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.

2. round (applications submitted from 04.07.2016 to 20.07.2016)

1. Algebraic, topological and generalized metric properties and methods in applied context structures

   The dissertation will be focused on study and development of methods with origins in algebraic and topological properties of the fundamental structures of formal concept analysis in the sense of B. Ganter and R. Wille. There will be investigated also generalized metric properties of these structures connected with the notions of a partial metric, quasi metric or quasi-pseudo metrics. Possible applications are - outside the mathematical sciences - also in computer science, cybernetics, physics and biomedicine.

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

2. Discrete equations describing electrical circuits with aftereffect.

   The aim is to derive algorithms for analytical solution of discrete equations and systems with aftereffect and their application to solving mathematical models of electrical circuits. The work will be a continuation of previous results derived in the paper „Solution of the serial circuit RLC“ by J. Diblík and J. Klimek:, Elektrorevue, 2007/22-13.6.2007, 22-1-22-10 (ISSN 12131539, http://www.elektrorevue.cz). Starting literature – parts of the book by A.V. Oppenheim, R.W. Schafer, J.R. Buck, Discrete-Time Signal Processing, Prentice Hall, 1999.

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

3. Numerical methods for solutions of matrix differential systems with delay.

   The aim of the work is to modify and extend numerical solution methods to solving some classes of matrix systems of differential equations with delay. Possible applications are, among others, e.g. in control theory and optimization.

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

4. Semianalytical methods and their applications to solving of partial differentila equations

   Dissertation will be focused on development of semianalytical numerical methods and their applications to solving initial and boundary value problems for partial differential equations. Convergence analysis of proposed methods will be discussed as well

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

5. Stochastic differential equations and their applications to electrical network

   By adding some randomness to the coefficients of an ordinary differential equation we get stochastic differential equations. Such an equation describes the current in an RL circuit with stochastic source. Then the solution of the equation is a random process. The subject involves creating stochastic models, numerical solutions of stochastic differential equations and examinations of the statistical estimates of the solutions.

   Tutor: Kolářová Edita, doc. RNDr., Ph.D.

1. round (applications submitted from 01.04.2016 to 15.05.2016)

1. Topological methods and properties 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.