The basics of cryptography and its levels of reliability. Secret key cryptosystem and symmetric ciphers, message authentication codes. Fundamentals of discrete mathematics, homomorphisms and isomorphisms. Modular arithmetic and function Euler's Totient.

The importance of research approach to a choice of model and to the search of alternative decisions. Some various methodically important approaches to the decision of elementary problems of search of the minimal speed allowing in "vacuum" conditions.

Дослідження регулярних цілих вектор-функцій половинного порядку зростання та відповідних їм безумовних базисів гільбертових просторів. Розв’язання задачі інтерполяціі функціями з вагових класів цілих вектор-функцій половинного порядку зростання.

Использование независимых событий в качестве результатов измерений, наблюдений, испытаний, опытов, анализа данных - основа вероятностно-статистических моделей. Установление критерия независимости событий - одна из важнейших задач теории вероятностей.

Correct solution of the location problems as one of most important tools of the operations research. The aim of location problem involves the location of one or more new facilities in the plane, when the number of possible locations is usually infinite.

Yangian for gln is the associative algebra historically first example of the quantum group. Bethe subalgebras in Yangians, theories and concepts used in this problem. Analysis and proof of lemmas. The Cartan subalgebra of the regular diagonal matrices.

The algorithm of the basic components of a linear analysis. Work on nonlinear PCA, or NLPCA, autoassociative's neural networks, principal curves and manifolds, kernel the combination's of these approaches. The problem areas that require research.

The results of the participants of the scientific seminar "Problems of elementary divisor rings" concerning the Bezout rings of finite stable range. The conditions under which these rings are elementary divisor rings. These rings introduced Kaplansky.

Mathematics as a fundamental science. The place in its structure of differential equations is one of the most harmonious ways of knowing the universe. Study of the algorithm for constructing compartmental (SIR) models, based on differential equations.

Analyzing multi-dimensional data with complex geometry and to identify low-dimensional "principal objects" that relate to the optimal projection while losing the least amount of information. The methods for dimensionality reduction of microarray data.

Using a generalized Dunkl translation, we obtain an analog of theorem 5.2 in Younis’ paper for the Dunkl transform for functions satisfying the (d, g)-Dunkl Lipschitz condition in the space L2(R,|x|2a+1dx). Consideration generalized Dunkl translation.

Arithmetic operations and properties of decimals, proportion and percents. Fundamental concepts of algebra, functions and graphs. The fundamental operations with complex numbers. Limits of function values, one-sided limits, infinitesimal functions.

Properties of Probability Distributions. Conditional Distributions and Expectation. Characteristic Functions, Moments and Cumulants. Parametric Families of Distributions. Distribution Theory for Functions of Random Variables, Approximation of Integrals.

Affine plane curves. A brief introduction to the p-adic numbers. Regular functions on projective curves. Plane projective cubic curves with a rational inflection point. Reduction of an elliptic curve. Cohomology of finite, infinite Galois groups.

Names of Greek letters and their pronunciation in formulas. Some facts on the development of the number system. Abbreviation and mathematical dictionary for the telecommunications specialists. Expressions and constructions used while retelling texts.

The concept, nature and purpose of mathematics. The process of identifying the "unknowns" in the process of solving the equation. Characteristic and distinctive features of types of equations, examples of possible solutions. Features Diophantine equation.

Аналіз функціонально-дискретного методу розв’язування задач з крайовими умовами третього роду, періодичними і антиперіодичними умовами. Розгляд обставин геометричної прогресії. Дослідження асимптотичних розвинень для значень задачі Штурма-Ліувілля.

Конструктивне представлення розв'язків абстрактних задач для диференціальних рівнянь гіперболічного типу першого та другого порядків в гільбертовому просторі. Побудова і обґрунтування чисельно-аналітичних алгоритмів, знайдення апріорної оцінки точності.

The theory of the scalar field, directed derivative. The calculation of the line integral. The divergence of vector fields, their properties. Complex numbers and operations with them. The concept of differentiability and analytic function of the complex.

Forgotten motives: varieties of scientific experience. Motives and homological algebra, physics. Early history of motives. Determination of the category of (pure) motives. Preservation algebraic-geometric objects, projective varieties over a Wark field.

Anyone who reads Frege with moderate care is struck by a puzzle about the central objective of his work. His main project is to explain the foundations of arithmetic in such a way as to enable us to understand the nature of our knowledge of arithmetic.

Boolean algebra as a mathematical language of thought. Demonstration of the role of Boolean logic in computer science through the development of design schemes, its use in cryptography as a significant example of the role of logic in modern computing.

Basic Concepts, examples of Floating Point Calculations. Gaussian Elimination with Partial Pivoting. Bisection, Newton’s Method, and the Secant Rule. Basic Quadrature Rules. Some Elements of the Theory. Special Devices for Integration and case study.

Several aspects of systems theory. Arithmetic of cardinal numbers. Crises of naive set theory. Constructions of ordinal and cardinal number systems. Growth of the polish school of mathematics. Bellman’s principle of optimality and its generalizations.

The Buquoy generalization of Newton's second law of motion for systems of bodies with variable masses driven by reactive forces produced by ejected burnt fuel. External forces depending on accelerations and higher order derivatives of velocities.

Description of a variational graph-theoretic. Brief review of linear graph principles. Generate the equations of motion with elastic deformations, the flexible bodies are discretized using two types of finite elements. Discretize unidirectional bodies.

The study of the theory of probability. Determination of the relative frequency. Moments of random variables. Central limit teorema. Aksioma Richesky Probability. Studies Cumulative Distribution Functions. A communication system for random fluctuations.

Дослідження властивостей L-пiдгруп на скiнченних групах. Характеристика множини L-пiдгруп на циклічних групах деяких порядків з простими числами, квазіциклічній та нециклічній групі. Доведення математичних тверджень та приклади деяких L-пiдгруп.

Решение задачи Коши для жестких систем дифференциальных уравнений. Исследование (m,к)-методов решения жестких задач, в которых на каждом шаге два раза вычисляется часть системы дифференциальных уравнений. Построение (4,2)-метода максимального порядка.

Bayesian hierarchical models for data analysis in this context. At the first stage of the model, survival times can he modelled via the Cox partial likelihood, using a justification due to Kalbfleisch. A questionable parametric assumptions are avoided.