• Жыццевы шлях рускага педагога-матэматыка першай паловы XVIII стагоддзя Л. Ф. Магніцкага. Самастойнае атрыманне матэматычных ведаў. Дараванне Пятром I прозвішчы. Стварэнне Магницким падручніка па матэматыцы і кораблевождению, яго значэнне для навукі.

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  • История развития квадратных уравнений. Эволюция подходов к решению Древнего Вавилона, Диофанта, Индии, ал-Хорезми, Европы в 13-17 веках. Краткая характеристика теоремы Виета. Особенности применения различных способов решения квадратных уравнений.

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  • Доклад немецкого математика Давида Гильберта на Международном конгрессе 1900 года в Париже "Математические проблемы". Суть 10-ой проблемы Гильберта, которая называется "Задача о разрешении диофантовых уравнений", на примерах алгебраических уравнений.

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  • Applications of the mathematics of harmony as a new interdisciplinary direction of modern science. Algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions.

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  • Assessment of convergence result for the sequential procedure in the form of alternating maximization to the maximum likelihood estimation for a family of models - Generalized linear models. Variable Linear Regression procedure. Using techniques ALS.

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  • Studying of the enumerative geometry of orbits of multidimensional toric action on projective algebraic varieties. Develop a new cyclic diferential-graded operad, conjecturally governing the real version of the enumerative geometry of these toric orbits.

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  • Queuing effect can be in the different components of ground operations. Causes of surface – movement delays are long taxi – in and taxi – out operations during departure and arrival of aircraft. Surface movement delays in an airport are analyzed.

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  • Regression smoothing, basic idea of smoothing. Smoothing techniques, the speed at which the smooth curve converges. Choosing the smoothing parameter. Data sets with outliers. Looking for qualitative smoothing and incorporating parametric components.

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  • The emergence of noncommutative geometry, its relationship with the corresponding selected algebra function. The establishment of the anti-equivalence between the category of spaces and the corresponding category of algebras of functions on such spaces.

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  • System of a quasidifferential equation with measures on the semiaxis. Linear differential operators generated by differential expressions. Asymptotics of a fundamental solution system for a quasidifferential equation with measures on the semiaxis.

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  • Auto-associative models as a new tool for building nonlinear principal component analysis methods. The successive approximations of a dataset by manifolds of increasing dimensions. The theoretical comparison between PCA and auto-associative models.

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  • Biographies of scholars such as Leonardo da Vinci, Kelly Miller, Rene Descartes, Leonhard Euler, Nicolaus Copernicus, Alan Turing and other scientists who have made an invaluable contribution to science. Their ways of life and achievements in science.

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  • The history of the discovery of Archimedes formula to calculate areas and volumes of spheres, cylinders and other plane and solid geometric figures. The Archimedes screw - a machine to transport water from low-lying sources in the irrigation ditches.

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  • Criterion of boundedness of L-index in direction for functions f(z; m). Analogue of Hayman’s theorem for entire functions of bounded l-index. The study of boundedness of L-index in direction for some infinite products. Possible ways of construct.

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  • Research of the level of informatization of the main spheres of life activity of citizens of foreign countries. Analyse the peculiarities and problems of the development of higher education in Ukraine in the context of information and digital inequality.

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  • Johann Carl Friedrich Gauss - a German mathematician. His outstanding scientific achievements. The fundamentals of modern balancing and mathematical statistics (the least squares method). Developing number theory, analysis, differential geometry.

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  • Comparative analysis for the algorithm for solving two-parameter game models. Comparison of the values of the game price and the probabilities of strategies. The accuracy and reliability of the results are analyzed with the help of a numeric example.

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  • Sums, floors and recurrences. Finite and infinite calculus. Hypergeometric functions and transformations. Special, exponential generating functions. Euler’s summation formula. Domino theory and change. Partial hypergeometric sums. Stirling numbers.

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  • 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.

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  • 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.

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