Mathematical Analysis (Eng.) – Field of study catalogue MU
Mathematical Analysis (Eng.)
“Infinitely small and infinitely large are two sides of one coin”
The study programme of Mathematical Analysis focuses on the studies of "analytical" relations between various mathematical objects, for example functions of real or complex variables, by means of inequalities and limit processes. The limits themselves belong to these processes, and also differentiation, integration, and techniques related to them.
In the doctoral degree programme of Mathematical Analysis the students obtain a deep knowledge of the theory of differential equations, functional equations, functional analysis, difference equations, theory of optimization, and other related mathematical disciplines. The applications of the obtained knowledge and methods in other scientific branches, such as technology, economics, and natural sciences - physics, biology, chemistry, and geology - form and integral part of studies. In the course of the studies the attention is paid to the independent research work under the supervision of the tutor. The aim of the studies is to write a thesis containing new scientific results published in mathematical journals.
Successful graduates will find employment not only in academic institutions doing research and teaching at universities or the Academy of Sciences, but also in areas where the application of analytical and creative thinking is essential for the analysis of complicated relations and processes (e.g. finance, insurance, and technology).
After successfully completing his/her studies the graduate is able to:
- do independent research, formulate and analyse new mathematical ideas, and relate them to the already known facts
- expand and apply methods of key areas of mathematical analysis, in particular theory of differential and difference equations, functional equations, functional analysis, optimization theory, complex analysis, measure theory, topology, or Fourier analysis
- understand advanced methods of mathematical analysis and apply them in related mathematical disciplines, natural sciences, or economics
- transfer specialized knowledge of mathematical analysis to the Bachelor's and Master's degree students (in the branches of mathematics, informatics, and natural sciences) in the form of lectures or semester seminars
- publish their scientific results in reviewed mathematical journals and present them at international conferences
The successful graduates are able to perform independent creative work in the theoretical areas of their specialization, as well as in applications of mathematical analysis. The graduates will find employment in mathematical institutes at universities, research organizations, and at those positions where analytical and creative thinking is needed for the analysis of complicated relations and processes.
The studies are organized according to an individual study plan.
The studies are completed with the doctoral state examination and the defence of the doctoral thesis.