Gerasimenko S.A., Pavlenko A.N., Pikhtilkova O.A.
ABOUT SOME ASPECTS OF ORGANIZATION OF INDEPENDENT WORK ON THE DISCIPLINES OF THE MATHEMATICAL CYCLE STUDENTS OF NATURAL SCIENTIFIC DIRECTIONS ^{[№ 8 ' 2017]}
Currently, the main trends of reform of higher education naturally leads to a significant reduction in the proportion of classrooms in the educational process, and as a consequence, to a sharp increase of a role of independent work of students. Full improving the efficiency of the latter is a necessary condition for better learning of students of educational material. Approach to the organization of classroom independent work at studying of mathematical disciplines cycle students of science and engineering should include the following stages: a demonstration of practical application have been studied on the lecture method; independent decision students the same tasks, generated with the help of information technologies; automatic verification of the correctness of the decision of tasks and conclusions on the basis of the assimilation of educational material each student. To enhance effective learning of mathematics and to organize the operational control of independent work, it is advisable to use interactive guidelines, integrated with applications written in different high level languages. The contents of the online guidance: explanation of the basics of the method, giving concrete samples of application using multimedia technologies; generated with the help of information technology options of the model jobs; tasks of a creative nature with elements of research work. Thus, students receive the first skills of independent work should take place in the classroom under the guidance of a teacher, require reliable and timely monitoring of independent work, appropriate use of information technology to reduce the burden on the teacher.

Pavlenko F.N., Pikhtilkova O.A., Chetverikova A.G.
TO THE QUESTION ABOUT ORGANIZATION OF THE INTRODUCTION COURSE "MATHEMATICAL PROCESSING OF EXPERIMENTAL DATA" ^{[№ 7 ' 2015]}
The various approaches to introduction of the course "Mathematical Processing of Experimental Data" are considered in the article. It is noted that application of traditional statistical approach has a lot of essential shortcomings. The possibility of experimental finding of the necessary number of direct measurements of physical quantity sufficient for receiving the limit absolute error is proved. It is offered to imitate results of direct measurements by means of a computer mathematical MathCAD package, generating the random variable having normal distribution. As a result of numerous measurements there is not displaced estimation of an average square deviation providing a limit absolute error of result. Expediency of finding of absolute errors of results of indirect measurements by means of a method of borders for which it isn't required the knowledge which is far going beyond the school program is proved. Features of application of this approach to processing of results of indirect measurements are illustrated on two examples . Expediency of use of the interactive methodical instructions integrated with a computer mathematical MathCAD package for increase of efficiency of assimilation of this course by students of the natural-science and engineering directions is noted. In this case the operating control of correctness of mathematical processing of experimental data in audience leads to sharp increase in motivation of students to studying of the considered material.

Kazakova O.N., Pikhtilkova O.A., Pikhtilkov S.A.
ABOUT ONE IMPLEMENTATION OF TORUS CRYPTOGRAPHY ^{[№ 3 ' 2015]}
The most popular cryptosystems with public key are: RSA codes, shifrosistem El-Gamalya, Mac-Ellis's shifrosistema and elliptic cryptography. Now the elliptic cryptography is considered as the most successful system providing good cryptofirmness in case of smaller key length. Recently there were works on torichesky cryptography where the new shifrosistem of CEILIDH based on algebraic Torahs is offered.

Mescherina E.V., Pikhtilkov S.A.
ON SOME PROPETIES OF LIE ALGEBRAS INNER IDEALS ^{[№ 9 ' 2013]}
The concept of the inner ideal Benkart Georgia was introduced. F. Lopez, E. Garcia, G. Lozano investigated the notion of inner ideal with respect to the Artinian Jordan pairs with. In this paper we study some properties of inner ideals. It is also considered the definition of Artinian in three senses and communication between them. Artinian special Lie algebras was considered earlier by Y.A. Bahturin, S.A. Pikhtilkov, and V.M. Polyakov.

Kucherov A.A., Pikhtilkov S.A., Pikhtilkova O.A.
ON THE HOMOLOGOUS DESCRIPTION OF LOCALLY NILPOTENT RADICAL FOR THE SPECIAL ALGEBRAS OF LEE. ^{[№ 9 ' 2010]}
In the work the authors discussed the possibility of determining the locally nilpotent radical of the special algebra of Lee in the form the intersection of the nuclei of irreducible ideas, irreducible PI-ideas and finite-dimensional irreducible ideas. It is shown that the locally nilpotent radical of the special algebra of Lee above the field of characteristic zero is contained into the intersections of the nuclei of irreducible PI-ideas and this part is strict.