The classification of competences of graduates of secondary and higher technical educational establishments is presented in the work. On the basis of the list of professional and mathematical competences offered by scientists, the professional-oriented mathematical competences of the future specialist, the most important and relevant for the professional activity of future engineers, are allocated. These include: conceptual, operational-algorithmic, applicable, design.The purpose of the article is to describe an experimental verification of the professionally-oriented mathematical competencies formation of future specialists in the electronics and telecommunications industry. The main research methods used by the authors: theoretical methods: analysis, synthesis, comparison and generalization of the research results of scientific and methodological literature on selected issues; empirical: observation, experiment, questionnaire, analysis of the obtained test results. During the study of higher mathematics, students are encouraged to take actions that promote the formation of skills that are part of mathematical competences. These actions are also performed by the engineer, he also needs to be able to analyze, synthesize, classify. Therefore, the formation of the above mathematical competences is appropriate and necessary for the professional training of the engineer.

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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.

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