МОЖЛИВОСТІ ВИКОРИСТАННЯ ІНТЕЛЕКТУАЛЬНИХ НАВЧАЛЬНИХ СИСТЕМ (ITS) В ЗВО ДЛЯ КУРСІВ ВИЩОЇ МАТЕМАТИКИ

The current state of mathematical knowledge among school graduates in Ukraine and worldwide is analyzed. A negative trend has been identified, requiring urgent changes in educational approaches. This study explores the potential of using intelligent computer-based learning programs to mitigate the adverse effects on the quality of mathematical education. Existing models of such programs are analyzed, and their application to mathematics teaching is examined. Mathematical modeling and analysis of open-source information were used as research methods.The results of the study include the development of mathematical models for intelligent computer-based mathematics learning. A classification of tasks into two subgroups is proposed: simple tasks (focused on algorithm application) and complex tasks (focused on algorithm creation). Key differences in the implementation of learning models for each class of tasks are examined. Particular attention is paid to tasks involving algorithm creation, such as theorem proving and formula derivation. A novel approach to teaching the resolution of such tasks is proposed, considering their unique structure and complexity.Additionally, the potential of using generative artificial intelligence to automate the creation of unique tasks and databases is explored. A combination of algorithmic precision and lexical flexibility of generative AI models is proposed to build comprehensive models for any educational task. Existing projects and technologies in this field are analyzed, with a comparative assessment of their advantages and disadvantages. A promising and underexplored area is identified—the development of a mathematical user interface for automated theorem-proof verification systems, which is crucial for improving the quality of mathematical education.The results of the study open new opportunities for enhancing intelligent learning systems and have practical value for engineers and entrepreneurs. The work provides researchers with a foundation for further investigations in the field of mathematical education automation and its adaptation to modern challenges.