Mathematical & Computational Science

Mathematical & Computational Science

6B06106

The educational program “Mathematical & Computational Science” is aimed at training specialists in the fields of mathematical modeling and understanding of processes in such areas as physics, chemistry, biology, social sciences, highly qualified applied methods based on computational technologies. The educational program trains qualified specialists in the following paths: computational engineering – the use of computational mathematics methods in physical and chemical processes in production; bioengineering – the use of methods of computational sciences and data analysis in biology and genetics; and social engineering – the use of mathematical modeling techniques and big data analysis in social networks to analyze social phenomena.

Profile subjects

Mathematics, Informatics

Career opportunities

IT developer
Data scientist
Researcher
Computer engineer
Influencer
Social media analyst

The goal of the EP

The goal of the Mathematical & Computational Science program is to intensively train students in theoretical and practical aspects in the fields of mathematical modeling and computational sciences in the areas of computational engineering, bioengineering or social engineering, as well as to improve their skills in related fields such as mathematics, programming and big data analysis. Upon completion of the program, students will be qualified to work as computation engineers, developers, data analysts in many sectors, including manufacturing, daily life, healthcare, and so on, as well as researchers in research institutes.

Objectives of the EP

Providing highly qualified specialists in the fields of mathematical, computer modeling and computational sciences to private and public companies, as well as research institutes.
Providing students with a wide range of competencies in the fields of mathematical, computer modeling and computational sciences, based on the results of the educational program, necessary to start working as an analyst, developer, junior researcher in IT companies of various sizes and research institutes.
Development in students of flexible (soft) qualities required for the development of leadership and patriotic sides in them, necessary for shaping them as successful and purposeful leaders in their industry.

Requirements for evaluating the learning outcomes of the educational program

The student, after mastering the entire educational program, should be able to perform the following points:

Formulate and solve problems arising during production activities that require in-depth professional knowledge. To formulate the problem, both mathematical apparatus and computer tools can be used;
Choose the necessary approaches and methods for analyzing problems, as well as modify existing ones and develop new ones, depending on the tasks of a particular case;
Apply psychological methods and means to improve the efficiency and quality of education in the learning process;
Know a foreign (English) language at a professional level, allowing students to conduct scientific research at a qualitatively high level and to teach special disciplines in universities;
Model and design complex systems using mathematical and computer models and computational methods;
Apply quantitative and qualitative methods and techniques to collect primary information for research, as well as develop effective solutions to problems;
Analyze and design software tools for mathematical, computer modeling, as well as algorithms, models and methods required for the development of computing systems, effective data analysis, modeling of physical, biological and social processes;
Manage a team of IT specialists in the process of implementing and deploying software systems, as well as models and methods for data analysis, mathematical modeling and computational experiments;
Choose standards, methods, technologies, tools and technical means for carrying out work on further maintenance of software systems;

