Natural science (STEM) module
ITPP1301
Information Technology for professional purposes
3 сredits/
Pre: no
1+0+2
Course objective: To provide a modern understanding of the
processes of transformation of the information in
information Society
Course Objectives: The ability to apply recent advances in
computer technology and software for the task. Knowledge of
methods of mathematical
modeling in the analysis of global issues on the basis of
knowledge of fundamental mathematics and computer science
disciplines. The objectives of the discipline is the study of
technology efficient processing of various kinds of information
through computer technology, human interaction with the
Knowledge about the structure of a computer, a basic
knowledge
of
modern
information
and
communication technology for the collection,
processing and reporting, knowledge of methods and
data
Ability to work in the operating system Windows;
ability to use modern information and communication
technologies for the collection, processing and
analysis of information, the ability to use and handle
complex documents using Microsoft Office;
Possession of the main methods of data collection and
manufacturing equipment and related software.
The ultimate goal of the discipline is to develop future
professionals of the basic theoretical knowledge and practical
skills on a PC with packages of applied programs of general
importance for the application in their professional activity and
a better mastery of knowledge of general and special subjects.
processing, modern computer and information
technology, with a working knowledge of common
software tools and professional use, possession of
basic
programming
methods
of
information
protection when working with computer systems and
organizational measures and techniques of anti-virus
protection.
TPQM2302
Theoretical Physics. Quantum Mechanics
3 сredits/
Pre: no
2+1+0
Theoretical physics - the branch of physics, which as a primary
way of knowing the nature of the creation of mathematical
models used
phenomena and their comparison with reality. Quantum
mechanics - the branch of theoretical physics that describes the
physical phenomena in which the effect is comparable in
magnitude to the Planck constant basic concepts of quantum
kinematics concepts are observed and
state. This discipline aims to study the students the basic laws
of theoretical physics and quantum mechanics and the
development of future professional skills to scientific
generalizations and conclusions.
Knowledge of the mathematical models used in
theoretical physics, knowledge of basic concepts,
theorems,
theoretical
physics
and
quantum
mechanics, knowledge of methods for solving
problems in theoretical physics and quantum
mechanics. The ability to select appropriate
mathematical model to describe the mechanical
processes, the ability to use appropriate techniques to
solve problems in theoretical physics, the ability to
analyze the results from the point of view of physics.
Possession of skills in solving problems in theoretical
physics and quantum mechanics analysis of the
results.
FK3303
Physical Kinetics
3 сredits/
Pre: no
2+1+0
The aim of the course study of the microscopic theory of the
processes in nonequilibrium media. In the kinetics of the
methods of quantum or classical statistical physics studying the
transport processes of energy, momentum, charge and matter
in a variety of physical systems (gas, plasma, liquids, solids)
and the influence of external fields. Physical Kinetics provides
a balance equation for the average density of mass, momentum
and energy.
Knowledge of the theory of physical kinetics, the
main methods of physical kinetics.
The ability to get the balance equation for the average
density of mass, momentum and energy.
Skills in solving problems of physical kinetics and
analysis of the results.
Ther4304
Thermodynamics
3 сredits/
Pre: no
2+1+0
Course objective: the study of the ratio and the conversion of
heat and other forms of energy, the study of the basic concepts
of thermodynamics, the study of methods for solving problems
of thermodynamics.
Thermodynamics can be applied in a wide range of issues in
the field of science and technology, such as engines, phase
transitions, chemical reactions, transport phenomena, and even
black holes. Thermodynamics is essential for other fields of
physics and chemistry, chemical engineering, aerospace
engineering, mechanical engineering, cell biology, biomedical
engineering, materials science, and it is useful in other areas
such as the economy.
Knowledge of the mathematical models used in
thermodynamics, knowledge of the basic concepts of
thermodynamics, knowledge of methods for solving
problems of thermodynamics. The ability to select
appropriate mathematical models, the ability to apply
appropriate methods for solving problems of
thermodynamics, the ability to analyze the results
from the point of view of physics. Be skilled in
problem solving and thermodynamics analysis of the
results.
Basic vocational modules
Module-1. Mathematical analysis
MA1301
Mathematical analysis – I
4 credits/
Pre: no
2+2+0
Objective: To introduce the basic ideas and methods of
mathematical analysis.
Objectives: The objectives of the course in mathematical
analysis included the development of students' logical thinking
and mathematical culture needed to explore other mathematical
subjects.
