Magistracy
Speciality Name:
Computational Sciences and Statistics
Faculty:
Mechanics and Mathematics
Qualification:
- Scientific and pedagogical direction - Master of Natural Sciences
- Model of graduating student
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Mandatory
disciplines
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Elective
disciplines
- Professional
ON 1 Develop and use algorithms for computational research and experiments using modern effective methods of computational mathematics
ON 2 Develop methods and algorithms for computational mathematics based on the approximation of differential equations by methods of finite differences, volumes or elements
ON 3 Conduct a fundamental analysis of computational methods and difference schemes for convergence and correctness, including in the case of high-performance algorithms using elements of mathematical logic and the theory of computability
ON 4 Solve computational problems with complex geometry of regions by building and using correct structured, curvilinear, unstructured computational grids
ON 5 Use deep learning-based data mining techniques, reinforcement learning to adapt the computational algorithm to efficiently predict outcomes
ON 6 Conduct classes in mathematical disciplines offline and online based on innovative technologies, developing methodological recommendations for independent student work, laboratory, practical, lecture courses, textbooks, teaching aids, educational work plans, etc.
ON 7 Develop parallel computing algorithms for engineering problems and implement them in high-performance systems, develop quantum computing algorithms.
ON 8 Develop and conduct computational simulations of probabilistic processes from various industries using stochastic analysis methods and stochastic differential equations
ON 9 Use the methods of mathematical statistics in various areas of the economy and production, on real data for the selection of parameters, adaptation and testing of computing systems based on real experiments
ON 10 Conduct independent scientific research, solving modern urgent problems, publishing results in rating journals and speaking at conferences
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Organization and Planning of Scientific Research (in English)
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to form the research culture of the future specialist, and to study the theoretical and methodological principles of organizing research activities in the context of the development of science and society. The discipline is aimed at developing the ability to conduct independent scientific research using methods and techniques of analysis, and information scientific resources.
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Quantum computing algorithms
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: to learn the basics of quantum computing, quantum computational models, efficient quantum algorithms. The course examines the history of the origin of quantum computing, introduces the necessary concepts based on the postulates of quantum mechanics, examines the well-known quantum algorithms that demonstrate the power of quantum computing.
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High performance computing
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: to provide knowledge and skills that allow to create high-performance implementations of well-known methods of computational mathematics, analysis and data processing.
Upon mastering the discipline, the master student will know the theoretical aspects of parallelization of algorithms; technologies for organizing clusters; methods of hardware implementation of data processing algorithms.
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Foreign Language (professional)
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose is to acquire and improve competencies by international standards of foreign language education and to communicate in an intercultural, professional, and scientific environment. A master's student must integrate new information, understand the organization of languages, interact in society, and defend his point of view.
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History and Philosophy of Science
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The course forms knowledge about the history and theory of science; on the laws of the development of science and the structure of scientific knowledge; about science as a profession and social institution; оn the methods of conducting scientific research; the role of science in the development of society.
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Unstructured grid generation methods
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of this course is to study advanced algorithms for triangulation and partitions of spaces, such as Voronoi partitions and Delaunay triangulation with additional constraints, for the further construction of computational grids and the implementation of finite volume and finite element methods on the constructed mesh structures.
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Pedagogy of Higher education
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose is the formation of the ability of pedagogical activity through the knowledge of higher education didactics, theories of upbringing and education management, analysis, and self-assessment of teaching activities. The course covers the educational activity design of specialists, Bologna process implementation, acquiring a lecturer, and curatorial skills by TLA-strategies.
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Psychology of Management
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The course reveals the subject, the basic principles of management psychology, personality in managerial interactions, personal behavior management, psychology of managing group phenomena and processes, psychological characteristics of the leader's personality, individual management style, psychology of influence in management activities, conflict management.
Data for 2021-2024 years
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Big Data analytics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to study the main concepts and tasks of Big data, such as data capture, storage, sharing, management and analysis. The discipline includes the modern big data technologies, the privacy and security concerns, popular big data platforms, techniques and tools to analyzing big data.
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Deep learning
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: First of all, the course is aimed at developing students' skills in solving applied problems using deep neural networks.
The course covers the fundamentals and practical applications of reinforcement learning and examines the latest techniques used to create agents that can solve a variety of complex problems with applications.
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Markov Decision Processes
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Markov decision-making processes or controlled Markov processes are considered. Markov decision-making processes are used to solve problems: in operations research, in system analysis, reliability theory, inventory management, queuing theory, forecasting, preventive maintenance of complex technical systems. The use of optimal control strategies for Markov processes gives a significant economic effect.
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Lattice Boltzmann method for multiphase flows
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: modeling of multiphase and multicomponent fluid and gas flows by the lattice Boltzmann equations method. The discipline includes the physical basics of multiphase and multicomponent flows, analysis of lattice Boltzmann models for multiphase and multicomponent flows, the theory of multicomponent diffusion, the implementation of the LBM algorithm.
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Lattice Boltzmann method for single-phase flows
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: modeling of single-phase fluid and gas flows by the lattice Boltzmann equations method. The discipline includes the physical basics of single-phase flows, analysis of lattice Boltzmann models for single-phase flows, the implementation of the LBM algorithm.
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Nonparametric statistics and factor analysis
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Nonparametric (the assumed distribution function does not depend on parameters) data processing methods are considered, which are comparable in their capabilities to the Gaussian one.
Factor analysis assumes that the observed variables are a linear combination of some latent (hypothetical or unobservable) factors.
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Stochastic approximation and control
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Stochastic approximation problems are solved: solving an equation by the stochastic approximation method, finding extrema and recurrent estimation of an unknown parameter of the distribution density in the presence of an additional control parameter. Problems of controlled Markov chains, optimal stopping of a controlled Markov chain are solved.
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Stochastic differential equations and their applications
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Stochastic processes and random functions, stochastic analysis of processes, the main properties of stochastic processes as continuity and discreteness are considered. The theory of Markov processes is considered as a consequence of stochastic processes. The definition of Markov processes is integro-differential stochastic equations and stochastic differential equations. The Cauchy problem for SDEs is considered.
Data for 2021-2024 years
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Pedagogical
- Type of control: Защита практики
- Description: Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.
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Research
- Type of control: Защита практики
- Description: The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.
Data for 2021-2024 years
