Mathematical and Computational Science

The course provides knowledge and skills in database design, starting from the conceptual stage and ending with physical implementation

Design patterns are one of the most important components of an object-oriented software development technology. This discipline is a formalized description of a frequently encountered design problem, its successful solution and recommendations on the application of this solution in various situations.

The course covers topics such as: Kinematics; dynamics; circular motion and gravity; energy; pulse; simple harmonic vibrations; torque and rotational motion; electric charge and electric force; DC circuits; thermodynamics and mechanical waves, field and potential; electrical circuits; induction of magnetism and electromagnetism; geometric and physical optics; and quantum, atomic and nuclear physics and sound.

The purpose of the discipline is to form a system of fundamental knowledge among students chemistry necessary for the subsequent preparation of a bachelor capable of An effective solution to practical tasks of modeling and calculations of practical tasks of chemical and bioenginean production

In this course, students learn about parallel algorithms. The emphasis will be placed on algorithms that can be used on parallel machines of common memory, such as multi -core architectures. The course will include both the theoretical component and the component of programming. Detailed topics include: modeling the cost of parallel algorithms, lower connections and parallel algorithms for sorting, graphs, computing geometry and string operations. The component of the programming language will include data parallelism, flows, planning, synchronization types, transaction memory and messages.

This course is a concept, languages, methods and patterns for programming heterogeneous, massive parallel processors. It covers heterogeneous computing architectures, software programming models, memory launching methods and parallel algorithms on the example of CUDA and OpenCl.

Differential equations in private derivatives in science and technology include tasks with initial and boundary conditions for parabolic, hyperbolic and elliptical equations of the second order. The emphasis is on the separation of variables, special functions, methods of transformation and numerical methods. The student will receive a clear intuitive understanding of the concept of the equation in private derivatives and his attitude to the description of physical phenomena, such as diffusion and the spread of waves, heat transfer.

Numerical methods are a set of techniques and approaches for the approximate solution of mathematical problems on a computer. Very rarely, the problems of approximation, interpolation, and differential equations are solved analytically, but in most cases a reliable numerical method can be proposed that allows one to obtain a solution with a given accuracy. The course is designed to give an idea of the current state of computational mathematics and its applications in data analysis and machine learning. Students will learn not only how to obtain theoretical estimates of convergence and reliability, but how to improve and build their methods to solve more specific problems in practice. The course offers practical assignments and design work.

This course focuses on the study of numerical methods for partial derivatives, with the focus on strict mathematical structure. Particular attention will be paid to a thorough understanding of the identified partial differential equatoins, the basis of finite differences, finite volume, finite elements and spectral methods, as well as consideration of concepts such as stability, convergence and error analysis. Problems: heat equation, wave equation, problems with convectional diffusion, Poisson equation, Navier-Stokes equation. Concepts: consistency, stability, convergence, weak equivalence theorem, error analysis, Fourier approaches. Methods: finite volumes, finite elements, spectral methods.

The course is devoted to the study of information security technologies.

The course is designed to study the basic methods and tools required for the introduction of scientific research. The course also introduces students to the most popular search and scientometric databases of scientific articles, such as Web of Science, Scopus, ScienceDirect and others. During the course, students will become familiar with the tools for citing and searching for the required scientific information.

This course aims to provide an introduction to quantum computing and algorithms. The paradigm change between conventional computing and quantum computing will be studied and several major quantum algorithms, including Shor and Grover algorithms will be introduced. The implications of quantum computing in fields such as cybersecurity and machine learning will also be considered.

The course presents the collection and analysis of materials for writing a graduation project

The method of final elements is an indispensable tool for engineers in all disciplines. This course introduces students to the fundamental theory of the method of finite elements as a common tool for a numerical solution to differential equations for a wide range of engineering problems. First of all, the tasks of Laplace, and Poisson”s equations are presented. All stages of MKE formulation are described. Specific classes of problems based on abstractions and idealization of 3D solids are discussed, such as flat stress and stress, the composition of the final elements for inconsistent flow tasks is introduced by sampling the equations of Euler and Navier-Koks.

