Ph.D. students in Applied Mathematics and Fuzzy Modelling then choose one of the following specializations:
- Differential equations: geometric, variational, and optimization methods
- Analytical number theory
- Fuzzy modeling
Ad 1) The study in the specialization “Differential Equations: Geometric, Variational, and Optimization Methods” of the Ph.D. study field Applied Mathematics and Fuzzy Modelling focuses on one of the following areas:
- global variational analysis,
- differential equations on manifolds,
- differential invariants and natural Lagrange structures,
- optimization in abstract and infinite-dimensional spaces,
- stochastic-heuristic algorithms in global optimization.
The study in this specialization also pursues applications, namely:
- applications in physics and engineering (variational principles, dynamical control, and optimization, non-holonomic mechanics and field theory,
- real-life, everyday operational problems in business, industry, entrepreneurship, sustainable development, etc. The solution involves a mathematical formulation of the problem, (finding a suitable method for its solution), acquiring real data, and solving the problem with a practical recommendation based on the computed solution.
- The focus of the student is supported by electing at least two compulsory elective subjects of this specialization, where the student acquires deep theoretical knowledge of mathematical theories and methods (topology, differential geometry, global analysis, geometric mechanics, variational equations, stochastic algorithms) of the given areas, and the ability to use the modern methods and means of mathematics to solve real problems.
Ad 2) The study in the specialization “Analytical Methods in Number Theory” of the Ph.D. study field Applied Mathematics and Fuzzy Modelling focuses on one of the following areas:
- Irrationality of infinite series
- Diophantine approximations
- Densities and measures of sets of positive integers or real numbers
- Characteristics of distribution of number sets and sequences
The study in this specialization is mostly theoretical, nevertheless, it involves also applications, namely:
- applications of uniformly distributed sequences,
- construction of low discrepancy sequences and their applications,
- Monte Carlo and Quasi Monte-Carlo methods in mathematics, physics, economics.
The focus of the student is supported by electing at least two compulsory elective subjects of this specialization:
- Diophantine approximations
- Uniformly distributed sequences
- Prime number theory
- Monte Carlo and Quasi-Monte Carlo Methods and their applications
- Selected topics in Number Theory
The students will acquire deep theoretical knowledge of mathematical theories and methods of the given areas, and the ability to use the modern methods and means of mathematics to solve real problems. They will be prepared for their scientific research work as well as for further pedagogical work.
Ad 3) The study in the specialization “Fuzzy Modelling” of the Ph.D. study field Applied Mathematics and Fuzzy Modelling focuses on one of the following areas:
- Algebraic structures of truth-values (residuated lattices, MTL-, BL-, MV-algebras, etc.).
- Fuzzy logic.
- Fuzzy Modeling.
- Time series analysis.
- Data analysis.
- Nature-inspired methods (evolutionary algorithms, swarm intelligence, etc.),
A substantial part of the study is devoted to the practical development of the methods mentioned above and their applications, especially in the following fields of activities:
- Data processing (data mining, time series analysis and forecasting, image processing, etc.).
- Control and decision making based on expert knowledge.
- Artificial intelligence and common sense reasoning.
The admissions procedure involves the selection of suitable applicants. The admissions board considers the following documents provided by the applicant:
- an officially recognized diploma proving the applicant's higher education (a Master's degree or equivalent) – see below,
- a copy of the Diploma Supplement (or another list of completed courses in the framework of the Bachelor's or Master's studies, confirmed by the university),
- a Curriculum Vitae,
- a list of publications,
- a copy of a thesis written for a Master's degree (on a CD),
- a covering letter (in English) specifying the applicant's area of interest and identifying the prospective advisor,
- two letters of recommendation (by university lecturers or researchers).
The documents must be delivered to the Department for Research and Doctoral Studies no later than a day before the meeting of the admissions board.
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