ИОТ 5 ( Оптимизация и оптимальное управление )
MMKP 3301
Mathematical programming
3 credits / 3 ECTS
Prerequisites: none
2+1+0
Mathematical programming is an area of mathematics,
developing the theory, numerical methods for solving
multidimensional problems with constraints. In contrast to
classical mathematics, mathematical programming deals with
the mathematical methods of the decision of tasks of finding
the
best
options
possible.
The aim of the course is the armament of students in
mathematical apparatus of programming for optimization
problems
in
analysis
and
planning
of
production.
Objectives of the course are: to Form the fundamentals of
knowledge in the field of the theory of algorithms and data
structures, to introduce the mathematical bases of computer
science, master programming in different paradigms and
enclosed in an examination of the following issues.
Upon completion of the course a student must:
- know: the basic aspects of the mathematical
simulation of linear programming, geometrical
interpretation of linear programming problems,
General formulation, the classification of the
problems of mathematical programming, solving the
simplest problems of linear programming graphical
method.
- be able to produce a mathematical model of the
simplest linear programming problems, solve simple
linear programming problem by the method of
graphic.
Theory of automatic control
3 credits / 3 ECTS
Prerequisites: none
2+1+0
The course aims to develop the capacity of analytical research
of economic processes, the ability to build and use models for
the description and forecasting of various economic
phenomena, to carry out their qualitative and quantitative
analysis.
While studying the discipline «Theory of decision-making
discusses the decision-making, linear models, theory of
management, inventory management, Queuing theory, network
models. Theoretical bases of economic and mathematical
methods: elements of convex analysis, convex, non-linear,
linear programming, necessary for production planning and
control, for solution of urgent problems of macromodels of
Economics
–
know:
- the essence of economic-mathematical modelling;
-
linear
optimization
methods;
-
principles
of
dynamic
programming;
be
able
to:
- to formulate and solve the dual linear programming
problem;
- to solve the tasks of dynamic programming;
- build algorithms for solving problems of
mathematical simulation and find their solution using
programming
tools,
spreadsheet,
specialized
mathematical
software.
Theoretical bases of economic and mathematical
methods: elements of convex analysis, convex, non-
linear, linear programming, necessary for production
planning and control, for solution of urgent problems
of macromodels of Economics
TOU 3307
Optimal control theory
3 credits / 3 ECTS
Prerequisites: MANL 1001, MANL 1002, PTHR
2001.
2+1+0
This discipline is the continuation of the course «Methods of
optimization». The course contains methods for optimization
in finite-dimensional spaces, calculus of variations, maximum
principle and dynamic programming in optimal control.
The main goal of the discipline «Optimal control» study:
methods of minimization of functionals defined on sets of
functional spaces.Main sections studied by students in the
discipline: the basics of differential calculus in Banach space,
fundamentals of convex analysis, the gradient of functionals
methods of minimization of functionals in Banach space,
fundamentals of convex analysis, methods of minimization of
functionals in a Hilbert space.
Students who complete the study of this discipline
should:
- have basic knowledge of optimization methods in
Banach
space;
to know methods of solving extremal problems in
functional
spaces;
to be able to apply the methods of minimization of
functionals in a Hilbert space for the solution of
applied science problems; to acquire practical skills
of implementation of numerical methods to minimize
the modern facilities of the computing engineering.
CHRNKZ 3302
General theory of extremal problems
3 credits / 3 ECTS
Prerequisites: none
2+1+0
At present, the demand practices promote the rapid
development of methods of approximate solutions of extremal
problems. The development of computers made it possible to
effective solution of many important application of extremal
problems, which in the past due to its complexity, were
inaccessible.
The aim of the course «Introduction to the theory of extremal
problems» is to familiarise students with the theory of extremal
problems, and the most used in practice methods of
approximate solution of extremal problems. Provides a
theoretical justification for brief overview of these methods.
Discusses methods of minimization of functions of one
variable and the minimization problem for functions of a finite
number
of
variables.
The main task of the course is to form an idea about the
approximate methods of solving extremal problems. To
develop the skills of using these methods in solving practical
tasks.
To know: the basic concepts associated with extreme
tasks; methods of solving optimization problems;
setting and rules for resolution of tasks of the
classical calculus of variations; the setting and the
rules
for
solving
optimal
control.
To apply the classical methods of mathematics for
solving fundamental and applied tasks; communicate
the solution of the optimization problem to almost
acceptable result (should be able to give evidence and
draw conclusions).
ORS 3303
Numerical methods of solving optimal control
problems
3 credits / 3 ECTS
Prerequisites: none
2+1+0
The inclusion of course « Numerical methods of solving
optimal control problems» in the curriculum due to the need to
study the constructive methods, oriented on application of
modern computer equipment, allowing to solve complex
application problems. Application of known results for the
solution of some boundary value problems of controllability
and optimal control, classical boundary value problems with
phase and integral restrictions difficult and unhelpful. Solution
of boundary-value problems with constraints requires different
approaches, one of which is the principle of immersion, which
allows to reduce the initial boundary problem to the particular
task for optimal control with free and right ends of the
–
As a result of studying the course of undergraduate
students should be able to reduce the boundary value
problem with constraints to the optimization tasks
with free and right ends of the trajectories; use known
methods for solving initial optimal control problems
for the answer on the solvability of boundary value
problems and build their solutions; have practical
skills in the implementation of algorithms for solving
boundary value problems, applied to concrete tasks.
trajectories.