The list of competencies and the results of the educational program

List of competencies of the educational program

CC1. The ability to understand the driving forces and patterns of the historical process, the place of man in the historical process and the ability to understand philosophy as a methodology of human activity, readiness for self-knowledge, self-activity, the development of cultural wealth as a factor in the harmonization of personal and interpersonal relationships
CC2. The ability to form and develop skills and competencies in the field of organization, planning and production management, the ability to apply the acquired knowledge to comprehend the environmental reality, the ability to generalize, analyze, predict when setting goals in the professional field and choose ways to achieve them using scientific research methodology
CC3. Ability for written and oral communication in the state language and the language of interethnic communication, as well as in a foreign (English) language. The ability to use foreign sources of information, to have communication skills, for public speaking, argumentation, discussion and polemics in a foreign language
CC4. The ability to be competent in choosing ICT methods and mathematical modeling for solving specific engineering problems, the ability to be ready to identify the natural scientific essence of problems that arise in the course of professional activity, and the ability to involve the appropriate mathematical apparatus to solve it
PC1. The ability to understand modern standards, regulatory framework, the basics of industrial knowledge, scientific ideas about project management and technological entrepreneurship.
PC2. The ability to professionally operate using modern computer equipment, network components, computer programs and complex computing systems (in accordance with the objectives of the program), as well as to follow the rules of safety, industrial sanitation, fire safety and labor protection standards.
PC3. The ability to formulate and use algorithms, data structures and modern analytical methods for the development and further maintenance of various software computing systems.
PC4. The ability to develop software for an information system based on modern development tools, ready-made modules, frameworks and libraries.
PC5. The ability to design the architecture of information system components, including the human-machine interface of hardware and software systems, to choose operating systems and information security methods.
PC6. The ability to develop and implement secure and testable solutions based on new methods and technologies of information security used when working with information and communication technologies.
PC7. The ability to use the basic provisions and methods for solving managerial problems, the ability to carry out project documentation in a software environment using computer graphics for various types of projects.
PC8. The ability to formulate and prove fundamental laws and theorems in the areas of mathematical modeling and computational sciences, conduct computational experiments, analyze and discuss the results of computational experiments.
PC9. The ability to competently choose the methods of mathematical modeling and to analyze of the convergence and stability of models for simulating and predicting the course of real processes in the relevant industry.
PC10. Ability to collect, process and analyze data, using the methodological and technological infrastructure existing in the organization and / or the target industry.
PC11. The ability to implement high-performance computing algorithms based on large-scale computing systems to solve real industrial problems.
PC12. The ability to theoretical and experimental research in the field of computational science methodology, such as high-order approximation techniques, modification of computational grids, etc.
PC13. The ability to select and implement numerical algorithms and computational methods for conducting computational experiments, building simulators and predicting the flow of processes from the relevant industry.
PC14. The ability to select and implement machine learning methods and artificial intelligence algorithms to predict the results of processes in various target industries.

Learning outcomes

LO1. To be able to think critically and analyze assigned tasks, possessing general flexible skills in the preparation and presentation of results and documents, knowledge of languages and social interactions to ensure fruitful work, both individually and in teams.
LO2. To be able to carry out all stages of the development of information systems and software at different scales to prepare parts or entire software products.
LO3. To formulate and prove fundamental laws and theorems in the fields of mathematical modeling and computational sciences, analyze and discuss the results of computational experiments for scientific research.
LO4. To know and select mathematical models and analyze them for convergence and stability in order to predict the course of real processes in the relevant industry.
LO5. To formulate and modify the methods of computational sciences in order to optimize, solve new problems, adapt algorithms to new computing platforms.
LO6. To be able to collect, process and analyze data, using the methods of mathematical statistics, data science and machine learning to make forecasts and prepare managerial and operational recommendations.
LO7. To apply high-performance computing algorithms based on embedded, medium- and large-scale computing systems to solve real industrial production problems.
LO8. To develop numerical algorithms and select computational methods for conducting computational experiments and predicting the flow of processes from the relevant industry.

Assessment of learning outcomes

№	Exam form	Recommended share, %
1	Computer testing	20
2	Writing	10
3	Oral	5
4	Project	30
5	Practical	30
6	Complex	5

Course Curriculum

The cycle of general education disciplines

Mandatory component

Modern history of Kazakhstan

The course considers the modern history of Kazakhstan, how part of the history of mankind, the history of Eurasia and Central Asia. The modern history of Kazakhstan is a period in which a holistic study of historical events, phenomena, facts, processes is carried out, the identification of historical patterns that took place on the territory of the Great Steppe in the twentieth century and to this day.

Philosophy

The course involves the study of the discipline of philosophy as a special form of spiritual studies in its cultural and historical development and modern sound. The main directions and problems of world and national philosophy are studied. Philosophy is a special form of cognition of the world, creating a system of cognition of the general principles and foundations of human life, about the essential characteristics of a person’s relationship to nature, society and spiritual life, in all its main direction.

