# Natural sciences

Number of the journal, №: 2017. № 4

Creating an electronic textbook on mathematics

Annotation:
The article considers basic principles and approaches for creation of an electronic textbook, the stages of

introduction of information and communication technologies in the learning process. The main stages of

creating an electronic publication in accordance with the requirements for the development of a modern

textbook are presented.

Peculiarities of the method of teaching discipline

Annotation:
"Information communication technologies" in English language

Annotation. The article discusses the use of the CLIL (Content and Language Integrated Learning)

methodology in the teaching of the discipline "Information and Communication Technologies" in English. The

use of this technology in polylingual groups is most appropriate, since the CLIL pursues two goals, namely, the

study of the subject through a foreign language, and a foreign language through the taught subject.

Integrability is determined by the fundamental nature of ICT and the nature of the basic objects of its

study; the ability to work with information refers to general educational skills. Teaching ICT in English allows

students to look at English from an information point of view.

To assimilate the material, the already existing knowledge of students in the user aspect is reinforced,

relying on the basic concepts of ICT and competence in the field of informatics, expanding the literacy skills of

ICT tools and English-language software, enriching vocabulary in English, forming orientation skills in the

English interface of applied and office programs ..

Active learning strategies for the development of numeracy of schoolchildren

Annotation:
This article describes the ways in which students can develop logical thinking skills. Currently, any form

of the exam takes precedence over logic. Accordingly, the article grouped logical tasks and provided their

solutions.

Number of the journal, №: 2017. № 3

On the solution of an equation of Pell type in integers

Annotation:
The Pell equations are a class of Diophantine equations of the second degree. These equations are found

in different areas of mathematics. In this paper we investigate the generalization of the Diophantine Pell

equation and find a solution in the form of polynomials of integer coefficients. A detailed study of the theorems

and proofs offered to the reader helps us to more deeply comprehend the essence of the Diophantine equation.

The result of this article is to find the smallest solution. The study is an additional source of study of Pell's

equations.

Number of the journal, №: 2017. № 1

Annotation:
The article deals with the application of information and communication technologies in the teaching of mathematics. These technologies contribute to the development of independent thinking, help to rationally use time, form interdisciplinary communication.

The application of combinatorics to the solution of certain tasks

Annotation: This article reveals the possibility of solving life situations with combinatorial coefficients and shows the practicality of applying formulas on the theory of probability and mathematical statistics. The solution of tasks with combinatorial coefficients consists mainly in the decomposition of these coefficients by the basic formulas and their manipulations.

Number of the journal, №: 2016. № 4

Research of one numerical series

Annotation: In the paper, we consider some fractional and irrational expressions, and prove the assertion that leads them to fractional and rational expressions, and also consider one general lower and upper bound (two-sided estimate) for a one numerical series. In obtaining some congruencies, we used the formula for binomial coefficients, then from the sum of the left side we cancel each other, and the summons with even numbers, where everywhere in an even degree in an uneven degree are doubled even after multiplier was put outside, all the summons remain free from the square root. Several variants of proofs are considered in the solution of certain problems and theorems.

Some examples of the application of complex numbers in geometry

Annotation: The article deals with the geometric interpretation of complex numbers, the possibilities of applying a transformation of the plane, and examples of solving problems.

Number of the journal, №: 2016. № 3

Graphite laminated materials strength properties and energy characteristics of polymer binders

Annotation:
The approach which was proposed earlier for composite materials strength prediction using

contact angle measurements was applied for graphite laminated materials. It was shown that the calculation of

the work of adhesion to polar and non-polar model liquids can be applied to the choice of polymer binder.

Some processes of irrational rationalization and two-sided evaluation of a single number series

Annotation: In this article we consider some fractional-irrational expressions and prove the assertion that reduce them to fractional-rational expressions and also consider one general lower-and-upper bound (two-sided estimate) for one numerical series.