Mathematical and Computer Modeling

Studying of disciplines of the educational program will allow the development of mathematical and computer modeling of natural-physical and other processes, acquire skills in system administration of operating systems, programming, production and scientific tasks, develop and manage the database.

After the end of the study of disciplines of the educational program «Mathematical and computer modeling», students must:

Know and understand:

• theoretical and practical bases of mathematical modeling;

• a model and methods of decision making;

• the concept "error";

• methods for designing information systems and stages of development of automated information systems.

• types of computer graphics, color models and types of raster images;     

• color model of the computer-based graphical modeling;

• overview of the Windows Server 2003, the Microsoft management console;

• main and common task of linear programming;

• classification of computers, Chipsets and motherboard BIOS.;

• methods of optimization web site promotion in the Internet;

• software side of the server used to create web pages;

• software tools for creating databases;

• software tools for development of the virtual server;

• basic principles of real configuration of the web server.

Be able to:

• create mathematical models for solving mathematical problems, development and implementation of a database;

• use of graphical editors for image processing, placed on the web-site;

• use graphics editors to create a design of pages of the web site;

• use the hypertext markup language HTML to create web pages;

• create dynamic web pages using JavaScript;

• use object-oriented technologies for creation of web-pages;

• access to databases when designing web-site;

• set the configuration of a web server.

Own:

• technology target of the study, the structure of computer networks, interactions of objects when you create a database;

• designing technology of the web-site as an information system;

• a common methodology for designing web-site;

• technologies of development and artistic registration of web-site;

• technology of creation of web-site by means of client-side programming;

• technology for optimizing images for posting on the website;

• technology optimization web site promotion in the Internet;

• technology of the web-site on the server;

• technology support and maintenance of web-sites.

• design technology web-site on the server side;

• the technology to create databases on the server side;

• technology of the web-site on the server.

Catalogue of disciplines of the educational program

Catalogue of disciplines of the educational program contains the description of each course separately indicating the prerequisites and postrequisites, number of credits, activities, information on managers of the program.

Basic disciplines

Religion studies – 1 credit

Prerequisites - history of Kazakhstan.

Brief course content:

Religion as a subject and an object of religious studies course. The emergence of the religion. The structure and content of religion as a phenomenon. The specificity of the religious system of Ancient East and the Ancient world. Tengrianism, as early form of religious consciousness. Buddhism. Christianity, its origin and essence. The Holy book of the Christians. Main currents in Christianity. Islam. The Quran, the Sunnah, the Sharia. Main currents. Religious phenomenon in the modern world and Kazakhstan.

Postrequisites: sociology.

Types of classes: practical lessons.

Program leaders: Shaimerden G.I., Bondarenko J.J.

Business etiquette – 1 credit

Prerequisites - history of Kazakhstan.

Brief course content: the History of development of etiquette. Peculiarities of business etiquette in different countries. Principles of etiquette of business relations. Formation of the image of a business person (clothing and appearance of a business man, a business woman). Business communication etiquette. Business communication, types, functions and levels. Rule of business etiquette. Ethics greetings, views. Business meeting. Presentation. Ethics of business telephone conversation. Business etiquette. Etiquette head. Etiquette Secretary. Everyday etiquette. Souvenirs and gifts in the business sphere. Code of honor of civil servants of the Republic of Kazakhstan (rules of ethics of civil servants). Code of ethics of students. Formation of corporate image. The modern Manager and its role in the formation of corporate image. Business rhetoric. Peculiarities of non-verbal means of communication. The basic precepts of business etiquette.

Postrequisites: sociology.

Types of classes: practical lessons.

Program leader: Bayakhmetova A.A.

Psychology of competitive personality – 1 credit

Prerequisites - economic theory

Brief course content: the Personality. Constructive communication. A conflict. Technology of search of work. The basics of self-presentation. Development of the individual professional. Professional deformation, destruction of personality and ways of their prevention.

Postrequisites: sociology.

Types of classes: practical lessons.

Program leader: Tashbaeva L.M.

Paperwork in the Kazakh language – 1 credit

Prerequisites - the Kazakh language.

Brief course content: Introduction. Name of official documents. Autobiography. Summary. A statement. Feature. A receipt. The power of attorney. Contract. The employment contract. Help. Resolution. Letters of congratulation. Official letters.

Postrequisites: the graduate's professional activity.

Types of classes: practical lessons.