Knowledge of theoretical material and thus be able to
choose their method of solving problems. Ability to
work independently with the literature, the ability to
work as a group together to discuss the challenges
and be able to explain to their fellow students
understood the material, the ability of students to
apply their knowledge in practice, the development of
creative thinking. Possession of scientific and
mathematical terminology, equally know different
areas of mathematics.
MA1302
Mathematical analysis – II
4 credits/
Pre: no
2+2+0
Objective: To study the functions and their generalizations
methods
differential and integral calculus.
Objectives of the course Mathematical Analysis II is the
development of students' knowledge of differential and integral
equations and methods of solving them.
Knowledge of theoretical material and thus be able to
choose their method of solving problems. Ability to
work independently with the literature, the ability to
work as a group together to discuss the challenges
and be able to explain to their fellow students
understood the material, the ability of students to
apply their knowledge in practice, the development of
creative thinking. Possession of scientific and
mathematical terminology, equally know different
areas of mathematics.
MA2303
Mathematical analysis – III
3 credits/
Pre: no
2+1+0
Objective: To study the differential
and integral calculus, theory
series (functional, power and Fourier transform) and multi-
dimensional integrals.
Objectives of the course Mathematical Analysis III is to
develop the students to apply their knowledge in practice, the
development of creative thinking
Knowledge of theoretical material and thus be able to
choose their method of solving problems. Ability to
work independently with the literature, the ability to
work as a group together to discuss the challenges
and be able to explain to their fellow students
understood the material, the ability of students to
apply their knowledge in practice, the development of
creative thinking. Possession of scientific and
mathematical terminology, equally know different
areas of mathematics.
Module-2. Algebra and Geometry
AGLA1301
Analytical geometry and linear algebra 1
3 credits/
Pre: no
2+1+0
The purpose of teaching the course - to help students basic
mathematical skills of professionally significant and notions of
analytic geometry and linear algebra methods for solving
systems of linear algebraic equations.
Objectives: The main objective of the course - the study of the
foundations of analytical geometry and linear algebra. It also
discusses methods for solving systems of linear algebraic
equations. The development of the logical and algorithmic
thinking, the formation of independent cognitive activity of
students, the ability to learn throughout life, the mastery of
basic algorithms of numerical methods of analytic geometry
and simple implementations
Knowledge of the theory of limits, integration,
differentiation, knowledge base of the course of
higher mathematics. The ability to calculate a system
of linear algebraic equations, the ability to find the
determinants of the second, third, and large orders,
ability to find solutions of matrix equations, the
ability to use mathematical tools for the study of real
processes and phenomena. Possession of ways of
calculating the definition; knowledge of methods for
solving systems of linear algebraic equations, the
basic theory of matrices, possession of basic
concepts, methods, and algorithms of analytical
geometry.
AGLA1302
Analytical geometry and linear algebra 2
3 credits/
Pre: no
2+1+0
The purpose of teaching the course, study the set of solutions
of equations defined by polynomials.
Objectives: The main objective of the course - the study of the
foundations of analytical geometry and linear algebra. Also,
the notion of affine variety, about the theory of Abelian
integrals, which were obtained remarkable results on algebraic
curves and having a purely geometric meaning.
Knowledge of the theory of limits, integration,
differentiation, knowledge base of the course of
higher mathematics. The ability to calculate a system
of linear algebraic equations, the ability to find the
determinants of the second, third, and large orders,
ability to find solutions of matrix equations, the
ability to use mathematical tools for the study of real
processes and phenomena. Possession of ways of
calculating the definition; knowledge of methods for
solving systems of linear algebraic equations, the
basic theory of matrices, possession of basic
concepts, methods, and algorithms of analytical
geometry.
DGTA2303
Differential Geometry and tensor analysis
2 credits/
Pre: AGLA 1302, AGLA 1304
1+1+0
Course content: The theory of curves and surfaces in Euclidean
space. The curvature, torsion, Frenet formulas. The first and
second quadratic
forms
of the
surface, Meunier's
theorem. Curvature
of
the
surfaces. Bonnet theorem on
thecongruence of the surfaces. The derivation formulas, the
Christoffel symbols.Intrinsic geometry of surfaces. Geodesic
curvature, the geodesic line. Euler-Lagrange equations and
extremal properties of geodesics. Gauss-Bonnet formula.
