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Applied Mathematics
The graduate of the doctoral study programme Applied Mathematics has a deep theoretical-methodological knowledge of several areas of mathematics, knows the theoretical foundations and scientific methods of research, is able to discover new regularities of the studied structures, to design mathematical models of tasks from various social-scientific and technical areas and to solve them with the help of computer technology. He has mastered methods of presenting research results in various forms, including publishing in foreign scientific journals and speaking at scientific conferences in a foreign language. He/she is able to keep in touch with the latest developments in his/her discipline, to follow the scientific literature and to communicate with the staff of the application areas.
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successful completion of the entrance exam
Additional information
Discrete models in game theory, mathematical economics and operations research:
Linear and convex programming: properties of convex sets, simplex method and its variants, duality, Kuh-Tucker theory.
Combinatorial optimization: algorithms on graphs, flows in networks, complexity analysis of algorithms, NP-complete problems.
Basics of game theory: games in extensive form, matrix and bimatrix games, n-player cooperative games.
Probability theory and statistics:
Probability theory: Random vectors, their distributions and characteristics. Characteristic functions. Laws of large numbers and central limit theorems. Random processes, their distributions and characteristics. Markov processes, Poisson process, emergence and extinction process.
Mathematical statistics: Methods of estimation of unknown parameters. Hypothesis testing. Matrix calculus used in statistics, g-inversionProperties and uses of linear model (regression, ANOVA, ANCOVA). Random number generation and simulation. Time series.
Differential equations and functional analysis
Differential equations: elementary methods for solving differential equations. Existence and uniqueness of solutions. Basic properties of solutions of a linear differential system and a linear differential equation. Comparison theorems.
Integral calculus of functions of several variables: definition of integral on an interval, some properties and computation of integral on an interval, integral on a set, some properties and computation of integral on a set, double and triple integrals. Intrinsic integrals - definition, existence theorems and methods of calculating integral. Parametric integrals - properties of a function given by a parametric integral, examples of computation of integrals, gamma and beta functions, Stirling's formula.
Functional analysis: linear spaces. Algebraic basis and dimension. Linear representation and functional. Algebraic dual space. Linear topological space. Locally convex space. Linear normed space. L(p)-spaces. Dual spaces to L(p)-spaces. Hilbert space. Applications of Baire's category theorem. The open mapping theorem. The closed graph theorem. The Hahn-Banach theorem. The spectrum of a linear compact operator.
In this study programme, the student chooses a dissertation topic from one of three specialised areas (see below) and therefore the emphasis is on knowledge from the chosen area roughly in the range taught at the first two levels of undergraduate mathematics studies. In addition to an interest in this area of science, the candidate should demonstrate the ability to think analytically and critically, and to formulate new mathematical theorems and algorithms independently. Due to the applied nature of several topics, programming skills or the ability to work with application software packages are required. The ability to independently study foreign language (mainly English) scientific mathematical literature is a prerequisite.
Form of entrance exam
oral
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Apply the application for study
01.03.2025 - 31.05.2025
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Performance of the entrance exam
16.06.2025 - 27.06.2025
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We will send you all the information about important events and deadlines.
- CV
- verified copy of the degree for applicant of other universities
- photocopy of the Diploma Supplement to candidates from other universities
Annual tuition fees
Standard length of study: cost free
The fee for admission procedure
application form: 50 €
E-application form: 40 €
Billing information
Bank: Treasury. Bank code: 8180
Account number: SK 28 8180 0000 0070 0007 8491
Variable symbol: 2996
Constant symbol: 0308
Specific symbol: birth number without slash
Recipient message: name and surname of the applicant
Always up-to-date news about university Pavol Jozef Šafárik University in Košice on your email.
We will send you all the information about important events and deadlines.
0911 154 882
0910 288 664
037 / 6414881
037 / 6414890
(7.30 - 15.30 h.)
Responsibility for content: Ing. Lucia Dancáková – lucia.dancakova@upjs.sk
Last update: 11.11.2024 10:59