The article describes the research carried by the authors in the global improvement framework of electronic tools in distance education. The text discusses digital transformation problems associated with using pedagogical concepts by universities in distance learning utilising learning management systems. In researching the problems, investigated the leading pedagogical technologies of behaviourism, cognitivism and constructivism, and aspects of personality-oriented and project-based learning. It was revealed a main regular concepts methods that can be applied in distance learning. The authors analysed a sample of the most popular LMSs for the sufficiency of functions to implement these pedagogical methods. As a result of research, the studied LMS has a fairly wide range of functions. However, these functions are not sufficient enough to allow all indicated pedagogical methods using. To compensate for the lack of LMS functionality, the authors recommend practising external electronic resources could be integrated into the learning management systems used by universities.

This article deals with the analysis of data obtained from databases of learning management systems to organize studentcentred learning with the application of course adaptation methods by changing the set of asynchronous and synchronous learning tools. The relevance of the research in this area is due to the current teaching paradigm as well as the increasing volume of digital data available to universities. The aim of the study is to investigate the possibility of effectively influencing the educational process based on the results of data aggregated from learning management systems (LMS) using cluster analysis. The results of the study confirm the possibility of dividing students into clusters based on their success in perceiving synchronous and asynchronous educational methods, and the effectiveness of corrective impact on the respective clusters of students to improve academic performance. As a conclusion the author made a statement about the effectiveness of practical everyday application of learning analytics aimed at person-centred learning.

The article presents a variant of optimizing the learning trajectory management system based on big data processing methods in LMS universities. To build an adaptive learning management system at the university, an integrative structure is proposed and a mathematical model for managing the learning trajectory in the "Big data LMS" module is optimized.

The problems and methods of multicriteria selection are discussed using the example of software efficiency analysis. The matrix of criteria (priorities) and methods of its construction are considered. The application of a matrix of criteria (priorities) for evaluating the effectiveness of software is proposed. The analysis results for the analogues of software to account and control contracts at an enterprise using a priority matrix are presented.

In the context of a massive transition to distance learning, learning management systems have become the primary tool for implementing the pedagogical function of universities. The study aims to identify the possibility of using the above systems as a full-fledged analogue of full-time education to implement pedagogical theories in the context of the transition to the learning paradigm. The work results exposed in concrete conclusions; in the discussion section, some recommendations given on the choice of learning management systems.