The paper deals with the theoretical consideration of surface plasmon-polaritons in the graphene monolayer, embedded into dielectric with spatially separated gain and losses. It is demonstrated, that presence of gain and losses in the system leads to the formation of additional mode of graphene surface plasmon-polaritons, which does not have its counterpart in the conservative system. When the gain and losses are mutually balanced, the position of exceptional point-transition point between unbroken and broken PT-symmetrycan be effectively tuned by graphene's doping. In the case of unbalanced gain and losses the spectrum of surface plasmon-polaritons contains spectral singularity, whose frequency is also adjustable through the electrostatic gating of graphene.
The paper is dedicated to the issue of finding ways to increase the efficiency of teaching mathematical logic and the theory of algorithms in pedagogical higher education institutions through the formation of future teachers' professional readiness for teaching the specified type of activity. The purpose of the study was scientific justification and experimental verification of the technology of training students of pedagogical institutions of higher education to study mathematical logic and the theory of algorithms. Methods. During research, a complex of general scientific and special methods aimed at achieving the purpose (theoretical (analytical, retrospective); empirical (diagnostic, observational, praxemetric); pedagogical experiment; statistical processing of empirical data) were used. The results. In the paper the purpose and content of training students of pedagogical higher education to study mathematical logic and the theory of algorithms have been defined, that involves the acquisition by students of higher education of knowledge of the basics of science, the formation of special abilities and skills of using its methods, the acquisition of experience of creative activity, the formation of emotional and valuable experience attitude to activity. The structure of the future mathematics teacher's readiness for professional activity has characterized, which is formed by motivational-axiological, content-activity, professional-personal components. It has been proven that each of the structural components of readiness has its own peculiarities in the learning process and requires the development of their scientific and technological support in order to form the readiness of future teachers of mathematics to learn mathematical logic and the theory of algorithms. The paper highlights the issue of developing scientific and technological support for appropriate training; the influence of the implementation of the proposed technological support on the level of students’ readiness to learning mathematical logic and the theory of algorithms has been revealed. Conclusions. Readiness as an integral criterion of quality assessing of the activity of a future teacher of mathematics to mathematical logic and the theory of algorithms involves the formation of positive motives, significant for the implementation of this type of activity, personal qualities, possession of the means to achieve the goal. The performed research does not cover the issue; it may be promising to further study the issues of differentiating the training of higher education students for the specified type of activity.
The article is devoted to the forms and means of information and communication support for students of mathematics in the pedagogical institution of higher education. The main purpose of the article is to define and characterize the forms and means of information and communication support for teaching mathematics in a pedagogical institution of higher education. To achieve this goal, the authors used the following research methods: analysis and generalization of scientific and methodological sources, government documents on the research topic for theoretical justification of the problem, modeling, synthesis of data. The results. The introduction to this article presents a theoretical analysis of educational technologies, in particular, highlights the «information technology» and defines the essence of this concept. The authors define the pedagogical goals of the use of information technology, as well as provide a classification of pedagogical software. The article highlights and substantiates computer training programs used in higher education institutions in the study of some disciplines, which by their purpose are divided into control (tests, questionnaires, etc.), reference and information (databases, dictionaries), modeling and electronic textbooks. In the process of analysis, the means of information and communication support for teaching mathematics in a pedagogical institution of higher education are identified: computer training and control programs (electronic textbooks, workshops, test systems, simulators), expert systems, electronic libraries, telecommunications, e-mail, teleconferences) and multimedia systems. Conclusions. The authors proved that spreadsheets and integrated mathematical packages can also be widely used in teaching students of mathematical disciplines. Integrated mathematical packages such as Matlab, MathCad, Maple, Mathematica are singled out and briefly described. It is noted that one of the leading types of ICT is computer telecommunications, in the system of mathematics education the use of the following types of computer telecommunications as teleconferencing, e-mail, electronic bulletin board and other Internet capabilities is quite possible. So, modern MultiMedia tools allow you to create a variety of information environments that increase the level of emotional perception of information, and to develop the ability to implement various forms of independent activities for information processing.
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