The postgraduate study programme aims at preparing top scientific and research specialists in various areas of mathematics with applications in electrical engineering fields of study, especially in the area of stochastic processes, design of optimization and statistic methods for description of the systems studied, analysis of systems and multisystems using discrete and functional equations, digital topology application, AI mathematical background, transformation and representation of multistructures modelling automated processes, fuzzy preference structures application, multicriterial optimization, research into automata and multiautomata seen in the framework of discrete systems, stability and system controllability. The study programme will also focus on developing theoretical background of the above mentioned areas of mathematics.

The graduates of the postgraduate study programme Mathematics in Electrical Engineering will be prepared for future employment in the area of applied research and in technology research teams. Due to the comprehensive use of computer engineering throughout the study programme, the graduates will be well prepared for work in the area of scientific and technology software development and maintenance. The graduates will also be prepared for management and analytical positions in companies requiring good knowledge of mathematical modelling, statistics and optimization.

The graduates of the postgraduate study programme Mathematics in Electrical Engineering will be prepared for future employment in the area of applied research and in technology research teams. Due to the comprehensive use of computer engineering throughout the study programme, the graduates will be well prepared for work in the area of scientific and technology software development and maintenance. The graduates will also be prepared for management and analytical positions in companies requiring good knowledge of mathematical modelling, statistics and optimization.

doc. RNDr. Zdeněk Šmarda, CSc.

1. A construction of a general solution of a linear system of three differential equations with constant coefficients and a weak delay

   The aim of the task is a construction of a general solution of a linear system of three difference equations with a weak delay.

   Tutor: Diblík Josef, prof. RNDr., DrSc.

2. Asymptotic properties of solutions of discrete and dynamics equations

   The aim of the task is to determine asymptotical properties of solutions for certain classes of difference and dynamic equations.

   Tutor: Diblík Josef, prof. RNDr., DrSc.

3. Discrete and continuous representation of mathematical information structures

   The dissertation will be focused on the study of spatio-relational discrete and continuous relationships in the mathematical information structures. The research will be concentrated especially on the topological and quasi-pseudometrical properties of these structures. Possible applications are, among others, e.g. in computer science, cybernetics, artificial intelligence (in connection with the formal concept analysis) and machine vision (digital topology).

   Tutor: Kovár Martin, doc. RNDr., Ph.D.

4. Investigation of asymptotical properties of systems of differential and difference equations with delay.

   The aim of the task is investigation of asymptotical properties of systems of differential and difference equations with delay and their application in control theory and optimization.

   Tutor: Baštinec Jaromír, doc. RNDr., CSc.

5. Multiautomata as a tool for modelling of processes in the theory of linear regulation

   In the field of analysis of non-linear systems there are used methods of a linearization in the framework of which - concerning approximation of non-linear models by linear models - linear transformations as Laplace and Fourier transforms are playing an importatnt role. Using a convenient functorial transfer into the field of multistructures, we obtain modelling tools corresponding to discrete dynamical systems, properties and applications of which should be an object of investigation.

   Tutor: Chvalina Jan, prof. RNDr., DrSc.

6. Qualitative methods of investigation of integrodifferential equations

   The study will be directed to modification of the Wazewki's topological method for integrodifferential equations and determination of conditions of existence and uniqueness of solutions using of some fixed point theorems . Results will be applied to solving of certain problems from the theory of electrical circuits.

   Tutor: Šmarda Zdeněk, doc. RNDr., CSc.

7. Topological methods in mathematical information and causal structures

   The dissertation will be focused on the study and development of certain suitable topological methods for the work with the mathematical structures, carrying some information.The research will be concentrated especially on the properties and the relationships of causal character. Possible applications are, among others, e.g. in computer science (concurrent and parallel processes), cybernetics, quantum information theory and physics (some aspects of general relativity versus quantum gravity).

   Tutor: Kovár Martin, doc. RNDr., Ph.D.