The study of a constructive method of solving boundary
problems of controllability, optimal control, as well as the
classical boundary value problems with constraints.
MFO 3304
Optimal control of distributed parameters
3 credits / 3 ECTS
Prerequisites: MA 2201 Методы оптимизации
2+1+0
This discipline is the continuation of the course «Methods of
optimization», studied at the bachelor. This course contains
methods for optimization in finite-dimensional spaces, calculus
of variations, maximum principle and dynamic programming
in
optimal
control.
The main goal of the discipline «Optimal control of distributed
parameters» study: methods of minimization of functionals
defined
on
sets
of
functional
spaces.
Main sections studied masters on the given discipline: the
basics of differential calculus in Banach space, fundamentals
of convex analysis, the gradient of functionals methods of
minimization of functionals in Banach space, fundamentals of
convex analysis, methods of minimization of functionals in a
Hilbert space.
A
student
must:
- have basic knowledge of optimization methods in
Banach
space;
to know methods of solving extremal problems in
functional
spaces;
to be able to apply the methods of minimization of
functionals in a Hilbert space for the solution of
applied
science
problems;
- to acquire the practical skills of implementation of
numerical methods
ChMPKS 3305
The theory of dynamical systems3 credits / 3
ECTS
Prerequisites: none
2+1+0
Mathematical control theory basis for the calculation and
designing of modern control systems of various purpose. In
particular, the problems of optimum management of nuclear
and chemical reactors, optimal control aircrafts, satellites and
space vehicles and others were solved on the basis of the
theory and methods of mathematical control theory.
The purpose of discipline study is to create a numerically -
analytical method of solving boundary problems of optimal
control with constraints focused on application of modern
computer
technology.
A method is proposed to narrow the area of admissible controls
to construct the optimal solution of the initial boundary value
problem of optimal control. Thus, the General scheme of the
paper is as follows: the principle of dive - admissible control is
the
optimal
solution.
The
main
objectives
of
the
course
are:
- presentation of the General solution of the tasks of the
calculus
of
variations
and
optimal
control;
- establishing relations between the methods of the theory of
extremum and different areas of the theories of differential
equations, equations of mathematical physics, theoretical
mechanics, functional analysis; - description of practical
methods
of
solving
extremal
problems.
Objectives: To achieve these goals it is necessary: - studying
The
main
forms
of
bachelor's
competence:
During the development of the course «Theory of
dynamical systems», students need to know:
- basic mathematical concepts included in the
program, their interrelation, interdependence and
mutual influence not only among themselves but also
with
other
mathematical
disciplines.
Bachelor
should
be
able
to:
- accurately and thoroughly justify the reasoning,
without cluttering it with unnecessary details.
Must
possess:
- acquire practical skills in solving the problems of
mathematical analysis to mathematically correctly put
simplest
specific
task
practices,
choose
the
mathematical apparatus and method for solving it,
solve
it;
- work with the special literature on the basic sections
of mathematical analysis.
and development of theoretical material in the context of this
work
programme;
- the decision of the volume of tasks in accordance with the
theoretical material studied; - execution of full volume of the
planned independent work of students on the mentioned
literature sources.
MKE 4306
Research of operations
3 credits / 3 ECTS
Prerequisites: none
2+1+0
Brief course description: operations Research (ISO) is a
science that deals with development and practical application
of methods of optimal control of organizational systems.
The object of ISO is a system of organizational management,
which are characterized by their composition, structure,
relationships and management bodies. The organization
consists of many interacting elements and has its own
structure, divided into subsystems perform a variety of duties,
aimed at achieving common goals of the system.
Organizational components interact with each other and with
the environment. The controls that define the goals of the
operation system, evaluate the quality of its functioning, and
can alter the composition, structure, communication and even
its own management system to achieve its goals (i.e. the
organisation should be adaptive and self-organizing).
The purpose of teaching the course the Aim of this course is
the quantitative substantiation of decisions on management of
organizational
systems.
The difficulties of solving the task of organizational
management determined by the complexity of the systems
studied. In addition, any organizational task always present
human
factors,
which
are
difficult
to
quantify.
Under the operation, we mean the set of actions, measures
aimed at achieving a specific goal (or goals), i.e. almost any
purposeful human action is an operation.
The
main
forms
of
student
competence:
During the development of the course «operations
Research»,
students
need
to
know:
- basic mathematical concepts included in the
program, their interrelation, interdependence and
mutual influence not only among themselves but also
with
other
mathematical
disciplines.
The
student
should
be
able
to:
- accurately and thoroughly justify the reasoning,
without cluttering it with unnecessary details.
