Master Degree in Mathematics
Сipher: 6B060100
Name: Mathematics
Purpose 
To provide students the fundamental knowledge of mathematics to the study of new quantitative relations and spatial forms of the real world in accordance with the requirements of technology and natural science. Specialist areas are mathematical analysis and function theory, mathematical logic and algebra, stochastic analysis and actuarial mathematics, differential equations, optimization and optimal control, equations of mathematical physics. 
Disciplines 
State Compulsory Module

History and Philosophy of Science Foreign language (Professional) Pedagogics Psychology

Basic Professional Modules: Required Core Modules :

Methods of teaching mathematics

Module 1:Methods of teaching in mathematics
 Organization and Planning of Scientific Research
 Methods of Teaching Higher Education Mathematics

Mathematical and stochastic analysis

Module 2: Mathematical and stochastic analysis
 Mathematical analysis on metric spaces and stochastic analysis
 Mathematical analysis on Manifolds

Algebraic structures

Module 3: Algebraic structures

Track 1: Differential equations and mathematical physics

Module 1: Qualitative theory of differential equations
 Dynamical systems theory
 Qualitative theory of differential equations
Module 2: Boundaryvalue problems for differential equations
 Boundaryvalue problems for ordinary differential equations
 Boundaryvalue problems for partial differential equations
Module 3: Equations of mathematical physics
 Inverse problems of mathematical physics
 Additional chapters on differential equations and mathematical physics
Module 4: Integrodifferential and Navier–Stokes equations
 Singularly perturbed integrodifferential equations
 Navier–Stokes equations

Track 2: Control theory

Module 1: Control theory of deterministic and stochastic systems
 Constructive theory of boundary value optimal control problems
 Inverse problems forstochastic differential equations
Module 2: Boundaryvalue problems and control systems
 Methods for solving boundary value problems
Module 3: Theory of dynamical systems
 Stability theory for dynamical systems
 Theory of phase systems
Module 4: Optimal control theory
 Boundary value optimal control problems
 Differential games

Track 3: Mathematical analysis and function theory

Module 1: Mathematical and Complex analysis
 Multidimensional Complex Analysis
 Numbertheoretic methods in approximate analysis and their applications
Module 2: Elements of approximation theory
 Approximations for functions of several variables
 Application of approximate calculations to the problems about eigenvalues
Module 3: Analytic functions theory
 NikolskyBesov spaces and their applications to boundary value problems for generalized analytic functions
 Boundary value problems and their spectral properties for equations of mixed parabolichyperbolic type
Module 4: Some actual problems of the theory of differential operators
 Theory of identification of the boundary conditions and its applications
 A nonlinear boundary value problem for an ordinary differential equation

Track 4: Actuarial mathematics

Module 1: Analysis of time series and regression
 Theory of time series and forecasting
 Nonparametric regression
Module 2: Application of the theory of random processes
 Martingales and their applications in finance
 Distributions theory and their application in insurance
Module 3: Actuarial mathematics1
 Pension plans
 Reliabilitytheoryand its applicationin insurance
Module 4: Actuarial mathematics2
 Methods for calculating the allowance for losses
 Theory of investment

Track 5: Stochastic analysis

Module 1: Foundations of Probability theory
 Mathematical Foundations of Probability theory
 Sums of independent random variables
Module 2: Statistical inferences
 Theory of statistical inferences
 Applied Statistics and Econometrics
Module 3: Random equations and diffusion processes
 Stochastic equations
 Diffusion Processes and Their Applications
Module 4: Random processes
 Introduction to the theory of martingales
 Statistics of Random Processes

Track 6: Mathematical logic and algebra

Module 1: Algebraic structures
 Theory of finite fields
 The Galois theory
Module 2: Computability theory
 Computable functions
 Automata and formal languages theory
Module 3: Model theory
 Elimination of quantifiers
 Structures and methods of model theory
Module 4: Actual problems of cryptography
 Algebraic foundations of cryptography
 Modern cryptographic systems

Internship

Professional
Teaching

Thesis


Employability 
Graduates of the master can work in research institutes, in government or private educational institution as a lecturer, in area of communication and banks, actuarial activities. 
Further studies 
Further studies. Master graduates can continue their education at the PhD level in the profession or professions related to this one. They can also continue to research activities in that economy grown back, which will directly apply their knowledge. Access to teacher training (education track); to Research and Pedagogic training 
Programme learning outcomes 
A graduate of the Mathematics (MSc) programme must possess the following knowledge, skills, and competences:

have general knowledge about historic stages of the development of Mathematics as a science as well as current world trends, main directions and scientific schools of Mathematics; topical problems of Mathematics and modern methods of their solution; current state of mathematical education and science;

know current problems of mathematical analysis, algebra and geometry, computational mathematics, differential equations and mathematical physics, probability theory and mathematical statistics and other fields of Mathematics;

know analytical, qualitative and numerical research methods necessary for independent research work; methods of creation and use of mathematical models to describe and forecast various physicalchemical and natural processes and phenomena;

be able to apply the theoretical knowledge received in the fundamental fields of Mathematics to solve theoretical, scientific practical and information searchrelated mathematical tasks; solve complex interdisciplinary problems; carry out qualitative and quantitative analysis of obtained results; construct standard mathematical and computer models of physical, technical, economic and other processes; teaching general mathematical modules; computerbased search, collection, preparation and processing of information used in his/her professional activity;

have skills of properly formulating goals and objectives of scientific research as well as the concept of scientific search; performing a patent search and applying for an invention; presenting results of studies (in the form of articles, reports, papers etc.); organising work on a scientific basis; acquiring new knowledge using modern information technologies;

know history and philosophy of science; research methods used in modern science and links between theory and practice; basics of bibliographic research; foundations of highereducation psychology and pedagogy, and methods of teaching mathematical modules; the methodology of labour and personnel management;

be competent in a foreign language to be able to conduct professional discussions, read and translate specialized literature.
Mathematical analysis and function theory:

ability to develop theoretical problems of mathematical analysis and function theory;

ability to assign new problems and solve using methods of mathematical analysis and function theory;

ability to apply your knowledge of functional spaces to the solving practical problems;
Actuarial mathematics:

ability to develop the skills needed to do empirical research in fields operating with random processes data sets;

have a good understanding of the basic concept of integration with respect to a probability measure and the basic properties of fair games;

ability to answer simple questions on martingales; experience applications of stochastic processes in discrete financial models.
Stochastic analysis:

ability to illustrate the basic concepts and important fundamental results of general theory stochastic processes;

ability to distinguish important classes of the theory of stochastic processes;

ability to prove the main theorems of the theory of stochastic processes;
Mathematical logic and algebra:

ability to solve standard problems of mathematical logic;

ability to explain and manipulate the different concepts in automata theory and formal languages such as formal proofs, nondeterministic automata, regular expressions, regular languages, contextfree grammars, contextfree languages, Turing machines;

ability to explain the power and the limitations of regular languages and contextfree languages;
 ability to solve problems in elementary number theory, apply elementary number theory to cryptography, develop a deeper conceptual understanding of the theoretical basis of algebra and cryptography.
