**Zoya Kondrashova (Russia), Nikolay Solokhin (Russia)**

Rapid changes taking place at present in the society determine the vector of education development, form requirements to an educated person. The connectivism theory, disclosing the features of education environment under conditions of education digitization, allows to outline the learning strategy in individual subjects. The connectivism education is a complex process including plunging into information environment, maximum use of accumulated knowledge, skills to determine timeliness of the acquired knowledge and its relevance under modern conditions, various trends of communication among participants in learning, ability to detect links among various areas of knowledge, theories, concepts. Objective of the research is to substantiate opportunities of application of connectivism education environment during studying mathematics in higher school, to disclose potential of the higher mathematics course and to confirm experimentally the efficiency of the proposed learning strategy. Methods used in the research were as follows: analysis, statistic methods, generalization, systematization, the method of rising from the abstract to the concrete upon consideration of functionality of digital products, system approach, experimental verification of research results. Results and novelty of the research implied the following: substantiation and development of principles of connectivism learning theory, development of the strategy for construction and implementation of educational programs of higher mathematics course, experimental verification of the dependence between the level of mastering the higher mathematics course and the level of use of digital technologies. The use of the connectivism learning theory allowed to outline the approaches to expansion of content of the higher mathematics course. The main features of the presented course are plunging of students into information environment by means of assignments aimed at maximum use of programs for symbolic mathematics. Studying of certain sections of the higher mathematics course, in particular, analytic geometry and linear algebra, is exemplified based on the developed learning strategy.