Описание:

• Basic principles of mathematical modelling. Direct and inverse problems of mathematical modelling. Universality of mathematical models. Analogy principle. Model hierarchy.
• Methodology of mathematical modelling. System analysis. Complex systems and decomposition. Static and dynamic models. Discrete and continuous. Deterministic and stochastic.
• Ordinary and partial differential equations. Theory and applications. Applied algebra and numerical analysis. Numerical methods and optimization methods. Variation methods. Approximation, stability, convergence.
• Probability theory and applied statistics. Stochastic processes. Combinatorics. Graph theory. Waiting line theory. Games theory. Statistical Theory of Expert Assessments.
• Theory of management, optimization and their applications. Statistical modelling and applications.
• New objects and methods of mathematical modelling. Fractals in mathematics. Dimensionality of self-similarity. Self-organisation and structure formation. Synergetics.
• Software tools for mathematical modelling. Applied packages for engineering analysis. Mathematical modelling of future internet and development of future technologies for internet security. Mathematical models and intelligent information systems.
• Mathematical modelling in fundamental and applied physics, mechanics, chemistry and biology.