Elementary number theory, cryptography and codes

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.

Подобные документы

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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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  • 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.

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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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  • 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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  • 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.

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  • Separating the foundations of mathematics from philosophy. Difference between the theory of formal systems theory and evidence. Classical first order predicate logic. Elementary and full analysis. Existing proof theory. Infinitely long expressions.

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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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  • 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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  • The notion of weighted sharing of sets improving theorem A.I. Lahiri. Idea of gradation of sharing of values and sets known as weighted sharing. The definitions of the value distribution theory. Nonconstant meromorphic functions having no simple poles.

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  • The importance of research approach to a choice of model and to the search of alternative decisions. Some various methodically important approaches to the decision of elementary problems of search of the minimal speed allowing in "vacuum" conditions.

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  • The results of the participants of the scientific seminar "Problems of elementary divisor rings" concerning the Bezout rings of finite stable range. The conditions under which these rings are elementary divisor rings. These rings introduced Kaplansky.

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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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  • Proving of the theorem on a normal limit distribution of the normalized number of false solutions of a beforehand consistent system of nonlinear random equations over the field GF(2) with additional condition on the number of nonzero components.

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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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  • Methods of rapid information. Reduce time of realization of cryptographic RSA transformations. Application of the principle of ring shift in the module number system. Increasing the speed of realization of cryptographic transformations with the open key.

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  • Basic formulas of combinatorial analysis. Theorem of addition of probabilities of incompatible events. Theorem of multiplication of probabilities. Bayes’s formulas. Mathematical operations over random variables. Properties of a distribution function.

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  • 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.

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  • 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.

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  • The paper attempts to state and prove a completeness theorem for the system S5 of supplemented by first-order quantifiers and the sign of equality. The basic modal language. A general strategy for proving completeness theorems for quantified modal logics.

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  • The theory of the scalar field, directed derivative. The calculation of the line integral. The divergence of vector fields, their properties. Complex numbers and operations with them. The concept of differentiability and analytic function of the complex.

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  • 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.

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  • Subject and method of statistical science. Elements of probability theory. Random variables and their distribution laws. Fundamental of statistical observation. Grouping, consolidated return and data presentation. Basics of averages statistics method.

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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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  • Role of Euler`s number in differential and integral calculus, in algebra. Consideration of a new limit for the number e and giving its rigorous proof using the apparatus of mathematical analysis. Combinatorial interpretation is given for Euler’s number.

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