• 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Writing interactive math tests in the LaTeX system. Using the system for writing interactive tests on the theory of probabilities in distance learning. Creation of tasks of the type "True/False", "Short answer", "Essay" ("Clarifying the definition").

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  • 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.

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  • 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.

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  • 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.

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  • Изучение методов обработки информации при помощи Mathcad, возможных алгоритмов написания программ и способов отображения информации. Построение графиков функций. Расчет количества информации при кодировании равномерным и неравномерным двоичным кодом.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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