Foreign Language (English)

The course includes an intensive English language study program focused on grammar and speaking skills. The course includes topics that reflect the latest advances in information technology, and a terminological dictionary makes them directly relevant to the needs of students.

Kazakh (Russian) language

The course occupies a special place in the system of training bachelors with an engineering education. For students of a technical university, the study of professional Kazakh / Russian languages is not only an improvement of the skills acquired in the school, but also a means of mastering the future specialty.

Information and Communication Technologies (in English)

The course includes the study of modern information technologies, including methods and means of communication of people in ordinary and professional activities using information technology. Technology data is studied in relation to the search, collection, storage, processing and dissemination of information.

Module of social-political education: Political science

The course is devoted to general political knowledge for specialties in the field of information technology. The course includes political self-awareness, improving one’s political outlook and communicative competencies. Teaching political knowledge is communicative, interactive, student-oriented, result-oriented, and largely depends on the independent work of students.

Module of social-political education: Sociology

The course includes knowledge of sociological subject areas, research methods and directions. The course will discuss in detail the basic sociological theories and the most effective ways of gaining deep knowledge about various aspects of our modern society. The special significance of this course for students is the opportunity to develop a sociological imagination, to understand the basic concepts of sociology as a science.

Module of social-political education: Psychology

The course presents questions of psychology in a wide educational and social context. The knowledge and skills acquired and formed as a result of mastering the course content give students the opportunity to put them into practice in various areas of life: personal, family, professional, business, social, in working with people from different social groups and age groups.

Module of social-political education: Cultural studies

The course will help to become the basis for studying the whole complex of social and human sciences, as well as an addition to general courses in history and philosophy. The course includes topics such as morphology, semiotics, anatomy of culture; the culture of the nomads of Kazakhstan, the cultural heritage of the proto-Turks, the medieval culture of Central Asia, the formation of the Kazakh culture, the Kazakh culture in the context of globalization, the cultural policy of Kazakhstan, etc.

Physical Culture

The course is devoted to the formation of physical culture of a person and the ability to use various means of physical culture in a targeted way to preserve and health promotion.

The cycle of general education disciplines

University component

Academic writing

The purpose of the course “Academic Writing” is the formation professional competence and expansion of communicative competencies related to analytical textual activity; the formation of students’ skills of linguistic and pragmatic
thinking, the ability to analyze the expressive units of the language and competently select the desired unit depending on the goals and conditions communications.

Cycle of profiling disciplines

University component

Professional English

The course includes an intensive, more advanced program of studying academic and applied (information technology) English, focused on professional speaking skills and understanding of common terminology. The course includes topics reflecting the latest developments in information technology, and the terminological vocabulary makes them directly relevant to the needs of students.

Ordinary Differential Equations

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve these equations and interpret the solutions. This course focuses on ordinary differential equations and their applications in science and engineering: Simulation of a simple physical system to obtain a first order differential equation. Plausibility check of the solution of a differential equation (DE) that models a physical situation.

Partial Differential Equations

Partial differential equations in science and technology. Topics include problems with initial and boundary conditions for parabolic, hyperbolic and second order elliptic equations. Emphasis is placed on separation of variables, special functions, transformation methods, and numerical methods. The student will gain a strong intuitive understanding of the concept of a partial differential equation and its relationship to the description of physical phenomena such as diffusion and wave propagation. Students will gain a deeper understanding of Fourier series by mastering the theory problems with boundary conditions.

Introduction to Machine Learning

The course introduces students to the main (basic) machine learning algorithms, as well as the application of these algorithms to solve real production problems. Also during the course will be partially considered data mining and pattern recognition. The course is built using the Python programming language and its core libraries.

Numerical Methods

To investigate complex systems, physicists, engineers, financiers, and mathematicians require computational methods because mathematical models are rarely resolved algebraically. Numerical methods based on computational mathematics are the main algorithms underlying computer predictions in modern systems science. Main topics: mathematical and computational foundations of numerical approximation and solving scientific problems; Simple optimization; vectorization; clustering; Polynomial and spline interpolation; integration and differentiation; solution of large-scale systems of linear and non-linear equations; modeling.

