Lenght of study: 4 yaers
Form of study: full-time or combined
Department: Department of Mathematics
Doctoral study is a continuation of Master study programs guaranteed by the Department of Mathematics. The doctoral study program is organized according to the scientific orientation of the Department. Applicants for admission to the Ph.D. program can also have a Master degree in mathematics or related study fields awarded by another university. 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 modeling; 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.
Organization of study
Doctoral study of applied mathematics is offered in two forms: full-time and combined. The full-time students become members of the Department team and of the corresponding Department Section according to the specialization of their doctoral theses. By agreement with the supervisor and the Department management, the students participate in teaching activities.
At the beginning of the study, the Ph.D. student, together with his/her supervisor, draws up his/her individual study plan, which is approved and regularly revised at the annual meetings of the PhD. Study Board. The plan includes the examinations the PhD. student has to take during the first part of his/her study, and the topic of his/her doctoral thesis, which the student must submit for defense according to the prescribed schedule.
The first part is concluded by the state doctoral examination (a Ph.D. student applies in writing for admission to the examination and submits a brief paper on the topic of the future doctoral thesis). The doctoral study is completed by the defence of the doctoral thesis (a Ph.D. student submits his/her application for the defense together with the documents required by the Study and Examination Rules of the University of West Bohemia). In general, the above stated rules also apply to students in the combined form of study. In fulfilling his/her duties, the Ph.D. student is monitored and guided by his/her supervisor and the Department and Section heads.
Depending on the space available to the Department, the Ph.D. student is allotted a place of work. Working hours are not fixed, but the Ph.D. student is expected to report regularly to his/her supervisors.
Immediately, after starting the studies, the Ph.D. student is required to contact the Department management.
Profil of the programme
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 the theory of life 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 job in applied and basic research, in 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.