-basic knowledge of probability theory and
mathematical statistics in the framework of finite-
dimensional
random
variables
without
strict
application of the measure theory and functional
analysis.
-the ability to solve problems in the theory of
probability and statistics using basic formulas of these
disciplines;
work as a group together to solve tasks related to TV
and MC; should develop probabilistic and statistical
thinking and the ability to cope with the tasks of the
probabilistic nature;
must learn to circulate freely with concepts such as
probability and its evaluation, the random variable, its
characteristics and their evaluation, point and interval
estimation.
Module-3. Differential equations control theory
PTMS2301
Probability Theory and Mathematical statistics
3 credits/
Pre: AGLA 1304, MA 1301, MA 1303
2+1+0
The purpose of discipline is to present basic information about
the construction and analysis of mathematical models that take
into account random factors. The main objective is to
familiarize students with the basics of probability theory and
mathematical statistics in the framework of finite-dimensional
random variables without the strict application of measure
theory and functional analysis. For a basis of a theory of
probability accepted universally recognized system of axioms
of AN Kolmogorov. Particular attention is drawn to the fact
that students have learned well the fundamental concepts of
probability theory, and mastered the main methods of
formulating and solving problems in mathematical statistics.
-basic knowledge of probability theory and
mathematical statistics in the framework of finite-
dimensional
random
variables
without
strict
application of the measure theory and functional
analysis.
-the ability to solve problems in the theory of
probability and statistics using basic formulas of these
disciplines;
work as a group together to solve tasks related to TV
and MC; should develop probabilistic and statistical
thinking and the ability to cope with the tasks of the
probabilistic nature;
must learn to circulate freely with concepts such as
probability and its evaluation, the random variable, its
characteristics and their evaluation, point and interval
estimation.
DE2302
Differential equations
3 credits/
Pre: MA 1301, MA 1303
2+1+0
The ability to plan changes to improve systems and develop
new systems, the possession of skills time management, ability
to work independently, possess basic computer skills, possess
the basic search techniques, data collection, preparation,
processing and analysis of information used in professional
activities with the help of modern computer technology.
Knowledge of the general theoretical and experimental
principles and methods of mathematics and a wide range of
knowledge in all areas of mathematics, knowledge of the
mathematical methods and their applications, knowledge of
electronics, computer programming and numerical methods in
the application of mathematics, knowledge of the basic
concepts of calculus, differential equations
Knowledge of the basic concepts of mathematical
analysis, the theory of limits, continuity functions,
differential calculus, the theory of integrals, definite
integrals and their applications, approximate methods
of calculating the roots of equations and definite
integrals, the theory of functions of several variables,
implicit functions, multiple integrals, curvilinear and
surface integrals. the ability to solve mathematical
problems in a different context, and the ability to
establish relationships between the problems and the
basic principles, knowledge of the general theory of
functions of several variables, the theory of multiple
integrals, the theory of curvilinear and surface
integrals, the possession of skills in solving problems
in this area of mathematics.
MPE2303
Mathematical Physics Equations
3 credits/
Pre: MA 1301, MA 1303, DU 2307
2+1+0
Course objective: the study of the basic concepts of
mathematical physics equations and partial differential
equations of the first order, the study of linear equations of
mathematical physics and nonlinear equations of mathematical
physics.
know the basic mathematical concepts involved in the
program, their interrelation, interdependence and
interaction not only between themselves but also with
other mathematical disciplines.
be able to accurately and thoroughly substantiate the
reasoning without cluttering it with unnecessary
details.
acquire practical skills to solve problems in order to
mathematically correct to put a specific practice the
simplest problem, select a method to solve it and
solve it.
COM3304
Computations and Optimisation Methods
2 credits/
Pre: AGLA 1302, AGLA 1304, MA 1301, MA
1303
1+1+0
The course includes a mandatory minimum corresponding to
the fundamental program of the course "Calculus of variations
and optimization techniques" approved by the Ministry of
Education of the RK. A large number of tasks for individual
work, and options typical control tasks. For graduate students
and part-time office daily mathematics departments of
universities, as well as for undergraduates, postgraduates,
researchers and students FPK studying additional chapters to
the theory of extreme problems.
knowledge of practical skills in solving problems of
mathematical analysis in order to mathematically
correct to put a simple practice a specific task, select
the mathematical apparatus and method for its
solution, to resolve it, to work with the special
literature on the main areas of mathematical analysis.
