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The article sums up the outcomes of mathematics teachers’ experience and presents the results of scientific-methodical work of the Department of Higher mathematics of Bauman Moscow State Technical University on the problems of training engineering students, implementation of learner-centered educational paradigm, the integration of mathematics in University science education. The authors present a system of theoretical conceptions worked out by a teaching staff of the Department of higher mathematics on engineering education in general and on mathematics as a core subject in engineering training and express their view on the relationship between technical and mathematical education. On theone hand, the students’ research activities of studentsis treated as anindependent problem, and on the other hand + in relation to studying physics and mathematics. The article discusses the possibility of organization of students’ independent cognitive activity involving students in the assessment workshop, the implementation of interdisciplinary connections in physics and mathematics. The article is addressed to the mathematics teachers at engineering universities and students of physical and mathematical faculties of universities, and to the methodologists.