Developing the Professional Competencies of Future Managers Through the Application-Based Problems in Advanced Mathematics

Abstract

The current paradigm of higher education in Ukraine, particularly in the context of training management professionals, is undergoing fundamental transformations. The shift away from a purely theoretical instruction toward a practice-oriented approach requires a rethinking of the role of foundational disciplines, among which advanced mathematics occupies a central place. A key element of this transformation is the introduction of applied problems, which serve as a bridge between abstract mathematical concepts and the real-world challenges of managerial activity. The “Advanced Mathematics” course serves as the foundation for shaping the student’s academic profile. The aim of the course is not only to master the terminological apparatus but also to develop students’ cognitive flexibility: the ability to construct complex logical structures, manipulate abstract categories, and gain a deep understanding of the integration of mathematical methods into the global technological context. Strengthening the mathematical foundation of students in economic disciplines is a primary object ive, as mathematical tools form the basis of professional skills. Knowledge of mathematical modeling methods and numerical data analysis is a prerequisite for solving practical economic problems and making efficient managerial decisions. The relevance of this article stems from the contradiction between the traditional abstract nature of advanced mathematics courses and the real needs of business in a wartime economy. Strengthening the applied focus through case studies and integration into LMS platforms allows for adapting manager training to conditions of uncertainty, where mathematical tools become the foundation for forecasting and minimizing risks. The process of training future managers requires a special approach to teaching mathematics, as students in this field often tend to perceive information through a humanities or social-behavioral lens. In this context, applied problems play a critical role in overcoming the psychological barrier between theory and professional practice. The implementation of this system of problems not only ensures a learning effect (the ability to apply mathematics in economics) but also plays an important developmental and educational role, shaping independent specialists with well-developed analytical thinking.