The article provides a possible option of how first-year students of Russian universities adapt to mastering higher mathematics. The purpose of the research is the development of methodological approaches to designing an online course that recaps school math material in a short period. The concept of individualization of educational activities is used as the main design method. Online training is used as the implementation technology. The article provides an overview of scientific papers on the use of an individual approach to learning and online resources in teaching mathematics. The social survey of first-year students confirmed the relevance of the stated purpose. The authors describe the design methodologies of the online training by taking into account age, social and psychological characteristics of students, and the opportunity for developing individual educational trajectories. The authors set the objectives of the course and structuralize each topic. Instructional content is developed in accordance with step-by-step leveling on mastering educational material. Extra attention is given toward presenting educational information in ways that take into account different types of cognitive processes. Foreign students who receive education in Russian universities are also welcomed to the online course to get familiar with the mathematical terminology in the Russian language.Acknowledgments: The authors sincerely thank the editors, the staff of the journal, and the three anonymous reviewers for helping improve the manuscript. We are grateful to all the authors whose research has been used, and hope that we managed to develop some of their ideas. In particular, the ideas concern aspects of individualization of the learning process. Conflicts of Interest:The authors declare no conflict of interest.

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Within the terms of multilevel training the to-be-economists are being taught to solve complex problems, comprising such tasks, as the analysis, forecasting and decision making in the real world. At that, the training standards place the main emphasis on the learners� ability to apply knowledge, skills and personal qualities (i.e. competences) in future professional activities, rather than on the educational content to be mastered. Competence-based approach is shaped through mastering various disciplines in the course of solving cross-disciplinary tasks. Of such nature are the cases, while the whole instrumental toolkit for mastering cases relies on the case-study method, or case-method. The authors assume, that the competences, stipulated by the Advanced Mathematics curriculum for bachelors in Economics, can be developed by means of the above mentioned case-method. The experiment, aimed at teaching the fi rst-year students of the Financial University, as described in the paper, is based on implementing the competence- based approach in training the to-be-economists.

The transition of the economy to a digital format requires universities to train graduates with special competencies. The most important of them, according to the government and employers, is the competence of communication and cooperation in the digital environment. For its sustainable formation, systematic work is required, covering the entire learning process. The article discusses the possibilities of developing communication competence in the framework of teaching mathematics to first-year undergraduate students of an economic university. The authors see the potential of online tests for building digital communication skills. Regular use of online response systems in the educational process makes it possible to prepare students for some of the features of digital communication: instant immersion on the necessary platform, communication under strict regulations and time constraints. The paper describes the experience of testing students using the Socrative and PollEverywhere resources. Methodical recommendations for the organization of the educational process are given. The effectiveness of using online tests is confirmed by a survey of students.