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  • The textbook includes topics of discrete mathematics. Relations: binary relations, pictorial representatives of relations, inverse relation, functional relation. Mathematical logic: propositions and compound statements, basic laws of logical operations.

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  • 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.

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  • 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.

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  • Further examples of population dynamics. Representation of real numbers in an arbitrary base. A geometrical model for continued fractions. The idea of computational complexity. Elementary applications of congruence. The fundamental theorem of arithmetic.

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  • The quart formula - a tool for describing the composition of functions, the modification of which directly changes properties, which are easily detected by numerical modeling. A complete infinite power-factorial functional series of the exponent.

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  • 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.

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  • Combinatorial description. Teichmuller curves. Recurrence relation. Asymptotics of numbers of branched coverings of a torus, volumes of moduli spaces of holomorphic differentials. The character of the infinite wedge representation. Cylinder decomposition.

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  • 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.

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  • Conditions for nite sequences of positive numbers to be certain parts of spectra of the Dirichlet-Dirichlet, Dirichlet-Neumann, Neumann-Dirichlet and Neumann-Neumann boundary value problems generated by the same Stieltjes string recurrence relations.

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  • 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.

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  • Monotonic Functions and Unordered Lists. The Pigeonhole Principle. Basic Concepts of Decision Trees. The Principle of Inclusion and Exclusion. Counting Structures with Symmetries. Concepts in Graph Theory. Equivalence Relations and Unlabeled Graphs.

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  • Normed linear spaces. Contraction mapping theorem. Applications to differential and integral equations. Linear transformations. Product spaces and Fubini's theorem. Projection and self-adjoint operators. Gram-Schmidt orthonormalization. Fourier analysis.

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  • Ways of representation of functions of two variables. Partial increment and derivatives of the first order. Application of the total differential to approximate calculations. Description of the largest and smallest values of a function of two variables.

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  • Finding common solutions of linear differential equations of the fourth order, the coefficients of which satisfy the system of three differential equations of the first order. The problem of conformal mapping of polygons, whose sides are arcs of circles.

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