On the Issue of Developing Research Competence of Higher Education Students in the Process of Solving Problems in Probability Theory

Abstract

The continuous improvement of the content and curriculum of mathematical disciplines to ensure the development of research competence of higher education students is a relevant educational and methodological challenge. Expanding the range of problems of varying complexity and form, including professionally oriented ones, can contribute to solving this issue. A powerful tool that not only simplifies calculations, facilitates verification and analysis of the obtained results, but also automates the solution of a formalized problem with a step-by-step demonstration, is the Maple computer mathematics system. Despite well-known and widely used examples of research mathematical problems, the range is usually limited to the use of elements from analytic geometry, differential and integral calculus, differential equations, etc. This paper emphasizes that the development of problems with a research component in the study of probability theory and statistics will help to cultivate the ability to carry out research work, formalize problems, select solution methods, and analyze the results at a modern scientific, technical, and professional level. The purpose of the paper is to address the issue of developing research competence of higher education students through solving problems in probability theory. The paper presents examples of probabilistic problems with a research component, along with code fragments for automated calculations using the Maple computer mathematics system. This will help students gain research experience and form a foundation for solving complex professional tasks within their chosen specialization.