Information for applicants

References to oficial pages


For whom the study branch Mathematical analysis is designed


Entry requirements


How to learn the missing topics


Information for foreign students

Entry requirements - mathematical part

In order the teaching in the master program may be effective and on an appropriate level, some entry requirements have been formulated. They are given in the degree plans and are explained in more detail here:


For students starting their studies in 2022 or later


We assume the knowledge of the following topics:

  1. Differential calculus of one and several real variables
  2. Integral calculus of one real variable
  3. Metric spaces, completeness and compactness
  4. Measure theory, Lebesgue measure and Lebesgue integral
  5. Elements of algebra (matrix calculus, vector spaces)
  6. Elements of general topology (topological spaces, compactness)
  7. Elements of complex analysis (Cauchy theorem, residue theorem)
  8. Elements of functional analysis (Banach and Hilbert spaces, dual spaces, weak convergence, bounded operators, compact operators, Fourier transform)
  9. Elements of the theory of ordinary differential equations (basic properties of solutions and maximal solutions, linear systems, stability)
  10. Elements of the theory of partial differential equations (quasilinear first order equations, Laplace equation and heat equation – classical solution and maximum principle, wave equation – classical solution in dimensions 1,2,3, finite speed of wave propagation)


The knowledge of the above mentioned topics is assumed in master courses. The topics given in items 1-5 are taught in basic courses of the bachelor program General mathematics. Without a sound knowledge of these topics studying mathematical analysis lacks any sense.


Knowledge of topics in items 6-10 is assumed as well. However, the absence of knowledge of some of these topic (which can be caused by a different curriculum of the student) is not a substantial obstacle to studying mathematical analysis. Nonetheless, the student should learn the missing areas.


For students starting their studies in 2021 or earlier


We assume the knowledge of the following topics:

  1. Differential calculus of one and several real variables
  2. Integral calculus of one real variable
  3. Metric spaces, completeness and compactness
  4. Measure theory, Lebesgue measure and Lebesgue integral
  5. Elements of algebra (matrix calculus, vector spaces)
  6. Elements of general topology (topological spaces, compactness)
  7. Elements of complex analysis (Cauchy theorem, residue theorem, conformal mappings)
  8. Elements of functional analysis (Banach and Hilbert spaces, dual spaces, bounded operators, compact operators, elements of the theory of distributions)
  9. Elements of the theory of ordinary differential equations (basic properties of solutions and maximal solutions, linear systems, stability)
  10. Elements of the theory of partial differential equations (quasilinear first order equations, Laplace equation and heat equation – fundamental solution and maximum principle, wave equation – fundamental solution, finite speed of wave propagation)


The knowledge of the above mentioned topics is assumed in master courses. The topics given in items 1-5 are taught in basic courses of the bachelor program General mathematics. Without a sound knowledge of these topics studying mathematical analysis lacks any sense.


Knowledge of topics in items 6-10 is assumed as well. However, the absence of knowledge of some of these topic (which can be caused by a different curriculum of the student) is not a substantial obstacle to studying mathematical analysis. Nonetheless, the student should learn the missing areas.