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The aim of improving the international competitiveness of the higher education Russian system at the global level by increasing the number of foreign students leads to the fact, that pre-university training is becoming essential for next years at higher educational programmes.Pre-university mathematical training of international students contributes to the scientific style formation of speech skills, which is so useful in higher educational institute. This article highlights some of the features of foreign students pre-university mathematical training.Design of “Mathematics” course methodical ware for preparatory departments of higher educational institutions is an important element of the educational process. Features of mathematics teaching are shown by the example of such important for foreign students pre-university mathematical training branch of mathematics like the set theory.The article also gives consideration to such aspects of mathematics teaching for foreign students as the inclusion of text mathematical problems in the “Mathematics” course programme for helping to achieve lexical skills and abilities, as well as the organization of individual work of the students with the use of information and communication technologies.The paper refers to the collection of exercises and tasks for the “Mathematics” course for foreign citizens studying at the preparatory departments of higher educational institutions, it additionally gives the themes of the course.