Program leader: Kulbaeva M.M.

Programming – 2 credits

Prerequisites: Informatics

Brief course content: the Concept of algorithm, the program of the processed information. Technologies of development and implementation of algorithmic languages. The elements of the language. Alphabet, constants, identifiers, keywords, comments. Structured, modular programming. Basic concepts and mechanisms of entry environment and implementation of the programs. Basic data types. Basic principles of organization and structuring programs. Ads. Basic concepts and the language of the description of software objects. Operators. The main data processing tools. Pre-processing tools. Algorithmic foundations of writing efficient programs. The main principles and means of the organization of a software interface. Function. Main principles of development programs.

Postrequisites: discrete mathematics and mathematical logic

Types of classes: practical, laboratory classes

Program leader: Satmagambetova Zh.Z.

Object-based programming – 2 credits

Prerequisites: Informatics, programming

Brief course content: the Visual Basic language to create visual applications. Forms and controls. Declaration of variables, data types. Functions and procedures. The conditional operator, operator of multiple-choice cycles. Work with graphics. Management program progress. Debugging programs. Creating DLL libraries. Working with the file system. Implementation of data exchange between applications. Applications programming in MS Office.

Postrequisites: applied mathematics

Types of classes: practical, laboratory classes

Program leader: Ivanova I.V.

Мathematical analysis 3 – 3 credits

Prerequisites: mathematical analysis 1, mathematical analysis 2

Brief course content: the number series Main definitions. Properties of converging series. Number series with nonnegative members, signs of convergence. Alternating sequences, signs alternating number series, a sign of Leibniz. Arithmetic on converging series. Functional sequences and series of Characteristics and properties of uniform convergence of functional sequences and series. Power series. Taylor Series. Weierstrass theorem on the uniform approximation of continuous functions by polynomials, trigonometric polynomials. Improper integrals I and type II. Properties. Absolute and conditional convergence of the improper integral. Integrals that depend on parameters of a Family of functions that his uniform convergence. The properties of limit functions. Own integrals that depend on a parameter; their properties, Leibniz formula. Improper integrals that depend on a parameter. Integrals Of Euler. G-function-function; their properties. Orthonormal systems and General Fourier series. The main theorem on convergence of trigonometric Fourier series. The principles of the Riemann localization. Some properties of the Fourier transform.

Postrequisites: differential equations, equations of mathematical physics

Types of classes: practical lessons.

Program leader: Dospulova U.K.

Мathematical analysis 4 – 3 credits

Prerequisites: Мathematical analysis 1, mathematical analysis 2

Brief course content: Multiple integrals. Properties of integrals. Fold integral over an arbitrary set. Fubini theorem on reducing a multiple integral to the re. The change of variables in multiple integrals. Geometrical and physical applications of integrals. Curvilinear integrals in the I-St and II-nd kind. Properties curvilinear integrals in the I-St and II-nd kind. Green's Formula. Calculating the area of a flat area using the green's formula. Conditions of independence integral curved from the path of integration on the plane and space. The concept of the surface in three-dimensional space and ways to define a surface. The tangent plane and normal. Surface area. Surface integrals of the first and second kind. Conditions for the existence of surface integrals. Formula Ostrogradsky-Gauss, Stokes. Scalar and vector fields. Differential operators of vector analysis: the gradient of a scalar field, divergence and curl of a vector field. Their properties. The main integral formulas analysis in vector form. Solenoidal and potential fields.

Postrequisites: differential equations, equations of mathematical physics

Types of classes: practical lessons.

Program leader: Dospulova U.K.

Мathematical stability theory – 3 credits

Prerequisites: mathematical analysis, differential equations

Brief course content: the Mathematical theory of stability. Basic concepts and theorems of the theory of stability. Stability of solutions of linear homogeneous systems of differential equations. The first method of investigation on stability. Direct method of investigation on stability. Stability in the first approximation. Stability of difference equations.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Dospulova U.K.

3D-Modeling – 2 credits

Prerequisites: Informatics, programming

Brief course content: the Types of computer graphics. Color models and types of raster images. Match colors and color management. Storage formats for graphic images. Processes screening. The frequency and colourseparating. Basics of screening. Editing tools. Higher-quality images. Sources of digital images. Enter digital images. The practical part of the course is implemented in programs such as Corel Draw, Adobe PhotoShop.

