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. Applied topological and algebraic mathematical information structures

   The dissertation will be focused in some more advanced study of the applied mathematical information structures and their general topological properties. Possible applications are, among others, e.g. in computer science, cybernetics and physics (more concretely, quantum gravity).

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

2. Asymptotical properties of solutions of difference equations and systems of difference equations

   The project deals with asymptotical properties of solutions of difference equations and systems of difference equations. Next we will study sufficient and nessesary conditions which guarantee at least one solution with prescribed properties. Wazewki's topological method and its modification for difference equations and systems of difference equations will be the theoretical base for investigation.

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

3. Construction of the general solution of linear discrete systems of three equations with constant coefficients and a weak delay.

   In the project will be considered problem on a contruction of general solution of linear discrete systems of three equations with a single weak delay. Attention will be focused on a generalization of recent results in this direction obtained by supervisor together with prof. D. Khusainov (Kiev State University) and associate profesor Z. Šmarda (Brno University of Technology). The goal is to give a classification of all solutions in dependence on properites of roots of quasi-characteristic equation and a construction of a general solution of given system for every considered case. A possibility of application of obtained results in study of electrical circuits will be discussed as well.

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

4. 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. Possible applications are, among others, e.g. in computer science, cybernetics and machine vision (more concretely, digital topology).

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

5. Mathematical structures generated by differential equations

   Qualitative behaviour of differential equations. The study may be directed not only to analytic methods, but also to algebraic and geometric approaches. Investigation may be extended to functional differential equations, as well as to functional equations only. The situations when the studied objects are not suffciently smooth may also be under consideration. Especially in these cases it will be useful to find possible applications, e.g. in the theory of signal processing.

   Tutor: Neuman František, prof. RNDr., DrSc.

6. 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.

7. 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.

8. Topological methods in mathematical information 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. Possible applications are, among others, e.g. in computer science, cybernetics and quantum information theory.

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