Numerical Methods for Differential Equations

This course contains numerical methods for partial differential equations, with an emphasis on a rigorous mathematical foundation. Many modern and effective approaches are presented after the establishment of the main approximation. Emphasis is placed on a qualitative understanding of the PDE under consideration, the fundamentals of finite differences, finite volume, finite elements and spectral methods, as well as important concepts such as stability, convergence and error analysis.

Problems: heat equation, wave equation, problems with convection diffusion, Poisson equation, Navier-Stokes equations. Concepts: consistency, stability, convergence, weak equivalence theorem, error analysis, Fourier approaches. Methods: finite differences, finite volumes, finite elements, spectral methods, projection.

Industrial practice

Industrial practice of students

Undergraduate practice

Undergraduate practice of students

Cycle of profiling disciplines

Component by choice

Introduction to Optimization Theory

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 to efficiently solve wide classes of optimization problems. The focus of the course will be on achieving provable convergence rates for solving large-scale problems.

Computational Fluid Mechanics

Computational fluid dynamics is an important tool for studying fluid flow problems in industry and academia. The dynamics of fundamental laws of fluid flow, partial differential equations, linear algebra and programming language will be studied. The main goal of this course is to get a solid foundation of numerical methods for convection diffusion problems. The emphasis is on physical processes and the underlying mathematics. The control volume method is taught, which is a robust physically intuitive numerical approach widely used in both industry and academia.

Cellular Engineering

Cell engineering is an emerging field that addresses the challenges of understanding and manipulating the interconnected functions of cell structure. This course is a bridge between biologists and engineers to understand the quantitative aspects of cellular biology. Cellular engineering is inherently related to the new field of tissue engineering. In the development of new tissues, which have always been considered too difficult to intervene, the use of cells plays a central role. In numerous medical applications, we want tissues to regenerate. We of10 try to use biodegradable scaffolds that are modified accordingly and can be loaded with osteoblasts. Central to these approaches is our use of cells and our understanding of their interaction with biomaterials. It’s important to understand

Fundamentals of Molecular Evolution

The course talks about methods for analyzing molecular evolution, such as the evolutionary construction of trees, methods from computational proteomics, and how evolutionary claims such as the origin of birds from dinosaurs and finding the region of origin of the human species were proved on their basis.

Tissue Engineering

This course is designed to cover the fundamentals of tissue engineering, the latest therapeutic approach for the treatment of degenerated or damaged tissues/organs. Topics in this course will include mathematical models and tissue engineering strategies such as the design, fabrication and use of biomaterials; cell engineering, including cell therapy, drug delivery; as well as cellular biomaterial interactions. Recent advances and major issues related to tissue engineering will also be presented and discussed.

Item Response Theory

Item response theory (IRT), also known as latent response theory, refers to a family of mathematical models that attempt to explain the relationship between latent features (an unobservable characteristic or attribute) and their manifestations (i.e., observed outcomes, responses, or performance) . They establish a relationship between the properties of the elements on the instrument, the persons responding to those elements, and the underlying feature being measured. IRT assumes that the latent construct (eg, stress, knowledge, attitude) and measure elements are organized on an unobservable continuum. Hence, its main purpose focuses on establishing the position of the individual on this continuum.

Computerized Adaptive Testing

Computerized Adaptive Testing (CAT) is based on the principle that additional information can be obtained when a test is adapted to the level of the person being tested, thus avoiding situations where a question is asked, the answer to which is known or understood in advance. Computational and statistical methods from Elemental Response Theory (IRT) and Decision Theory are combined to implement a test that can behave interactively throughout the testing process and adapts to the knowledge and level of the person being tested.