Postrequisites: computational methods using computers

Types of classes: practical, laboratory lessons.

Program leader: Salykova O.S.

Equations of mathematical physics – 3 credits

Prerequisites: mathematical analysis, analytical geometry, basic algebra

Brief course content: Examples of physical problems leading to equations of mathematical physics. Setting of the Cauchy problem and boundary-value problems for the basic equations of mathematical physics. Notion solutions: classical and generalized. The correctness of the problem and the examples of ill-posed. Classification of equations and systems of equations with partial derivatives of the second order and bringing them to the canonical form. The concept of characteristics. Cauchy problem in a generalized setting. The Theorem Of Cauchy-Kovalevskaya. Cauchy problem for the wave equation and the wave propagation in unlimited space. The formulas of Duhamel, Poisson and Kirchhoff. Duhamel and its application for solving the Cauchy problem for these equations. The function of the Riemann problem for a hyperbolic equation with two independent variables and its properties. The task of the Cauchy and Goursat. A fundamental solution of the heat equation. Solution of the Cauchy problem for the heat equation. Formula For Poisson. The uniqueness of a solution of mixed problems. Thermal potentials, their properties and applications.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Dauletbaeva Zh.D.

Discrete mathematics and mathematical logic – 3 credits

Prerequisites: elementary math, algebra

Brief course content: the set, elements of the set task sets. Set-based operations. Properties of the operations on sets. Combinatorics. Graph theory. The basic concepts and tasks of the theory of graphs. Charts-types, methods of setting the graphs. The coloring of graphs. Chromatic number. Euler on planar graphs. Estimates of the number of graphs. Logical operations on the statements. The formula. Complete systems of logical connectives. The formal system. Axioms. Provability formulas. To derive formulas of the hypotheses. Models. Atomic predicate logic formulas, free and bound variables, quantifiers. Predicate logic formulas. Proven formula and formulas derived from a variety of hypotheses. Provability particular cases of tautology. Deduction theorem for calculation of predicates. Axiomatic building Peano arithmetic. Examples of formal conclusions of the laws of Peano arithmetic. Elements of the theory of algorithms. Turing Machine. The program of calculation of the simplest numerical functions. Composition of Turing machines. Encoding. Encoding. Encoding scheme. Alphabetic coding. Inequality Macmillan. Data compression. Compression texts. Dictionary. Algorithm of Lempel-Ziv. Encryption. Cryptography. Encryption by using random numbers. Public key cryptography.

Postrequisites: computational methods using computers

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Theory of function analytic 3 credits

Prerequisites: mathematical analysis, analytical geometry, basic algebra.

Brief course content: the set of complex numbers. Algebraic form of a complex number. Functions of a complex variable. Continuity. Differentiability of functions of a complex variable. The integral of a function of a complex variable. Number series. Functional series. Power series. Theorem Abel. The radius of convergence. Laurent Series. Region of convergence of series of Laurent. Deduction of analytic functions in an isolated particular point. Conformal display.

Postrequisites: applied mathematics

Types of classes: practical lessons.

Program leader: Ysmagul R.S.

Introduction to mathematical modeling – 3 credits

Prerequisites: computer science, mathematical analysis 1, programming.

Brief course content: Models and methods of decision making. Basic concepts and definitions. General formulation of the problem of linear programming (LP). Geometrical method of solving the problem PL. Finding the optimal solution through the basic variables. Computational algorithm of the simplex method. Simplex table. The algorithm of the simplex method. Solution of the problem PL method of artificial basis. Duality in linear programming. Mutually dual task PL and their properties. Transport task and methods of its solution. Methods for constructing the initial reference of the plan. The method of potentials and an algorithm of its solution. The overall objective of the nonlinear programming. The task of nonlinear programming and methods of its solution. Geometric method of solution. Method of Lagrange multipliers.

Postrequisites: calculus of variations and optimization methods

Types of classes: a practical training, laboratory classes.

Program leader: Ismailov A.O.

