Abstract

Distance learning systems in the form of electronic textbooks being actively developed and used in real educational process of school and university. Such a spread of technology necessitates scientific research in the field of their design and application. Scientific researches currently being conducted in the framework of didactics, psychology, information technologies, computational mathematics, are multidisciplinary, since the solution of didactic problems is the object of research in other scientific fields. At the same time, there are many prerequisites for research, the subject of which can be an electronic textbook. Reason of the need for interdisciplinary research in the development of electronic textbooks, as a result of solving a multitasking problem, is presented as the goal of this article. The main part of the work presents the key features of the architecture of a distance learning system (DLS) from the standpoint of designing it as a software product. In addition, the proposed description of specific mathematical algorithms that have been implemented in practice in the construction of electronic textbooks of the Moscow Aviation Institute, as well as new mathematical approaches to the design of an electronic textbook. One of such approaches is represented by graphed orientation. The model of generating of time-limited text is analyzed, in which weighted convolution of normalized values, namely deviations of the test complexity from a given level and quantile of test run time, is used as an optimization criterion. The basic modern technologies and programming tools that are used in designing the architecture of the control shell and make it possible to effectively apply the obtained mathematical algorithms when solving didactic problems are described. The conclusion contains a conclusion about the effectiveness of the cumulative research of specialists in various scientific fields, which is supported by the implementation in practice.

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