Modeling Personality Traits

The concept of the Big Five personality traits is taken from psychology and includes five broad areas that describe personality. These five personality traits are used to understand the relationship between personality and various behaviors. These five factors are supposed to represent the basic structure underlying all personality traits. These five factors have been identified and described by several different researchers over several research periods. This course is focused on methods for predicting public opinion based on modeling using personality traits.

Introduction to Chemical Engineering

The course “Introduction to Chemical Engineering” includes work on material and energy balances, thermodynamics, reaction engineering, heat and mass transfer, separation processes, chemical process control, process safety and plant design.

Cycle of basic disciplines

University component

Linear algebra

The course involves the study of the basics of algebra and geometry at the university level and includes the theory of matrices, systems of linear equations, the theory of vectors, analytic geometry, limit and differentiation of functions of one variable

Calculus 1-2

The course introduces students to important branches of calculus and its applications in computer science. During the educational process, students should familiarize themselves with and be able to apply mathematical methods and tools to solve various applied problems. Moreover, they will learn fundamental methods for studying infinitesimal variables using analysis based on the theory of differential and integral calculations.

Discrete Mathematics

The course is a part of mathematics dedicated to the study of discrete objects (here, discrete means consisting of separate or unrelated elements). More generally, discrete mathematics is used whenever objects are counted, when relationships between finite (or countable) sets are studied, and when processes involving a finite number of steps are analyzed. The main reason for the growing importance of discrete mathematics is that information is stored and processed by computers in a discrete manner.

Probability and Statistics

The course is devoted to the probability and statistics of any events, as well as the relationship between mathematics and programming, operating systems within the framework of an interdisciplinary curriculum covering the section of mathematical analysis, modern statistical methods and economic theory.

Calculus 3

Calculus 3 extends methods and ideas from calculus to the case where there is more than one independent or dependent variable. The calculus of many variables is a fundamental tool in many applications of mathematics to science and technology. From a mathematical point of view, multivariate calculus explores methods that are a fundamental prerequisite for advanced topics, including optimization, ordinary and partial differential equations, probability and statistics, differential geometry, and complex analysis.

Calculus 4

This course develops the calculus of real and vector functions of one and several variables. Topics include matrix algebra and line maps; vector functions and their analysis; geometry of Euclidean N-space; functions of several variables and their differentiation; gradients and directional derivatives; private derivative; arc length; vector fields, divergence and bending; Taylor’s theorem for several variables; extremity of real functions in n-space; Lagrange multipliers; several integrals and chain rule; incorrect integrals; linear integrals; surface area; surface integrals; Green’s theorem; Gauss theorem; Stokes’ theorem.

Algorithms and data structures

The course is designed to study algorithms and data structures for solving various applied problems. For this, the program structure, principles of constructing algorithms and programs, methods of solving, algorithmization, and programming are considered.

Introduction to Programming (С++)

The course is designed to study programming, debugging and implementing tasks. During the course aanalyzes the principles of operation of network technologies, gaining access to local and remote network resources,programs using the C++ language.

Object-Oriented Programming (Java)

The course is designed for students to teach them how to write applications using an object-oriented approach in the Java programming language.

Cycle of basic disciplines

Component by choice

Web Technologies

The course teaches students the basics of designing websites and applications using the HTML markup language, planning the style of a website using Cascading Style Sheets (CSS), and using the JavaScript scripting language to perform basic functions.
The course teaches students how to use the PHP programming language to develop functional websites, and also allows you to master the basics of working with the MySQL database, and involves the development of secure server-side client web applications.

Parallelization of Algorithms

In this course, students will learn about parallel algorithms. Emphasis will be placed on algorithms that can be used on parallel shared memory machines, such as multi-core architectures. The course will include both a theoretical component and a programming component. Detailed topics include: modeling the cost of parallel algorithms, bottom links, and parallel algorithms for sorting, plotting, computational geometry, and string operations. The programming language component will include data concurrency, threads, scheduling, synchronization types, transactional memory, and message passing.