Algebraically systems – 3 credits

Prerequisites: elementary mathematics, discrete mathematics and mathematical logic

Brief course content: Binary relations. Algebraic operations. The basic property relations: reflexivity, symmetry, transitivity, connectivity. Equivalence relation and auditing classes. Order relation. Factor set. Binary algebraic operations, examples. n-ary operations. Properties of binary relations in the two forms of recording. Algebraic systems. The Group Algebra. Algebraic systems. Semigroup. Subgroups. Theorem Of Lagrange. Normal divisors and the group factor. The kernel of the homomorphism. .Rings. Ideals. Basic concepts. Examples of rings. Homomorphisms and isomorphisms of the rings, their properties. The kernel of the homomorphism. Zero divisors. The ratio of divisibility in a ring. The ratio of divisibility in the areas of integrity. Right and left ideals. Operations on the values .Main ideals and their properties. Classes deductions module. Classes deductions ideal. Euclidean rings. Factor-ring. Field and body. Archimedes’ ordered field. Numeric fields. Algebra Bull. Basic numeric system. The system of natural numbers. Axioms Of Peano. Method of complete mathematical induction. Arithmetic operations. Order relation. Ring of integers. The system of real numbers. Commutative rings with identity. Arithmetic operations and relations order. The ratio of divisibility in the ring of integers. Field of rational numbers. Ordered fields, thick ordering. Arithmetic operations. An equivalence relation. Factor set.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Differential Geometry and Topology – 3 credits

Prerequisites: mathematical analysis, analytical geometry, basic algebra

Brief course content: the Theory of curves. Vector-valued functions. Definition of the curve in differential geometry. Ways of setting. Arc length and natural parameterization. The main theorem of the theory of curves. Theory of surfaces. The definition of the surface. Ways of setting. The curves on the surface. The first quadratic form. The second quadratic form of a surface. A surface of constant Gaussian curvature. Metric Euclidean space in curvilinear coordinates. Euclidean metric space (Minkowski space). A Riemannian metric on the surface. The metric of the Lobachevsky plane. A topological space. The topology of metric spaces. Continuous maps of topological spaces. Homeomorphism. Closed sets. Base topology. Compact topological space. Basic concepts of the theory of manifolds. Differentiable manifolds. Manifolds with edge. Oriented diversity. Functions on manifolds. Mapping of manifolds. Curves on a manifold. Vector fields on a manifold. Tensor fields on a manifold. Examples of tensor fields in mathematics and physics. Vector, quadratic forms, tensors of stress and strain and other Algebraic operations over tensor fields. A Riemannian metric on the manifold. External forms. The integration of differential forms on a smooth manifold. The General theorem Stokes equations. Special cases of a General formula for the Stokes equations.

Postrequisites: no

Types of classes: practical lessons.

Program leader: Askanbaeva G.B.

Computational methods with computers using – 3 credits

Prerequisites: computer science, programming, introduction to mathematical modeling

Brief course content: the Concept "error". Definition of absolute and relative errors of approximate numbers. Actions on approximate numbers. Estimation of error result. Error of calculations (a fatal error, the error of the numerical method and rounding errors). Algorithms and schemes to solution of the nonlinear equations. Development of algorithms of solutions of nonlinear equations by methods of half the division of the chords, tangent and simple iteration. Examples. Formulas evaluation of errors. Conditions of the convergence of iterative methods. Formulation of the problem of interpolation. Interpolating zooming on images in the narrow and the broad sense. The concept of finite differences. Table of finite differences. Step interpolation. The concept of interpolation polynomial. Construction of interpolation polynomial of Lagrange. Estimation of the error polynomial Lagrange. Construction of the first and second interpolation formula of Newton. Calculation of values of a function by means of interpolation polynomials. Finding the first and second derivative of the function with the help of formulas on the interpolation formulas Newton, Gauss. Algorithms for finding the approximate values of definite integrals by the formulas rectangles, trapezoids, Simpson, «three-eighths». Construction of block diagrams. Error estimation formulas of the trapezium, Simpson. Approximate methods of solution of ordinary differential equations. Setting of the Cauchy problem. Approximate solution of a differential equation by the method of Euler - Cauchy, by the Runge - Kutt and Adams.

Postrequisites: mathematical programming

Types of classes: a practical training, laboratory classes

Program leader: Baimankulov A.T.

Profiling disciplines

Methods of optimization and operations research – 3 credits

Prerequisites: programming.

Brief course content: deals with the construction of convex sets and functions, mathematical models of the basic types of linear programming problems and their solutions.

Postrequisites: mathematical programming

Types of classes: a practical training, laboratory classes

Program leader:

Internet technology – 3 credits

Prerequisites: computer science

Brief course content: the Concept of the Internet, search the web, HTML. Creation of sites. Work with electronic resources: websites, blogs, forums. Participate in videoconferences, online seminars, participation and conducting online consultation. Browsers. Creating a portfolio, personal website, online shop, guest books. Freelance earnings in the Internet. Account. Creation of the account. Creation of e-book (electronic books), dictionaries and electronic library. E-government.

