Functional Analysis and Analytical Economics

Head of the department: Doctor of Physics and Mathematics. Sciences, Professor Lebedev Andrey Vladimirovich

Leading specialist in supporting the educational process: Sorokoletova Olga Nikolaevna

Teaching staff: 6 professors, 10 associate professors

Scientific directions

mathematical analysis;
complex analysis;
dynamic systems;
linear and nonlinear integral equations;
qualitative theory of differential equations;
general theory of partial differential and functional differential equations;
approximate methods for solving operator equations;
stochastic differential equations;
control theory and mathematical economics.
Disciplines assigned to the department

Basic courses

optimization methods;
calculus of variations;
operations research;
statistical methods in economics;
combinatorial modeling and operations research.

Main disciplines of specialization

convex analysis;
ordered linear spaces;
mathematical foundations of consumption theory;
economic and mathematical models;
chapters on multivariate analysis and economic applications;
elements of queuing theory;
stochastic analysis of financial markets;
information theory;
probabilistic models of market prices;
mathematics and mathematical models;
inventory management models.

Coursework topics for the 2022/23 academic year

Floyd’s algorithm with step-by-step implementation in Python.
Multiple regression and correlation.
Amenable groups.
Time series analysis using the R language.
Pairwise regression and correlation.
Fourier series.
Geometric and analytical properties of spaces with scalar product.
Fractals and their properties.
Hardy spaces in the half-plane.
Hardy spaces in a circle.
Dynamic programming.
Random walk process. Tasks and applications.
Functions of limited variation.
Dijkstra’s algorithm with step-by-step implementation in JS.
Banach-Tarski paradox.
Random walk process and neural networks.
Cones in infinite-dimensional space.
Code sequences.
Models of financial mathematics.
Carleson measures.
Genomic sequences.
Closed operators.
Algorithms for finding the shortest routes.
Generalized Leontief model
Information theory. Information entropy.
Luzin approximation in Gaussian spaces.
-Nilpotent and -soluble groups and their classes.
Finding the shortest paths from a fixed vertex of the graph to the rest.
Ideal spaces.
Network models.
Hausdorff measure and dimension.
Ideal spaces.
Combinatorial foundations for constructing probability spaces.
Classical probability-theoretic models.

Dissertation topics for the 2022/23 academic year

Fractional integrals
Expansion of entire functions into an infinite product
Statistical Machine Learning
Galois theory
Linear and nonlinear mathematical
Network models
Trigonometric series with decreasing coefficients
Green’s formula
Financial risk analysis
Examples of solving Bayesian games
Dynamic programming problems
Voting systems
Kurzweil-Henstock integral
Reinforcement learning and its applications
Network models
Hardy’s inequality
A Rigorous Approach to Defining Elementary Functions
Optimization methods in machine learning
Statistical analysis of homogeneity
Methods of entropy analysis in machine learning
Wiener process. Theory and applications
Inductive limits of topological spaces
Modeling and filtering noise in signals
Models of financial mathematics
Algebraic and topological properties of linear operators in normed spaces
Classical inequalities and functional analysis
Network planning, building a network model, Gantt chart