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.