Heterogeneous Parallelization

This course introduces concepts, languages, methods, and patterns for programming heterogeneous, massively parallel processors. It covers heterogeneous computing architectures, software programming models, memory bandwidth management techniques, and parallel algorithm patterns using CUDA and OpenCL as an example.

Finite Volume Method

The Finite Volume Method (FVM) is one of the widely used numerical methods in the scientific community and industry. In this approach, differential particle equations, which represent conservation laws to simulate fluid flow, heat transfer, and other related physical phenomena, are converted over differential volumes into discrete algebraic equations over finite volumes (or cells). After that, the system of algebraic equations is solved to calculate the values of the dependent variable for each of the elements to represent the physical processes.

Finite Element Method

The finite element method is an indispensable tool for engineers in all disciplines. This course introduces students to the fundamental theory of the finite element method as a general tool for the numerical solution of differential equations for a wide range of engineering problems. The field problems described by Laplace and the Poisson equations are presented first, and all stages of the MKE formulation are described. The application of the method to elasticity problems develops from fundamental principles. Specific classes of problems are discussed based on abstractions and idealizations of 3D solids such as plane stress and stress. Time dependent problems and time integration schemes are presented. Ad hoc themes are being introduced, such as multiple constraints, mixed compositions, and substructuring.

Fractional Step Methods

This discipline aims to study some approaches of the finite difference method, namely fractional step methods for solving problems with boundary conditions for partial differential equations. Such methods include methods of alternating directions, stabilizing corrections, longitudinal-transverse sweeps, etc. After mastering the discipline, the student should know: basic methods of fractional stages, algorithms for iterative solution of problems with boundary conditions for parabolic and elliptic equations; be able to: solve practical problems using the described methods, investigate the convergence of solutions, etc.

Software Design Patterns

The course involves the study of one of the most important components of object-oriented software development technology – software design patterns. This course is a formalized description of a frequently encountered design problem, its successful solution and recommendations for applying this solution in various situations.

PL/SQL Programming

This course is intended for students to learn the basics of procedural programming using the Oracle PL/SQL programming language and the Oracle database.

Mobile Development (Android)

This course introduces students to programming, design and development technologies related to mobile applications. Topics include access to device capabilities, industry standards, operating systems, and mobile application programming using the OS Software Development Kit (SDK). Upon completion, students should be able to create basic applications for mobile devices.

Research Methods and Tools

The course is designed to study the basic methods and tools required for the introduction of scientific research. The course also introduces students to popular search 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.

Quantitative Analysis

The course is designed to study the basic methods and tools required for the introduction of scientific research. The student will learn to apply the classical approaches of quantitative and qualitative analysis, learn to analyze scientific works and write their own work with a high degree of analytical value. During the course, students will become familiar with the tools of citation, plagiarism and search for the required scientific information.

Database Management Systems

The course includes and involves the study by students of the most popular relational and non-relational database management systems, as well as a set of general or special-purpose software and linguistic tools that manage the creation and use of databases.

Introduction to Data Science

The discipline introduces students to the subject area of data science and develops skills in solving data processing and visualization problems using the Python language. The course covers the basics of interactive work with Python in a Jupyter Notebook, provides the necessary minimum of Python syntax for data processing tasks, and considers basic analytical packages: pandas, matplotlib. The issues of loading data of different formats, data cleaning, exploratory analysis, data visualization are considered.

Introduction to Quantum Computing

It is known that quantum computers will fundamentally change the way we perform calculations, and the implications for many applications (including communications and computer security) will be enormous. This course aims to provide a first introduction to quantum computing. Paradigm shifts between conventional computing and quantum computing will be explored and several basic quantum algorithms will be introduced. The implications of quantum computing on fields such as computer security and machine learning will also be considered.

Deep & Reinforcement Learning

Deep Reinforcement Learning is a type of machine learning where an agent learns how to behave in an environment by performing actions and seeing results. During this course, the student will learn how to implement agents with Tensorflow and Pytorch learning how to play Space Invaders, Minecraft, Starcraft, Sonic the Hedgehog and more! By studying these methods, the student will immerse himself in the implementation of agents based on deep reinforcement learning in applied industries.

