Аналіз актуальності проблеми важливості розвитку креативності молодших школярів під час LEGO-конструювання. Характеристика комплексу ігрових завдань для формування креативності учнів початкових класів на уроках математики за допомогою цеглинок LEGO.

The Cartesian product of copies. The set of all nonnegative real numbers. The algebra of polar operators (poles). Definition of a binary operation. Polarized elements, extension of the algebra of poles to the whole plane. Classes of equivalence.

Класифікація некомпактних поверхонь з краєм. Типи некомпактних поверхонь. Можливі причини некомпактності. Поняття та властивості ідеальних меж (кінців) некомпактних поверхонь. Теорема про повну топологічну класифікацію некомпактних поверхонь з краєм.

The mathematical principles of the operation of cryptocurrencies. Mathematical formulas for calculating the public key from the private key. Properties of elliptic curves and the principle of their application during the creation of cryptocurrency.

List of the adopted abbreviations and designations. The complexity of configurations. Architecture – models and their appendices. Extreme constructive possibilities. The complexity of finite configurations. Formal discrete models of self reproduction.

Consideration of the process of evolution and prospects of mathematical methods and models in economic research. Characterization of advantages and identification of disadvantages of mathematical formalization in the conditions of a new economic paradigm.

The article is devoted to the study of the place of plot mathematical problems in the course mathematics of the primary school of Ukraine; determination of results in teaching problem solving; clarification of the essence of the problem-solving process.

Характеристика одного из подходов к идентификации динамики импульсной системы, основанного на использовании предварительной информации. Анализ двумерного пространства с дополнительными информационными свойствами. Пример реализации подхода в MatLAB.

Fundamentals of the method of least squares for the case of vector and matrix of observations. Advantages of MNCs to predict performance in the telemedia business. MNCs use algorithm for the matrix of observations with the ability to scale the data.

The methods developed by Hamilton 1989 and Chib 1996 to identied multiple-equation models. It details Bayesian estimation and inference for a class of models with different degrees of time variation and discuss analytical and computational difculties.

Normed linear spaces and Banach spaces. Basic properties of inner-products. Best approximation and orthogonal projections. Compact operators on a Banach space. Boundary value problems. Dierential calculus in Banach spaces and the calculus of variations.

Teaching students of mathematical fields of training to inverse problems. Implementation of the scientific, educational potential of teaching university students inverse problems for differential equations. Computational methods of mathematical physics.

Examination of unlimited closed convex subsets of Banach space X, having the same recessive cone, and metric spaces, which they form with the Hausdorff metric. Receiving an analog of the theorem of approximation of convex compacts by normal polyhedrons.

Первая и вторая квадратичная форма. Построение проекции вектора кривизны линии на нормаль поверхности в точке, через которую проходит эта кривая. Изучение кривизны всех линий на поверхности, рассмотрение плоских сечений. Уравнение индикатрисы Дюпена.

Using methods of discrete mathematics in the field of virtual isolation and its application in the scientific theory of numbers, groups, combinatorics and graph theory. Specifics arithmetic methods data comparisons. Construction of a matrix atom.

Description of combinatorial DG-Hopf color cooperadic models for configuration spaces of points in the first quarter and in the N-gon. The proof version of the formality theorem of Kontsevich to the two subspaces in the vector space and for the morphism.

Search of the Dirichlet series with zero abscissa of absolute convergence. Study of asymptotic equality features. The convergence at different points. The role of the Dirichlet series in number theory. The behavior of the three-dimensional function.

Characteristics of the main principles of construction of cubic maps and base points. Planarizations, their common properties. The proof of the theorem determine a cubic, quadratic and normal forms of planarizations. Complex and real classification.

Characteristic of a Krull–Schmidt Theorem for nonassociative algebras. Definition of the upper annihilating series. Study of some families of nilpotent evolution algebras. Classification of four- and five-dimensional nilpotent evolution algebras.

Determination of p-groups with nilpotency class 3 where all proper subgroups have nilpotency class less or equal 2. The necessary and sufficient condition for finite p-group to be a minimal group of nilpotency class 3.

The study of optimal control problems for linear parabolic equations with unbounded coefficients in the main part of elliptic operator. The peculiarities of this type of equations. Setting of the optimal control problem and its preliminary analysis.

Korobov polynomials as paradeterminants of triangular matrices. Some of the formulas of interpolation of functions of many variables and the discrete analogue of the summation formula of Euler - basic use of mathematical polynomials of this type.

The order and lower order of an entire function. Using the Fourier series method to study the properties of subharmonic functions. The subharmonic function in the complex plane. The finite system of rays. The class of delta-subharmonic functions.

Mathematical methods of optimizing statistical research. Solution the problem of computation the entropy value of binary messages of increased length generated by Bernoulli information sources. Development of methods to reduce the number of calculations.

The optimal method of teaching trigonometric equations in the high school mathematics course based on the curriculum. The place and meaning of trigonometric equations and inequalities in the school mathematics course, features of their solution.

Formulation of the lemma before solving the problem. The search for the principle of solving the paradox. Mathematical problem solving. Philosophical proof of the theorem. Justification of conclusions that can be applied in solving paradoxical problems.

The construction of lower-dimensional manifolds from high-dimensional data is an important task in data mining, machine learning and statistics. The authors consider principal manifolds as a regularized, non-linear empirical quantization error functional.

Hilbert scheme of points and induction scheme. Cellular decompositions for various nested Hilbert schemes of points. Hodge classes on self-products of K3 surfaces. On the cotangent sheaf of Quot-schemes. Algebraic families on an algebraic surface.

Rules for binary addition, multiplication, subtraction and division. Time complexity of extended Euclidean algorithm. Existence of multiplicative inverse. Cancellation law of congruence. Introduction to finite field theory. Corollary of Euler’s theorem.

Approximations in Scientic Computation, сomputer Arithmetic, mathematical Software. Linear Systems, solving Linear Systems, Iterative Methods for Linear Systems. Linear Least Squares, eigenvalues and Singular Values, Nonlinear Equations, optimization.