-the ability to acquire practical skills and theoretical
foundations of the laws of the construction and
operation of the systems, the methodological
principles of analysis and synthesis, modern
mathematical approaches to the solution of practical
problems of analysis, design and management of
complex socio-economic systems.
Module-4. Mechanics
TM2301
Theoretical Mechanics
3 credits/
Pre: AGLA 1302, AGLA 1304, DU 2307
2+1+0
This discipline aims to study the students the basic laws of
nature, the acquisition of skills of mathematical models
occurring in nature and engineering processes and their
analysis using the methods and tools of modern mathematics,
the development of future professional skills to scientific
generalizations and conclusions.
The objects of study of this discipline are the physical laws of
nature, mathematical models of material bodies, the basic
methods and techniques of solving problems in mechanics.
Knowledge of the mathematical models used in
theoretical mechanics, knowledge of the basic
concepts and theorems of theoretical mechanics,
knowledge of methods for solving problems in
theoretical mechanics. Be able to: select appropriate
mathematical model to describe the mechanical
processes to apply appropriate techniques to solve
problems in theoretical mechanics and analyze the
results obtained from the mechanical point of view;
Have skills: solving problems in theoretical
mechanics analysis of the results.
CM3302
Continuum Mechanics
3 credits/
Pre: AGLA 1302, AGLA 1304, DU 2307
2+1+0
In continuum mechanics with and based on the methods and
data developed in theoretical mechanics, motion of material
bodies, which fill the space of continuous, continuous manner,
and the distance between the points in which the movement is
changing.
This course is a theoretical course of continuum mechanics,
which would address the mathematical methods of studying
the motion of deformable media.
Know: mathematical models used in continuum
mechanics;
the basic concepts and theorems of continuum
mechanics, methods of solving problems;
Be able to: select appropriate mathematical model to
describe the
mechanical
processes
to
apply
appropriate techniques to solve problems of
continuum mechanics and analyze the results
obtained from the mechanical point of view;
Have skills: problem solving continuum mechanics,
analysis of the results.
Module-5. Computational Mathematics
NM2301
Numerical methods– 1
3 credits/
Pre: AGLA 1302, AGLA 1304, DU 2307
2+0+1
The mathematical study of the processes of the surrounding
world is reduced to the analysis of mathematical models of
these processes. The vast majority of mathematical models
encountered in practice, is so complex that finding their
explicit (analytical) solution is not possible. In these conditions
may be possible to approximate the solution of these problems,
which is associated with the approximation of the problem.
However, it must be convinced that the solution of the
approximation problem is in some sense close to the unknown
solution of the original problem, which requires study the
convergence of the approximation method.
Knowledge of the basic problems of algebra and
analysis of the theory of ordinary differential
equations. Ability to apply the methods of
computational mathematics for the numerical solution
of problems of algebra and analysis of the theory of
ordinary differential equations.
Skills in the numerical solution of the problem,
programming and construction of algorithms, study
the correctness of the tasks of comparative numerical
analysis, mathematical modeling tasks, personal and
problem-based learning various topics of the course
as part of seasonal schools, special seminars,
conferences and student clubs.
NM2302
Numerical methods – 2
3 credits/
Pre: AGLA 1302, AGLA 1304, DU 2307
2+0+1
In the course detail and strict enough described the modern
methods for solving applied problems of optimal control.
Covered substantially all of the major models of problems of
optimization, including deterministic, game and stochastic.
There given many new results in the theory of optimal control
(necessary optimality conditions for some classes of
degenerate problems, the optimal filtering for systems with
correlated noise, etc.). Considerable attention is given to
various numerical methods for solving optimal control and
issues of implementation numerical algorithms. Exposition of
the theory is accompanied by a large number of detail worked
examples solutions of various applied problems, including the
optimal control problems of aircraft.
Know the basic problems of mathematical physics
and the concept of difference schemes.
To be able to apply the methods of computational
mathematics for the numerical solution of problems
for differential equations of mathematical physics.
Be skilled in the numerical solution of the problem,
programming and construction of algorithms, study
the correctness of the tasks of comparative numerical
analysis, mathematical modeling of problems, the
study correctness of difference problems, personal
and problem-based learning various topics of the
course as part of seasonal schools, special seminars,
conferences and student clubs .
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