The aim of the study programme is to train highly qualified specialists in mathematics in the sub-branch of differential equations completing their studies with the defence of the doctoral thesis, the specialists who are able to raise and independently solve most essential problems of contemporary mathematics.
Tasks of the study programme are:
to equip the students with knowledge adequate to the level of contemporary mathematics in the sub-branch of differential equations;
to acquire the contemporary research methods in mathematics;
to practice for managing the scientific and teaching/learning process at school;
to create optimal conditions for doctoral students’ research activities – opportunities to work in libraries, to use modern information and communication technologies, to regularly participate in scientific conferences in Latvia and abroad, to have in-service training courses at other universities and research centres;
to provide conditions for preparing and the defence of the doctoral thesis.
As a result of the programme’s acquisition, the graduate will acquire and be able to demonstrate:
Knowledge:
Classical questions of the theory on boundary-problems of ordinary differential equations (existence, continuous dependence of solutions on parameters of differential equations).
Current questions of the contemporary theory of ordinary differential equations (evaluation of the number of solutions, bifurcations etc.).
Applications of abstract branches of mathematics (function analysis, topology etc.) in the research on differential equations.
Basics of dynamical systems and analysis on time scales.
Mathematical terminology in English.
Software for the research of differential equations and dynamical systems (Mathematica, Maple, Matlab etc.)
Texts on mathematics in LaTeX language.
Skills:
To process literature relating to the research theme.
To carry out numerical and symbolic experiments relating to the research theme.
Students are able to apply the acquired theoretical knowledge to investigating a concrete research theme.
They can critically analyze the obtained results and prepare them for the presentation at international conferences.
Competence:
Students are able to link the theme of their research with topical developmental trends in the contemporary theory of differential equations.
They can see opportunities for the application of new software programs for their research theme.
They are able to take decisions on fulfilling and planning academic and professional tasks in today’s global and changeable world.
They are able to take the opportunities provided by modern information and communication technologies in order to achieve the goals set for their research.
They are able to compete in the labour market offering their knowledge and skills.
Doctoral students have possibilities:
to publish the results of their research in local periodical publications, scientific journals of Baltic region, internationally reviewed journals that are included in acknowledged data bases (SCI and the like);
to participate in annual scientific conferences at DU and LU, MMA international conferences (in Baltic region), as well as in serial conferences of European and the world scale (Equadiff, AIMS (Amer. Inst. Math. Studies), etc.);
to become members of Latvian Mathematical Society and members of other professional associations;
to participate in the implementation of European and international research programmes;
to receive scholarship if the student studies for the state budget means.
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