Monte Carlo Methods

In this course, students solve the problems of generating random samples from target distributions using transformation methods and Markov chains, optimizing numerical and combinatorial problems (eg the traveling salesman problem) and Bayesian calculations for data analysis.

Stochastic Differential Equations

Stochastic differential equations (SDES) are the evolution of systems that affect randomness. They offer a beautiful and powerful mathematical language, similar to what ordinary differential equations (ODEs) do for deterministic systems. From a simulation standpoint, randomness can be an intrinsic feature of the system, or simply a way of capturing small, complex perturbations that are not explicitly modeled. The CDS has many applications in various disciplines such as biology, physics, chemistry and risk management.

Biostatistics

This course will use case studies to discuss the problems and applications of biostatistics. Topics will include research on survival analysis with applications in clinical trials, evaluation of diagnostic tests, and statistical genetics. The course will conclude with an overview of the areas of current biostatistical research.

Biochemistry & Molecular Biology

Introduction to the main classes of biomolecules and the metabolism of these molecules. This course is designed to provide an introduction to the relationship between food components and components of living organisms. Particular attention is paid to biochemistry in the context of human nutrition. This course is particularly applicable to students wishing to pursue a career in modeling processes in living organisms.

Genetics

This course covers the principles of prokaryotic and eukaryotic cell genetics. Emphasis is placed on the molecular basis of heredity, chromosome structure, Mendelian and non-Mendelian inheritance models, evolution, and biotechnological applications. Upon completion, students should be able to recognize and describe genetic phenomena and demonstrate knowledge of important genetic principles.

Mathematical Population Biology

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

Fuzzy Logic

The course is designed to provide a solid foundation in the fundamental concepts of fuzzy logic and its applications. The course contains work with fuzzy operators, fuzzification, defuzzification, TSK systems, their application in machine learning and fuzzy databases.

Psychometry

This course discusses principles and issues in the field of psychometrics, the branch of psychology concerned with the quantification and measurement of mental attributes, behavior, and performance, and the design, analysis, and improvement of tests used in such measurements.

Decision theory

Decision theory is concerned with methods for determining the optimal course of action when a range of alternatives are available and their consequences cannot be predicted with certainty. This course will use quantitative methods (models) for problem solving and decision making. Theories and models to be mastered include probability theory, utility theory and game theory, linear programming models, non-linear programming models, and integer programming models.

Stochastic processes

Many systems evolve over time with an inherent element of randomness. The goal of this course is to develop and analyze probability models that capture the essential features of the system under study in order to predict the short and long term effects that this randomness will have on the systems under consideration. Training probability models for stochastic processes involves a wide range of mathematical and computational tools.

Cloud computing

This course is intended for the development of software systems and applications where the main emphasis will be placed on the use of cloud solutions where it will show the greatest efficiency. Students will have the opportunity to work with various cloud providers such as Amazon, Google, Microsoft.

Introduction To Big Data Analytics

The course is designed to study the basics of working with big data and the principles of high-performance computing. Big data implies the presence of huge arrays of structured and unstructured information, and the choice of tools for their efficient processing and extraction of useful information.

Computability Theory

The course contains a continuation of mathematical logic and an introduction to the theory of computability, also known as the theory of recursive functions, a section of modern mathematics that lies at the intersection of mathematical logic, the theory of algorithms and computer science, which arose as a result of studying the concepts of computability and non-computability, provability and unprovability.

Chemistry

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
effective solution of practical problems of modeling and calculation of practical problems of chemical and bioengineering production.

Physics

The purpose of the discipline is to form a system of fundamental knowledge among students
physics necessary for the subsequent preparation of a bachelor capable of
effective solution of practical problems of modeling and computing practical problems of physical production and forecasting the results of physical processes.

Mathematical & Computational Science