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Abstract: The current system of higher education has a focus on fundamentalization, through which students receive the necessary basic knowledge for self-education and the formation of a unified worldview scientific theory in the learning process. Mathematics occupies a special place in the system of Sciences. In training of future teachers of computer technologies mathematics has a significant role and is an important component of basic training. The paper presents the main objectives of mathematical training of students in information science, defines the concepts of "mathematical culture", "math training" and "algorithmic thinking" and describes their relationships. On the basis of mathematical training of students it is possible to form mathematical culture and algorithmic thinking. The paper discusses the main factors influencing low level of quality of mathematical training of future Computer Technologies teachers: a drop in the quality of mathematical training of University entrants, clip-thinking of contemporary students, the low interest of students to studying of disciplines of a mathematical cycle. To solve this problem, the authors proposed a comprehensive approach based on the combination of methodological approaches, such as differentiated, system and personal-activity. Also, a hypothesis is proposed about the efficient use of information technology in teaching mathematics to increase the level of mathematical training of future Computer technologies teachers.