Doctoral study is a continuation of master study programmes guaranteed by the Department of Mathematics. The doctoral study programme is organized according to the scientific orientation of the Department. Applicants for admission to the Ph.D. programme can also have a Master is degree in mathematics or related study fields awarded by another university.
WHAT WILL I LEARN?
Doctoral research topics are from the following areas:
- study of qualitative properties of nonlinear differential equations in one-dimensional and multi-dimensional cases,
- formulation of nonlinear mathematical models on time scales and their analysis,
- study of nonlinear eigenvalue problems, especially problems with degenerate and singular operators,
- bifurcations of solutions of nonlinear systems,
- effective methods of algebraic geometry for applications in geometric modelling; symbolic manipulations in computer-aided geometric design and symbolic-numerical computations,
- optimization of the choice of models of random variables in lifetime theory and regression analysis,
- study of properties of discrete structures (graphs, hypergraphs, matroids, codes); investigation of their mutual relations (colourings, homomorphisms) and the existence of special substructures (cycles, paths, factors),
- study of graph operators, especially graph closures, and related methods for the investigation of properties of graph structures,
- numerical analysis of problems of multi-phase flow and contact problems in biomechanics,
- development of new computational conservative schemes for numerical simulations in fluid mechanics.
Graduates demonstrate deep knowledge of advanced mathematical techniques in the fields of nonlinear differential equations, in the research of mathematical models on time scales, in the study of bifurcation of solutions in nonlinear systems, in the development of new methods for describing complex-shaped objects, in the optimalization of the choice of models of random variables in lifetime theory and regression analysis, in the study of the properties of discrete structures and graph operators, in the numerical analysis of problems in biomechanics, or in mathematics education, in methodology and educational psychology, and in historical and philosophical aspects of mathematics and education. Graduates will find jobs in applied and basic research, in the management of analysis groups and in the academic environment. Graduates will be able to work creatively in a chosen field in scientific and academic institutions and in the department of mathematics at some university.