PřF MANA Mathematical Analysis
Name in Czech: Matematická analýza
doctoral full-time specialized
Included in the programme: PřF D-MA_ Mathematics and Statistics

Final state doctoral examination and defence of the doctoral thesis

Before submitting an application for the state doctoral exam, the candidate must have fulfilled all the obligations set out in the individual study plan to this milestone.

The state doctoral exam is oral and is held in the following areas of mathematics. The field committee will select three topics based on the suggestion of the advisor.

- Qualitative theory of ordinary differential equations
- Linear functional analysis
- Nonlinear functional analysis
- Measure theory and integration
- Calculus of variations and optimization theory
- Theory of fixed points and its applications
- Topic related to the dissertation thesis

The dissertation must contain own original and published results or results accepted for publication.

Requirements of the study

The student passes at least four semester courses during the study, which are outside of the topic of the dissertation (5-15% of the total workload).
Upon agreement with the advisor, a separate study will focus on broadening the knowledge in the given field and on special parts required for the dissertation.

Research activities:
- Dissertation preparation - takes place during the whole study period and constitutes 60-70% of the workload
- Publications – As a standard in this field it is expected that the student will be the author or co-author of at least two quality publications in peer reviewed international journals, from which at least one publication will be in a journal with impact factor.
- Pedagogical activities (participation in teaching) – the student can take part in supervising bachelor theses, conducting seminars, etc., up to a maximum of 150 hours per study (5-10% of the workload)
- The results of the dissertation must be presented orally in English at an international forum. The expected extent of this activity is about 5-15% of the total workload.
- Student will actively participate in the seminar of this specialization (5-10% of the workload).

The duties in the doctoral study program include the completion of a part of the study at a foreign institution in the duration of at least one month, or some other form of student's direct participation in international cooperation.

The basic form of doctoral study is a full-time form. It is expected that if a student will properly fulfill all his / her duties, he / she will successfully complete his / her studies after four years of standard study period (he / she will present his / her application for defense and defend in the following period). The combined form should be used exceptionally, especially in cases where, for serious reasons, the student fails to finish his studies after 4 years, although he has properly fulfilled his duties within the ISP. The only task within the combined form is the work on the dissertation project.

Proposal of dissertation topics and topics of defended dissertations

Asymptotic Behaviour of Third Order Differential Equations
Petr Liška (školitel Zuzana Došlá)
https://is.muni.cz/auth/th/eiwiu/?fakulta=1431

Almost periodic solutions of limit periodic and almost periodic linear difference systems
Martin Chvátal (školitel Michal Veselý)
https://is.muni.cz/auth/th/vgrc8/?fakulta=1431

Periodic and quasiperiodic solutions of differential equations of Van der Pol-Mathieu type
Zdeněk Kadeřábek (školitel Josef Kalas)
https://is.muni.cz/auth/th/ofmk9/?fakulta=1431

Oscillation Theory of Higher Order Half-Linear Differential and Difference Equations
Vojtěch Růžička (školitel Pavel Řehák)
https://is.muni.cz/auth/th/p5jwb/?fakulta=1431


On the solvability of some non-local boundary value problems for functional differential equations
Mgr. Vita Pylypenko (školitel András Rontó)
https://is.muni.cz/auth/th/q2hv8/?fakulta=1431

Recommended progress through the study plan

Warning:

The study plan does not contain any courses.