This discipline is aimed at studying some approaches of the finite difference method, namely, fractional step methods for solving boundary value problems for partial differential equations. Such methods include methods of alternating directions, stabilizing corrections, longitudinal-transverse sweep, etc. Upon mastering the discipline, the student must know: basic methods of fractional steps, algorithms for iterative solution of boundary value problems for parabolic and elliptic equations; be able to: solve practical problems using the described methods, investigate the convergence of a solution, etc.

This course focuses on Finite Volume Methods (FVM), which is one of the most widespread numerical methods within a single scientific community and industry. Students will acquire theoretical knowledge and practical skills for solving one-dimensional and multidimensional elliptical, parabolic and hyperbolic differential equations useing finite volume methods as well as analyzing their convergence and stability.

Many systems develop over time with an integral part of chance. The purpose of this course is to develop and analyze the probability models that capture Significant features of the studied system for predicting the short -term and long -term perspective; The effects that this accident will have on the systems under consideration. Education of probability models for stochastic processes includes a wide range of mathematical and computing tools.

The discipline introduces students to the subject area of the science of data and forms the skills of solving the problems of processing and visualization of data using the Python language. The course considers the basics of interactive work with Python in the Jupyter Notebook notebook, the necessary minimum of Python syntactic constructions for data processing are given, basic analytical packages are considered: Pandas, MatPlotlib. The issues of downloading data from various formats, data purification, exploration analysis, data visualization are considered.

This course focuses on the study of stochastic differential equations (SDE) which offer beautiful and powerful mathematical languages for random systems in comparison with what ordinary differential equations (ODE) do for deterministic systems. In ordinary training, students master theorems of existing for SDE, solution properties to SDE, integrating methods of SDE.

The course is designed to give a solid foundation in fuzzy logic concepts and its applications. It contains work with fuzzy operators, phasing, defuzzification, TSK systems, their application in machine learning and fuzzy databases.

The main goal of this course is to introduce biomolecules and metabolism of these molecules into the main classes to create mathematical models. This course is intended in order to represent the introduction into the relationship between food components and components of living organisms. Particular attention is paid to biochemistry in the context of human nutrition. The main methods of mathematical modeling of biochemical processes are considered.

This course will use thematic studies to discuss problems and use of biostatistics. Topics will include cohort studies and control over the analysis of survival with applications in clinical trials, evaluating diagnostic tests and statistical genetics. The course will end with a review of areas of current biostatistical research.

In this course, students solve the problems of generating random samples from targeted distributions using Markov’s transformation methods and chains, optimizing numerical and combinatorial problems (for example, the task with the seller -participating) and Bayesian calculations for data analysis.

The course is designed to study the basics of Big Data, accumulated massives of structured and unstructured information. Students learn to work with MapReduce, Hadoop, Spark technologies to implement big data analytics and machine learning.

This course introduces students to the field of computational geometry and its application in numerical methods. Students will learn the fundamental geometric concepts and algorithms used in computational geometry, and how they can be applied in numerical methods for solving problems in various fields such as engineering, physics, and computer graphics. The course will cover topics such as geometric primitives, convex hulls, Voronoi diagrams, Delaunay triangulations, and spatial data structures and how they can be used in finite element analysis, finite volume methods. Throughout the course, students will gain hands-on experience with computational geometry tools and libraries such as CGAL and Boost.

The theory of decision -making is devoted to methods for determining the optimal course of actions when a number of alternatives are available, and their consequences cannot be predicted with confidence. This course will use quantitative methods (models) to solve problems and decision -making. Theories and models that should be learned, include probability theory, utility theory and games theory, linear programming models, non -linear programming models and integer programming models.

This course covers the principles of prokaryotic and eukaryotic cells of cells. The emphasis is on Data analytics, taking into account the molecular basis of heredity, chromosomal structure, models of Mendelev and Non-Mendelev inheritance, evolution and biotechnological applications. Upon completion, students should be able to recognize and describe genetic phenomena, demonstrate knowledge of important genetic principles, use tools to analyze large -volume genetic data

Introductory course that covers the fundamental principles of Markov chains and their applications in modeling stochastic systems. The course begins by introducing the concept of Markov chains, their properties, and basic definitions. Students will learn how to construct and analyze Markov chains, including the calculation of transition probabilities and stationary distributions. The course then covers more advanced topics, including the classification of states, hitting times, and limiting behavior of Markov chains. Students will also learn about various applications of Markov chains, including queuing systems, random walks, and simulation methods.

