Doctoral Study – Mathematics

Degree: Doctor, Ph.D.
Standard Length of Study: 4 years
Form of Study: full-time / part-time
Language: Czech / English

Possibility of study internships abroad

DESCRIPTION

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.

CAREER

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.

doc. Ing. Bohumír Bastl, Ph.D. Advanced symbo lic-numerical computations in geometry and geometrie modelling
prof. RNDr. Miroslav Lávička, Ph.D. Advanced symbo lic-numerical computations in geometry and geometrie modelling
doc. RNDr. Jan Vršek, Ph.D. Advanced symbo lic-numerical computations in geometry and geometrie modelling
   
doc. RNDr. Jiří Benedikt, Ph.D. Nonlinear boundary value problems for differential and difference equations
doc. Ing. Radek Cibulka, Ph.D. Nonlinear boundary value problems for differential and difference equations
prof. RNDr. Pavel Drábek, DrSc. Nonlinear boundary value problems for differential and difference equations
prof. Ing. Petr Girg, Ph.D. Nonlinear boundary value problems for differential and difference equations
doc. Ing. Gabriela Holubová, Ph.D. Nonlinear boundary value problems for differential and difference equations
prof. RNDr. Milan Kučera, DrSc. Nonlinear boundary value problems for differential and difference equations
doc. RNDr. Petr Stehlík, Ph.D. Nonlinear boundary value problems for differential and difference equations
   
doc. Ing. Marek Brandner, Ph.D. Numerical models, methods and algorithms: design and analysis
doc. Ing. Josef Daněk, Ph.D. Numerical models, methods and algorithms: design and analysis
doc. Dr. Ing. Miroslav Rozložník, DSc. Numerical models, methods and algorithms: design and analysis
doc. RNDr. Tomáš Vejchodský, Ph.D. Numerical models, methods and algorithms: design and analysis
   
doc. Ing. Radek Cibulka, Ph.D. Variational analysis and nonsmooth optimization algorithms
   
doc. Ing. Roman Čada, Ph.D. Algorithms for hard problems in combinatorial optimization
   
doc. RNDr. Petr Stehlík, Ph.D. Mathematical models of theoretical ecology
   
prof. RNDr. Eduard Feireisl, DrSc. Mathematical Models of Fluid Dynamics
RNDr. Šárka Nečasová, Ph.D. Mathematical Models of Fluid Dynamics
   
doc. Ing. Roman Čada, Ph.D. Structural graph theory
doc. RNDr. Přemysl Holub, Ph.D. Structural graph theory
prof. RNDr. Tomáš Kaiser, DSc. Structural graph theory
prof. RNDr. Roman Nedela, DrSc. Structural graph theory
prof. RNDr. Zdeněk Ryjáček, DrSc. Structural graph theory

Ing. Petr Nečesal, Ph.D. Nonlinear boundary value problems for differential and difference equations
Ing. Jan Pospíšil, Ph.D. Nonlinear boundary value problems for differential and difference equations
   
RNDr. Jan Papež, Ph.D. Numerical models, methods and algorithms: design and analysis
Ing. Jakub Šístek, Ph.D. Numerical models, methods and algorithms: design and analysis
   
Mgr. Ondřej Kreml, Ph.D. Mathematical models of fluid dynamics
RNDr. Mgr. Václav Mácha, Ph.D. Mathematical models of fluid dynamics


The list is updated based on the decision of the Dean, who appoints additional specialist consultants according to the supervisors' recommendations for specific students.