The article reveals some approaches to the interpretation of the concept of the cognitive component of mathematical competence, reveals some ways of forming the cognitive component of mathematical competence of students of technical specialties. Based on the analysis of literature sources, the purpose and objectives of the study, the research hypothesis are substantiated. The purpose of the study is to check the effectiveness of the proposed method of improving the level of mathematical training of students of technical specialties (STS) in the form of checking the formation of the cognitive component of mathematical competence of STS. The method of improving the level of mathematical preparation consists in its fundamentalization. The paper also presents a statistical verification of the reliability of the obtained results. The methodological apparatus of the research covered modern principles and approaches of higher school pedagogy. The main approaches to improving the quality of mathematical training through its fundamentalization include: synergistic, systemic, activity, competence, knowledge-activity, personality-oriented; teaching and research approach. Also, the idea of forming professionally oriented mathematical competence is substantiated in the work. The work describes the structural scheme of the concepts of the proposed methodological system for improving the mathematical training of students of technical specialties through its fundamentalization. The obtained results of the study clearly confirm the effectiveness of the proposed concept of improving the quality of mathematical training of STS, and confirm the impact on improving the cognitive component of mathematical competence. The obtained results of the study indicate the need for further development in order to improve the quality and level of mathematical preparation of STS.