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.

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.

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.

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 fundamentals of the theory of automata, formal languages, and regular, context-free grammar. Discussion of the principle of Turing, which formalize the concept of soluble and insoluble problems, the definition of time and space evaluation algorithms.

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.

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.

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.

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.

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.

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.

The Italian system of numeration of propositions. Account of Peano's Logical Symbolism. Russell's "Logic of Relations". On Finite and Infinite Cardinal Numbers. Connect of the proposition. Combinations and Permutations, the class of infinite numbers.

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 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.

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.

Putnam argues that, by reinterpretation, the Axiom of Constructibility can be saved from empirical refutation. This paper contends that this argument fails, which leaves Putnam’s sweeping appeal to the Lowenheim - Skolem Theorem inadequately motivated.