktů v Německu. Součástí práce je zároveň otestování efektivnosti využití Bonus, Diskont a Outperformance certifikátů při správě finančních prostředků. Analýza ukazuje, že je možné pomocí Diskont a Bonus certifikátů dosáhnout vyššího výnosu očištěného o riziko. Outperformance certifikáty umožňují dosáhnout vyššího výnosu pouze při výrazném růstu (zároveň s vyšším rizikem). Veškeré investice do strukturovaných produktů jsou porovnávány s výnosem u indexu DJ Euro Stoxx 50 (Total Return).


Java Grid Computing or how to find large primes
PAPEŽ, Petr
This Bachelor work contains methods of searching for Mersenne primes using Grid Computing technology. The goal of this work is to implement a networkbased computing framework and an implementation of an algorithm for searching for large Mersenne primes. Part of this work is a theory of searching for Mersenne primes and historical methods of searching for such numbers, GIMPS project description and its results, Grid Computing technology explanation, and Grid Computing capabilities of Mathematica 7 software for searching for Mersenne primes.

 