### Degree programme objectives

The aim of the program is to prepare high-quality scientific specialists in the fields covered by the Institute of Mathematics and Statistics at MU. Graduates should be prepared primarily for further scientific work in academic institutions, but also for possible application in practice. Upon graduation, graduates who wish to continue their research work are motivated to gain long-term foreign experience as post-doctoral students.

The individual research teams of the Institute of Mathematics and Statistics cover the following research themes in which PhD students are also trained:

- Categories and ordered sets, number theory, semigroup theory

- Geometric structures, geometric complex analysis, algebraic topology

- Theory of Differential and Differential Equations, Calculus of variations and optimal control

- Mathematical modeling, statistics and data analysis, applications in biology and medicine

Attention is also paid to the preparation for pedagogical work at universities. The study is based on an individual study plan and is completed by a state doctoral examination and a defense of doctoral dissertation. In addition to Czech, English is also the working language of the program.

### Study plans

## Studies

- Objectives
The aim of the program is to prepare high-quality scientific specialists in the fields covered by the Institute of Mathematics and Statistics at MU. Graduates should be prepared primarily for further scientific work in academic institutions, but also for possible application in practice. Upon graduation, graduates who wish to continue their research work are motivated to gain long-term foreign experience as post-doctoral students.

The individual research teams of the Institute of Mathematics and Statistics cover the following research themes in which PhD students are also trained:

- Categories and ordered sets, number theory, semigroup theory

- Geometric structures, geometric complex analysis, algebraic topology

- Theory of Differential and Differential Equations, Calculus of variations and optimal control

- Mathematical modeling, statistics and data analysis, applications in biology and medicine

Attention is also paid to the preparation for pedagogical work at universities. The study is based on an individual study plan and is completed by a state doctoral examination and a defense of doctoral dissertation. In addition to Czech, English is also the working language of the program.

- Learning Outcomes
After successfully completing his/her studies the graduate is able to:

- independently and creatively plan and implement scientific and research activities and master mathematical methods and models of their specialization.
- write and publish a scientific text in the form of specialized mathematical or statistical articles in their specialization.
- present and defend the results of their own research at an international scientific forum in their specialization
- understand and know how to use broader professional and theoretical knowledge in mathematics and statistics
- know and critically evaluate the latest findings and scientific developments in mathematics and statistics
- Understand and manage fluent English technical communication
- to use the experience gained from international cooperation
- to transfer knowledge and experience through their pedagogical experience
- to use the experience gained from project planning and communication and teamwork

- Occupational Profiles of Graduates
Graduates will apply to mathematical workplaces of basic research, universities and scientific research institutes of the Academy of Sciences of the Czech Republic.

The best graduates are fully prepared to successfully apply for postdoctoral positions at high-quality universities abroad.

Graduates can also act as college teachers at universities with a technical, economic and pedagogical focus.

Graduates of applied specializations will also find use in practice, in institutions where the use of deterministic and stochastic models of real processes where specialized statistical software is being developed, and in institutions focusing on research in the field of probabilistic and mathematical-statistical methods.

- Practical Training
Practical training is not a mandatory part of this program.

- Goals of Theses
The dissertation should be based on original journals or similarly published or published results. Primarily it should be magazines with an impact factor above median, belonging to the major in the field concerned. In the case of extraordinary quality results suitable for potential publications in excellent journals, with a long expected time to accept them for publication, discuss the prestigious quality of the previously unpublished publications at the suggestion of a supervisor before the defense of the dissertation. The dissertation can be structured either as a so-called cumulative dissertation (ie a series of reprinted texts of already reviewed articles, supplemented by an informative introduction to the work in a broad context of related international research and its wider contexts or motivations) or in the form of a separate scientific discourse. Dissertations are written in English, exceptions can be discussed and recommended by the Board of Directors.