Must
possess:
- acquire practical skills in solving the problems of
mathematical analysis to mathematically correctly put
simplest
specific
task
practices,
choose
the
mathematical apparatus and method for solving it,
solve
it;
- work with the special literature on the basic sections
of mathematical analysis.
ChRUNTUF 4307
Constructive methods for solving boundary
value problems
3 credits / 3 ECTS
Prerequisites: none
2+1+0
The course examines the complex constructive methods for
solving boundary value problems, i.e. where there except for
the objective functional and boundary conditions, phase
constraints and integral constraints on the phase coordinates
system, and restrictions on the values of control.
The main task is to define such boundary conditions of the
specified sets and departments of the given functional space
satisfying constraints on control, which will help to achieve the
main objectives of the control when the phase and integral
restrictions.The aim of the course: research of the complex of
constructive methods for solving boundary value problems of
A student must:to have fundamental knowledge in
solving complex constructive methods for solving
boundary value problems of optimal control with
disabilities;-know principle dive information source
constructive methods for solving the boundary
problem to the problem of optimal control with the
free end of the trajectory;-be able to build
minimisation
sequence, estimate their rate of
convergence;-to acquire the practical skills of
implementation of numerical methods to minimize
the modern facilities of the computing engineering.
optimal control, to formulate the conditions of optimality in the
form, proof of convergence andestimation of the rate of
convergence.
CNTT 4001
Game theory
3 credits / 3 ECTS
Prerequisites: MANL 1001,
MANL 1002, PTHR 2001.
2+1+0
«Game theory» explores the economic system and is aimed at
construction of mathematical models. At the same time it is
one of the core courses required for the training of specialists
in the field of applied mathematics, Informatics, Economics.
Aim of the course is to cover the coalition, antagonistic, matrix
games, as well as the main minimax theorems, and the
construction of mathematical models and using well-known
methods in practice.
To know:
- fundamentals of economic-mathematical models of
objects, phenomena and processes;
- mathematical analysis; theory of probability and
mathematical
statistics;
the
fundamentals
of
microeconomics.
be able to:
- apply the methods of mathematical analysis and
modeling, theoretical and experimental studies for the
solution of economic problems;
to own:
- the skills of application of modern mathematical
tools for the solution of economic tasks;
- the methodology of the construction, analysis and
application of mathematical models for assessment
and forecasting of the development of economic
phenomena and processes
PPURD 4309
Differential games
3 credits / 3 ECTS
Prerequisites: none
2+1+0
Many topical application: the optimal organization of the
production, transportation problems, the problem of optimal
accommodation and transport, optimal control of nuclear and
chemical reactors, traffic control of aircraft and satellites,
optimal control of technological processes and others can be
solved by methods of the theory of extremal problems, studied
the
course
"Differential
games".
The main goal of the discipline «Differential games»: to study
modern
methods
of
optimization,
components
of
controllability and optimal control, decision-making methods.
The main tasks of the surveyed students in the discipline: the
calculus of variations, minimization of a function of the
number
of
variables,
convex
programming,
linear
programming, computational methods in optimization, linear
and nonlinear control systems, controllability and observability
of linear systems, theory of choice and decision-making, the
allocation of the many variants of some subsets satisfying
some criteria of optimality.
A
student
must:
a) to have an idea about the main methods of
optimization and methods of decision-making,
systems
of
automatic
control.
b) know: methods for solving extremal problems for
functionals
and
functions,
basic
dynamic
characteristics of the theory of automatic control.
a) be able to produce a mathematical model of
practical extremal problems, use known methods of
decisions
and
conclusions,
g) to acquire practical skills to implement algorithms
for solving extremal problems, for specific tasks.
5B070500 – MATHEMATICAL AND COMPUTER MODELING
Discipline code
Discipline name, quantity of the credits, pre,
distribution by types of occupations
Purpose, mission, summary of the module (course)
Results of trainig (knowledge, abilities, skills)
1
2
3
4
HK1101
History of Kazakhstan
2 credits/
Pre:
1+1+0
POK(R)L1102
Professional-oriented Kazakh (Russian) language
3 credits/
Pre:
0+2+1
POFL1103
Professional-oriented Foreign language
3 credits/
Pre:
0+2+1
PSK2104
The philosophy of scientific knowledge
2 credits/
Pre:
1+1+0
PIC3201
Psychology of Interpersonal Communication
2 credits/
Pre:
1+1+0
TAPS3202
Theoretical and Applied Political Science
2 credits/
Pre:
1+1+0
EPSS3203
Ethics of personal and social success
2 credits/
Pre:
1+1+0
CR3204
Culture and Religion
2 credits/
Pre:
1+1+0
GAS3205
General and Applied Sociology
2 credits/
Pre:
1+1+0
FLS3206
Fundamentals of Life Safety
2 credits/
Pre:
1+1+0
ESD3207
Ecology and Sustainable Development
2 credits/
Pre:
1+1+0
KL3208
Kazakh law
2 credits/
Pre:
1+1+0
FE3209
Fundamentals of Economics
2 credits/
Pre:
1+1+0
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