Mathematics

Bachelor Degree in Mathematics
Сipher: 5B060100
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:

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
  • 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: Boundary-value problems for differential equations
  • Boundary-value problems for ordinary differential equations
  • Boundary-value 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: Integro-differential and Navier–Stokes equations 
  • Singularly perturbed integro-differential 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: Boundary-value 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
  • Number-theoretic 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
  • Nikolsky-Besov spaces and their applications to boundary value problems for generalized analytic functions
  • Boundary value problems and their spectral properties for equations of mixed parabolic-hyperbolic 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 mathematics  -1
  • Pension plans
  • Reliabilitytheoryand its applicationin insurance
Module 4: Actuarial mathematics  -2
  •  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 pedagogigcal and professional

Thesis
Employability Graduates of the bachelor can work in research institutes, in government or private educational institution, in area of communication and banks, actuarial activities.
Further studies Bachelor graduates can continue their education at the graduate 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

The graduate can demonstrate:

  •  understand and apply the principles and laws of mathematics to solving the theoretical and practical problems;
  • knowledge of  basics of  Mathematics, especially,  the definitions, theorems, rules, general research methods for solving specific mathematical formulate tasks
  • knowledge ofhowto convey to theinformation, to….
  •  demonstrate an understanding of the history and the role of professionals and institutions in the development of mathematical science;
  •  demonstrate an understanding of the diversity of peoples and cultures and of the significance and impact of mass communications in a global society;
  •  understand concepts and apply theories in the use and presentation of images and information;
  •  demonstrate an understanding of professional ethical principles and work ethically in pursuit of truth, accuracy, fairness and diversity;
  • demonstrate skills of using digital technologies and creating web content;
  •  think critically, creatively and independently;
  •  conduct research and evaluate information by methods appropriate to the communications professions in which they work;
  •  write correctly and clearly in forms and styles appropriate for the communications professions, audiences and purposes they serve;
  •  critically evaluate their own work and that of others for accuracy and fairness, clarity, appropriate style and grammatical correctness;
  •  apply basic numerical and statistical concepts;
  • ability to formulate mathematical problem news writing and advanced writing for print journalism.
  • ability to write articles, and learn to broadcast, particularly he/she deals with depth reporting, audio and video production.
  •  ability to construct a variety of projects using the latest communication tools
  • ability to be able towork in a team.

Mathematical Analysis and Function Theory Track:

  • ability to calculate the limits of functions;
  • ability to find derivatives of functions and use the differential calculus on the functions’ research;
  • ability to calculate integrals and know the methods of integration, used integral calculus to calculate the area of plane figures, volume, the work of physical bodies;
  • ability to investigate the convergence of the series;

Mathematical logic and algebra Track:

  • ability to  find bases of subspaces, an orthonormal set of vectors, find the Jordan form of a matrix of a linear operator and compute the canonical basis, lead to the canonical form of the quadratic forms.
  • ability to design and guide a video production and broadcast delivery;
  • ability to cover important and interesting topics on Gender, Children and Youth;
  • ability to produce documentary products;
  • ability to use visual journalism in broadcasting.

Stochastic Analysis and Actuarial Mathematics Track:

  • ability to design and guide a video production and broadcast delivery;
  • ability to cover important and interesting topics on Gender, Children and Youth;
  • ability to produce documentary products;
  • ability to use visual journalism in broadcasting.