The dissertation substantiates the theoretical and methodological principles of the fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications», the terminological apparatus of fundamentalization of mathematical training is specified, the concepts and structural-functional model of implementation of the fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications» are developed. The essence of the fundamentalization of knowledge in the socio-historical context is defined as the separation from all the accumulated scientific information of the main basic invariants that ensure the transition of science to a new level. The phenomenon of fundamentalization is characterized as the passage of scientific knowledge through «epistemological», «synergistic», «synthetic», «dialectical» stages and their exit to a new level of development - a new round of fundamentalization. The concept of fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications» has been built, covering theoretical, methodological and technological concepts, which provide for the selection and justification of general scientific and specifically scientific approaches, observance of general didactic and specific of approaches.
The fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications» is defined as the concept of improving the quality of mathematical training, which involves the construction and implementation of a pedagogical system in the educational process, based on the identification of fundamental mathematical knowledge and skills for professional direction; changing the content of mathematical disciplines as a result of a strict selection of material, determining the invariants of the mathematical apparatus, which ensures the potential of professional adaptability and realization of the own educational trajectory of future bachelors in the field of knowledge «Electronics and Telecommunications».
Given the fact that the fundamentalization of mathematical training is the basis of its professional focus, the formation of professionally oriented mathematical competence is substantiated through the implementation of a pedagogical system for the fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications», a matrix of professionally oriented mathematical competence is built, the elements of which form the components of professionally oriented mathematical competence competence (motivational, cognitive, design- algorithmic, operational-activity). The pedagogical conditions for the fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications» are substantiated, including: the selection of fundamental sections and topics of higher mathematics - basic for future specialists, systematic influence on the formation of motivation to study mathematical disciplines, formation of the motive for acquiring knowledge; strengthening of research and independent work; regular systematization and classification of acquired knowledge, taking into account the structuring of educational material; introduction into the educational process of the educational and methodological complex of the fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications»; application of information and communication technologies in the process of fundamentalization of mathematical training of future bachelors in the field of knowledge «Electronics and Telecommunications».
The criteria, indicators and levels of formation of the components of professionally oriented mathematical competence have been clarified. The result of the implementation of the pedagogical system of fundamentalization of mathematical training in the educational process is the improvement of mathematical training, in particular, the positive dynamics of changes in the levels of formation of the components of professionally oriented mathematical competence.
According to the results of the conducted research, the effectiveness of the pedagogical system of fundamentalization of mathematical training was established, and the effectiveness of the structural and functional model of the pedagogical system of fundamentalization of mathematical training was ascertained.