Postrequisites: programming in Micromedia Flash

Types of classes: a practical training, laboratory classes

Program leader: Usembaeva A.E.

Mathematical programming – 3 credits

Prerequisites: basic algebra, analytical geometry, mathematical analysis, the programming

Brief course content: the General and main tasks of linear programming, properties of the main tasks of linear programming, geometrical interpretation of a problem of linear programming, the simplex method, the method of artificial basis, modified by the simplex method, dual linear programming problem, the stability of the dual estimates.

Postrequisites: Web-programming

Types of classes: a practical training, laboratory classes

Program leader: Abatov N.T.

Computer-graphic simulation – 2 credits

Prerequisites: computer science, programming

Brief course content: the Main color models of computer graphics simulation. The controls. Commands and operations on the objects in the graphic editor 3D max. Spline graphics. Creating geometry or modeling. Animation and visualization of three-dimensional objects. Versions of basic materials. Types of toning. Techniques direction of light and camera. Principles of the use of texture maps. Maps. Image classification. Enter the image. Convert images. The practical part of the course is implemented in a graphical environment 3D Studio Max. Flash.

Postrequisites: programming in Micromedia Flash

Types of classes: a practical training, laboratory classes

Program leader: Salykova O.S.

Programming in Micromedia Flash – 2 credits

Prerequisites: computer science, programming

Brief course content: Drawing and animation, buttons, menu. Symbols Flash. Transformation of character. Morphing (motiontween)). Management морфингом. Morph shapes (shapetween). Fundamentals of programming in MacromediaFlash, complex and non-obvious properties programming system based on FlashMXActionScript. Features of work with the interpreter, and the system of external objects (characters, frames etc), which are created in Flash manually. Comparative analysis of the system types and classes and comparison with other high-level languages. Creation of Flash-projects.

Postrequisites: Web-programming

Types of classes: a practical training, laboratory classes

Program leader: Omarkhanova Zh.T.

Web-programming – 3 credits

Prerequisites: computer science, programming, mathematical programming

Brief course content: the hypertext markup Language HTML. The rules for building HTML documents are static and dynamic HTML pages. Tags block-level and consistent tags. Logical and physical formatting. Division into paragraphs. Translation strings. The headers. Horizontal lines. Using a pre-formatted text. The special characters. Inclusion of comments in the document. The organization links. Rules of registration links. Bulleted lists. Numbered lists. List of definitions. Nested lists. Ways to store images. Background images. Embedding images in НТМL documents. Creating the simplest tables. Representation of the tables on the page. Formatting data within the table. Nested tables. Features of construction of tables. The scope of application of frames. Description rules frames. Interaction between the frames. Floating frames. The basics of using the card images. A graphical representation of the map image. Description configuration card-image. Their advantages and disadvantages. Client option card images. The means of reproduction of sound. Embedding audio files in a Web page. Cascading style sheets. (CSS) document Object model. Dynamic НТМL in Internet Explorer.

Postrequisites: Economic-mathematical modeling

Types of classes: a practical training, laboratory classes

Program leaders: Ivanova I.V., Bermagambetov A.K.

Economic-mathematical modeling – 3 credits

Prerequisites: Actuarial mathematics, mathematical analysis, basic algebra, analytical geometry

Brief course content: the Stages of economic-mathematical modeling. Classification of economic-mathematical Form of entry of a problem of linear programming and their interpretation. Geometric interpretation of the problem of linear programming. The simplex method. Duality theorems and their economic value. The concept of dual evaluate and objectively conditioned assessment of the resource. Cost interpretation of the dual estimates. Review of adequacy of the linear mathematical model using the dual estimates. Formulation and variants of the transport problem. The solution of the transport problem by the method of potentials. Assignment problem. Formulation of the problem of dynamic programming. Bellman's principle of optimality. The algorithm of solving the problems of dynamic programming. The concepts of simulation models and computing experiment. The basic assumption of the simulation of the imposed constraints on the cognitive abilities of the method. Simulation tools. The concept of an econometric model.

Postrequisites: no

Types of classes: a practical training, laboratory classes

Program leader: Kalzhanov M.U.