The use of SCM Maple in solving problems on calculating geometric probability

Abstract

The introduction of modern information and communication technologies in the teaching of disciplines with a mathematical component, including probability theory and mathematical statistics, is an urgent educational and methodological task. Maple, the computer mathematics system can be considered a powerful tool for solving it, as it provides a wide range of opportunities for using an intellectual environment for mathematical research of various spectrums and levels of complexity. However, despite the existing examples of using the Maple computer mathematics system to solve problems with elements of vector algebra, function theory, mathematical analysis, and mathematical modeling, the use of this powerful tool to solve problems in geometric probability has not been practically studied. This paper emphasizes that the development of applied materials with the use of computer mathematics systems in teaching probability theory and statistics, which relate to improving visibility and algorithmization, will help higher education students master the basic stages of solving typical probability problems, their unification, and the use of programming elements. The purpose of the work is to solve the problem of using the Maple computer mathematics system in the educational process when solving problems of calculating geometric probability of different levels of complexity. The paper demonstrates the capabilities of the graphical package and the mathematical analysis package of the Maple computer mathematics system in order to improve the visualization and simplify calculations in problems requiring the calculation of the area or volume of objects. The developed code snippets in the Maple computer mathematics system allow to build appropriate shapes in an automated mode, calculate definite and multiple integrals when solving typical problems of calculating geometric probability. This will make it possible to use the proposed developments in the design of new types of tasks.