Web site: http://mmpo.univer.kharkov.ua

History

The department was formed in 1972. It was headed by professors Korop V.F., Lviv V.A. and from 1986 to present day by professor Rutkas A.G. Today on the department 9 members work ( 2 Full Professors (Rutkas A.G., Vlasenko L.A.) and 5 PhD). Over 25 former post-graduate students and researchers of the department are currently teachers of different universities (including 16 teachers of V.N. Karazin Kharkiv National University) and researchers of Ukraine, the USA, Armenia, Estonia, Algeria and Nigeria. 20 of them upholded their Ph.D. theses (including 10 under the supervision of professor Rutkas A.G.) and two doctoral theses.

Scientific work

The main subject matters of the department:

1. Mathematical modeling of evolution of physical, financial and economic systems.
   Application of spectral analysis and probabilistic-statistical methods.
2. Theory of differential-operator, functional-differential, impulsive and differenсe equations of Sobolev type. Application of the equations in partial derivatives of not Kovalevska type to the evolution of electrodynamics, radio engineering, mathematical economics and ecology.
3. The spectral theory of operator sheafs and not-self-adjoint operators in Banach and Hilbert spaces, in spaces with indefinite metrics of Pontryagin and Krein.

In 2006 professor Vlasenko L.A. published a monograph “Evolutionary Models of Implied and Degenerated Differential Equations”.

For students who want to enter the university

The department trains students specializing in the field of “Mathematics” and “Applied Mathematics” and this is main for 3 specialities:

• mathematical modeling;
• mathematical and software computer systems;
• applied mathematical statistics and financial mathematics.

Students who specialize in "Mathematical Modeling" study both the classic mathematical models of ecology, physical, biological, financial and economic systems and processes and modern mathematical methods of analysis models. Students in the specialization of “Mathematical and Software Computer Systems” study mathematical foundations of the theory of parallel computation, mathematical methods for analyzing and processing digital audio and video information, the basis of cryptanalysis. And finally in the specialization of “Applied Mathematical Statistics and Financial Mathematics” students are taught mathematical methods for analyzing stochastic models of financial markets, problems of investment, lending and insurance, statistical methods of data analysis.

Educational work

The Department provides general courses for the students of Mechanics and Mathematics Department: “Measure and the Lebesgue integral”, “Probability Theory”, “Mathematical Statistics”, “Random processes”, “Mathematical Modeling”, “Data Analysis”, “Architecture of computers”, “Algorithms and data structures”, “Databases and Information Systems”, “Programming”, “Computer Networks”.

The special courses for bachelors and masters include: “Theory of finite and infinite graphs and its application”, “Non-negative Matrices and Applications”, “Mathematical Models with Equations of Sobolev's type”, “Optimization Models for Descriptor Systems”, “Theory of Martingales with Application to Mathematical Models of Finance”, “Evolutionary Models with Implicit and Degenerated Differential Equations”, “Theory of Functional Differential Equations and its Application”, “The Abstract Cauchy Problem”, “Implicit Difference Equations”, “Operator-differential Equations and their Application”, “Numerical Methods for Solving Degenerated Equations”, “Flows in Networks”, “Probabilistic and Statistical Methods in Econometrics”, “Stochastic Models of Financial Markets”, “Introduction to Insurance Mathematics”, “Mathematical Models of the Investment Process”, “Mathematical Models in Economics”, “Stochastic models in Problems of Insurance”, “Optimal Statistical Decisions”, “Multivariate Statistical Analysis”, “Queuing Theory”, “Markov Decision Processes”, “Fundamentals of Modern Cryptanalysis”, “Distributed Computing”, “Introduction to Digital Signal Processing”, “Technology and Standards for Data Processing”, “Regular Expressions”, “Parallel and Network Programming”, “Data Compression Algorithms for Multimedia”.

In 2004 Professor Rutkas A.G., Professor Bondarenko M.F. and Associate Professor Bilous N.V. (KNURE) published a co-authored textbook "Computer Discrete Mathematics” (in Russian and Ukrainian), recommended by the Ministry of Education of Ukraine. The authors received the State Prize of Ukraine on Science and Technology for this textbook in 2008. In 2007 the professors of the department Vlasenko L.A., Rutkas A.G. and associate professor Podtsykin M.S. published a co-authored textbook called "Discrete Probability Theory and its Application”.