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| 1 | The decline in quality of mathematical training of the students entering the department “Applied Mathematics and Informatics” has negative effect on the implementation of the requirements put in the standard. Therefore, in order to create the conditions necessary for successful training at the University we need to adjust mathematical training of the first-year students. Problems of improvement of quality of mathematical preparation and adaptation of first-year students are relevant not only in our country, but also abroad. In article the works devoted to this subject are considered. As a solution to this problems the authors of this article offered the organization of the leveling course in mathematics. The analysis of typical mistakes made by the first-year students and also the abilities necessary for studying of the main sections of high school mathematics allowed to define the maintenance of the leveling course. The system of multilevel individual tasks; conscious storing of educational material; work in small groups including cross-checking; various ways of math problem solution with identification of their efficiency; critical thinking techniques were used during the organization and carrying out this course. The efficiency of the developed leveling course was noted by the teachers of mathematical sciences and it was also confirmed by the results of the first session. Keywords: mathematical training of students, leveling course of Mathematics, Bachelors of the department “Applied Mathematics and Informatics”, professional competence, methodical features of the organization | 1279 | ||||