This article considers the issue of implementing a model of blended learning to prepare master students majoring in Mathematics (speciality code in Ukrainian educational system “014 Secondary Education. Mathematics”). The research analyses the existing developments of the issue about the use of blended learning while training would-be mathematics teachers. The researchers determined and explained the stages of work on developing the online course “Methods for Teaching Mathematics to Students at Technical Universities”, that is used when students learn methodological subjects of the curriculum. The research describes the development of the theoretical online course model and methodological recommendations on the learning materials and preparing papers for the course. The article offers recommendations related to the course structure. The course developers defined the usability criteria of the educational platforms, determined the stages of course users’ activity, their content, and organization. The research describes the areas of online course activity management, the course tutors’ and moderators’ teamwork is defined as the main condition of its development and support. In order to prove the efficiency of implementing blended learning of the methodological subjects, an experiment was carried out during the assistant practice in technical universities that master students of the specialization “Mathematics” had. The results allowed confirming the efficiency of students’ practical training during blended learning of the methodological subjects that in its turn encouraged the improvement of the assistant practice results.

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This paper is aimed at studying scientific communication as an integral part of a scientists activity. The authors of this article analysed the development of informational technologies, which gave rise to a new paradigm of scientific communication Research 2.0. In the present study the analysis of research papers, describing models of scientific communication is done. The findings allow to define the structure and content of a comprehensive program of activities, connected to scientific communication in compliance with the Scientific Communication Life Cycle Model. In order to implement the program, aimed at developing core skills through scientific communication of scientists, a target audience, comprising postgraduate students and young researchers in Mathematics and Teaching Methods was engaged. A five-stage program of activities, which was developed, prompted scientific activity of young researchers and gave them an opportunity to learn about means of presenting research results, elements of management, mechanisms for applying the findings. A constructive description of each module of the program is done, actions and a strategy are described, communication between participants and tutors through the platform Higher School Mathematics Teacher is arranged in this research. In order to assess the efficiency of implementing the program, Researcher Development Framework (RDF) is used. The study also presents the results of the activity of young researchers, who were engaged in the program. Following the change in the phase of the development of researchers characteristic features and in compliance with RDF, a conclusion is made about a positive impact of the program on the development of career skills of young scientists, their interaction skills, awareness of professional behavior procedure.

Получена ассимптотическая формула для верхних граней уклонений сумм Фейера на классах интегралов Пуассона. В ряде случаев полученное соотношение обеспечивает решение задачи Колмогорова-Никольского для сумм Фейера и классов интегралов Пуассона. Ключевые слова: ряд Фурье, задача Колмогорова-Никольского, класс интегралов Пуассона