This course is intended to develop software systems and applications with focus on cloud solutions where it is most effective. Students have the opportunity to work with a variety of cloud technology providers such as Amazon, Google, Microsoft. They will learn how to deploy cloud solutions for databases, data analytics, and machine learning. The course contains following topics: “Load Balancing”, “Scalability, Availability and Fault Tolerance”, “BigQuery”, “Machine Learning on Unstructured Datasets”, etc.

This course will introduce the theoretical foundations of continuous optimization. Starting from the first principles, it will be shown how to develop and analyze simple iterative methods for an effective solution to wide classes of optimization problems. The focus of the course will have the achievement of proved convergence indicators to solve large -scale problems.

This discipline introduces undergraduate students to cellular engineering, a field that addresses the problems associated with understanding and managing the interconnected functions of cell structure. The course is a bridge between biologists and engineers covering the following topics: Basic cell biology and processes, Mechanics of cells and subcellular elements, flow, hydrostatic pressure, tension, torsion, bending and combined loads, Enzyme kinetics, Metabolic pathway engineering.

This course will introduce students to classical test theory (CTT) and models of Item response theory (IRT) commonly used for the analysis of dichotomous and polytomous test data. Although most of the course will be applied, some technical details will be provided to facilitate understanding of IRT and emphasizing its advantages over CTT. By the end of the course, the student should understand the following: differences between IRT models for dichotomous and polytomic scoring items; mathematical and theoretical assumptions underlying IRT; difference in latent feature scores and standard measurement error between IRT and CTT; performing IRT analyzes with IRTPro.

This course is intended to cover the basics of tissue engineering, the latest therapeutic approach for the treatment of degenerated or damaged tissues/organs. Themes in this course will include mathematical models and fabric engineering strategies, such as the design, manufacture and use of biomaterials; cell engineering, including cell therapy, drug delivery; as well as cellular biomaterial interactions. The latest achievements and the main problems related to fabric engineering will also be presented and discussed.

The course describes the use of the concept of personal features of the “big five”, taken from psychology and including five wide areas that describe the personality. These five personality traits are used to understand and model the relationship between personality and various behavior. It is assumed that these five factors represent the main structure underlying all personality traits. These five factors were defined and described by several different researchers during several periods of research. This course is focused on the methods of predicting public opinion based on modeling using personal features

The course “Introduction to Chemical Engineering” includes work on material and energy balance, thermodynamics, development of reactions, heat and mass exchange, separation processes, chemical process management, process safety and installation design.

The course contains mathematical models in the biology of the population, in biological areas, including demography, ecology, epidemiology, evolution and genetics. Mathematical approaches include methods in areas such as combinatorics, differential equations, dynamic systems, linear algebra, probability and stochastic processes.

In this course student learns to implement agents based on Deep Reinforcement Learning, a type of machine learning where an agent learns to behaves in the environment by performing an action and acquiring responce. Students create agents using Tensorflow and Pytorch to learn on their own in simple games. By exploring this methods students will enter agents based on deep reinforcement learning in applied areas.

This course discusses the principles and problems in the field of psychometry, the industry of psychology related to the quantitative assessment and measurement of mental attributes, behavior and performance, as well as with the design, analysis and improvement of tests used in such dimensions.

This discipline introduces undergraduate students to cellular engineering, a field that addresses the problems associated with understanding and managing the interconnected functions of cell structure. The course is a bridge between biologists and engineers covering the following topics: Basic cell biology and processes, Mechanics of cells and subcellular elements, flow, hydrostatic pressure, tension, torsion, bending and combined loads, Enzyme kinetics, Metabolic pathway engineering.

The course is aimed at studying computerized adaptive testing (CAT), based on the principle that additional information can be obtained when the test adapts to the level of the tested person, which avoids situations when the question is asked, the answer to which is known or understandable in advance. Computational and statistical methods from the theory of an elemental response (IRT) and the theory of decision -making are combined for the implementation of the test, which can behave interactively during the testing process, and adapts to the knowledge and level of the tested person.

The course tells about the methods of analysis of molecular evolution, such as the evolutionary structure of trees, methods from computing proteomics, and as they have proved such evolutionary statements as the origin of birds from dinosaurs and finding the region of the origin of the human species.