Abstract
<jats:p>The formation of students’ mathematical competence in the process of studying higher mathematics is an important factor in ensuring the professional training of future specialists and developing their analytical, logical, and critical thinking skills. The purpose of the paper is to investigate the methodological principles of forming mathematical competence in both specialist and non-specialist students, as well as to identify effective pedagogical technologies and digital resources that contribute to the development of theoretical knowledge and practical skills. The logic of the paper involves systematizing theoretical provisions regarding mathematical competence; analyzing pedagogical technologies, the integration of digital resources, and practice-oriented tasks; and summarizing methodological approaches for forming a comprehensive system of competencies. The research methodology is based on general methods of analysis and synthesis, comparison, generalization, abstraction, and modeling, which allow for the systematization of approaches to teaching higher mathematics and evaluating the impact of various methodological and digital tools on the development of students’ mathematical competence. The results of the study showed that effective formation of mathematical competence is ensured through the integration of cognitive, activity-based, motivational, and personal components. The use of problem-based, project-based, and case-based learning stimulates students’ ability to apply mathematical methods in professional and socio-economic contexts, while practice-oriented tasks contribute to the development of algorithmic thinking and interdisciplinary knowledge integration. The integration of digital resources, such as GeoGebra, MATLAB, and Python, enhances motivation, encourages independent work, and promotes the development of analytical, logical, and spatial thinking. The practical significance of the paper lies in the fact that the proposed methodological approaches and technologies create conditions for the holistic development of students’ mathematical competence, improve the efficiency of the learning process, and prepare students for professional activity in the modern scientific and technological environment. The originality/value of the study consists in the comprehensive combination of theoretical knowledge, pedagogical technologies, and digital tools for forming competencies necessary for the effective professional training of both specialist and non-specialist students.</jats:p>