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The problem of individualisation in education in terms of e-learning remains relevant despite a lot of research done in the area. The present article is intended to review existing education practice individualisation in e-learning and to determine the prospects of development of adaptive e-learning courses that provide the student with an individual educational environment content which focuses on the individual characteristics of students. The authors arrive at the conclusion that building an individual educational trajectory in the adaptive e-learning course has a significant advantage in organising education in the electronic environment for both the student and the teacher. The main feature of these courses becomes the selection of educational content that best matches the individual abilities, needs and needs of the student in an electronic environment. The results of the research are universally applicable and can serve as a basis for organising adaptive web-based teaching not only for mathematics, but also for other disciplines in institutions of secondary, higher and further education

Adaptation of learning process for students with regard to their individual characteristics has currently become topical. The article proposes a technological approach to development of adaptive e-learning system, principles of its elaboration and description its structure and components. The scientific novelty of the study consists in structuring the educational content as a hierarchy of terms, original methods and algorithms of adapting learning material, and the learning outcomes assessment model which provides for the assessment of the level of subject competence development. The structure of the system which includes the educational content model, the user model, the adaptation model, and the learning outcomes assessment model is presented in the article. The proposed approach to development the educational content model is based on the integration and development of the methods of logical-andgnoseological concept analysis with graph theory methods. The adaptive elearning course of a mathematical discipline is developed and implemented into educational process. System of web-based teaching includes a set of organizational and pedagogical conditions contributing for student to acquire knowledge and experience, to develop the skills which result in developing competence required for his or her professional activities. Materials of this study are of interest for both teachers who develop electronic educational courses and managers of educational institutions interested in implementing such courses into educational process

This article is devoted to the development of algorithms for the adaptation of mathematical educational content and their implementation in the e-learning system. The adaptation of a mathematical content consists in the selection of an optimal edition of the material that best suits the individual characteristics of the student. The novelty of the work is the organization of the adaptation algorithms of the educational content in a three-level system: "introductory content adaptation" (an adaptation of the content of introductory materials of the discipline based on the initial level of students) - "current adaptation of the content" (an adaptation of the mathematical content based on current effective actions of students in the electronic course) - "appraisal-correcting adaptation" (an adaptation of normative parameters of the level of assimilation of materials, taking into account the results achieved by students). The introduction of the proposed three-stage system makes it possible to implement in individual educational trajectories and to form for each student a personal space of mathematical educational content that adapts to its level of mastering the material, which helps to improve the quality of instruction in mathematical disciplines. An approbation of the proposed algorithms was carried out in the adaptive e-course in discrete mathematics, implemented at Siberian Federal University in Russia.

The rapid development of digital technologies and the direction of education modernization, which takes into account the individual characteristics of students, allows us to talk about the need to ensure the individualization of the educational process in the electronic information and educational environment. Adaptive e-learning courses are a promising means of individualizing the educational process, providing the construction of individual learning trajectory based on the level of academic performance, perceptual modality and the level of student activity in the electronic environment. The experimental work was among students of the program 09.03.02 "Information systems and technologies" of the Siberian Federal University. The experiment involved 115 students in the study of the discipline "Mathematical Logic". Analysis of observations and evaluating the effectiveness of adaptive e-learning course in the educational process was carried out using the Kruskal–Wallis test by ranks. As a result of the experiment, it was revealed that at the beginning of the experiment there were no statistically significant differences in the groups (χ2 = 0,26005, p = 0,6101), at the end of the experiment, p < significance value 0,05 (Kruskal-Wallis χ2 = 127,57, p <0,001). This indicates that the compared groups are significantly different and the experimental hypothesis about the effectiveness of introducing the developed adaptive e-learning course into the educational process is confirmed. These results demonstrate that the introduction of adaptive e-learning courses, which ensure the construction of learning trajectories, into the educational process, is effective and has a good potential for the individualization of teaching mathematical logic in an electronic information and educational environment.