We attract an attention to some problems in the fundamental mathematical education of university students and found that it is an actual goal to find and develop some new methods and technologies that allows to improve this education. It is introduced some basic concepts of the interactive technologies of teaching and found a possibility of their using in the process of fundamental mathematical education. In particular we consider interactive technologies for seminar classes that use some aspects of professional education. It is also described some other forms of mathematical education such that discussions in student groups, referring process, comparison of concepts and methods. Basing on our statistical investigations we show that these methodical technologies are rather effective and give a positive influence on the mathematical knowledge of university students.

Keywords: mathematical education, university, interactive technology, seminar

The analysis of causes of insufficient quality mathematical knowledge of students of technical colleges. There are formulated some problems which must be solved for the improvement of the quality of fundamental mathematical education in a technical university. It is introduced a notion of the system of adaptation of the first year students for studying high mathematical course.  Elements of the  realization of the adaptation system are described and main goals of this system are formulated.  It is defined a technology of professional directionality of education in the fundamental  mathematical preparation in colleges. It is described a content of the technology of the professional directionality of  teaching mathematics which consists of regular demonstration of tasks, examples and models connected with the future professional work of students. It is given some results of the experiment of using in some colleges the technology of the professional directionality in mathematical education. It is analized the results of surveys on different steps of using the system of the professional directionality of education which are devoted to the level of students motivation to study high mathematics. It is supposed to involve undergraduate student into research projects in mathematics as one of the directions to improve fundamental mathematical education.

Keywords: fundamental mathematical education, system of student adaptation, technology of professional directionality of education