Doctoral Studies

Mathematical Analysis - Field

Brief description of field

The field mathematical analysis provides a theoretical basis for analytical study of phenomena in science, technology, and economics. The subject of the study are differential and difference equations, half-linear equations, Hamiltonian systems and symplectic systems. Students work on recent problems in asymptotic and oscillation theory, spectral theory, boundary value problems, properties of almost periodic functions and systems, and their applications in calculus of variations and optimal control theory. The field of mathematical analysis prepares students for positions in academic or commercial employment, where the independent analytical thinking is required. This field has a long-term tradition at Masaryk University and an extensive international collaboration

Profile of a typical graduate

The principal aim of the study program is to prepare students for indiviual research work in the field of mathematical analysis and its applications, and to possible activity as a university teacher of mathematics. The doctoral dissertation must contain original research results. It is required that these results are published or accepted for publication in international mathematical journals, and presented in English on an international meeting.

Requirements for applicants

The knowledge at the level of master's state exam in mathematics is required. In particular, the applicant should be well familiar with courses of functional analysis and differential equations. The knowledge of English language is required on the level of understanding English mathematical publications and oral discussion on general topics. It is advisible that students contact possible advisor before they submit the aplication to the study program.

Points awarded during the enrance examination:

  • Mathematical knowledge       min 30 points             max 50 points
  • Language skills                       min 20 points             max 30 points
  • Others                                     min 0 points               max 20 points
  • Total                                       min 50 points             max 100 points

The cathegory „others“ contains in particular own scientific results (e.g. from the master diploma thesis), or taking part on activities, which are directly related with the scientific work of the applicant.

Study requirements and completion of studies

In the course of doctoral studies, the student has to pass six one-semester courses determined for the doctoral study program.

Students also regularly participate in scientific seminars and assist in teaching the undergraduates. There are two forms of the doctoral study

- the regular form (maximum 4 years, the scholarship is available for that period), or in combined form for eployed students (maximum 7 years, scholarship is not available for this form).

The subject and the extend of the state doctoral exam, the required knowledge.

 

The doctoral exam covers the following fields:

  • theory of ordinary and functional diferential equations,
  • functional analysis,
  • topic associated with the orientation of the doctoral dissertation.

Dissertation

The dissertattion must contain own original and published results or results accepted for publications. The results must be presented by the student in English on an international event (e.g. a conference). It is standard in this field to have at least two quality publications in refereed international journals, from which at leat one publication is in journal with impact factor. These minimal requirements must be seen from the context of the content of the publications (number and difficulty of the results).

General Topics for PhD theses:

  • Singular solutions of higher order differential equations
  • Symplectic difference systems and associated quadratic functionals and Riccati type difference equations
  • Qualitative theory of functional differential equations and systems
  • Asymptotic analysis of quasilinear differential ad difference equations
  • Boundary value problems for functional differential equations

Individual study plan

Individual study plan

The student will need to completes six one-semester courses appointed for doctoral studies.
After consultation with the supervisor, self-study will focus on gaining more knowledge in the field and on special aspects needed to write a good dissertation. The student will also regularly attend seminars and help with preparing/teaching undergraduate courses.

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List of members of doctoral committee

List of supervisors

Commission for state doctoral exams and defenses

List of current doctoral topics

Department pages


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