MAPLE AS A TOOL FOR VISUALIZATION AND ANALYSIS OF GRAPHS IN THE COURSE OF DISCRETE MATHEMATICS IN THE PROCESS OF PROFESSIONAL TRAINING OF FUTURE MATHEMATICS TEACHERS

Abstract

Discrete mathematics occupies a special place in the education of future mathematics teachers. In a pedagogical context, it is important for future mathematics teachers to have the skills of visualization and analysis, which allows for a deeper understanding of the essence of discrete structures and the mechanisms of their functioning. Visualization in the form of graphs is a central tool for representing discrete structures in Maple. The system supports the construction of graphs as objects consisting of nodes and edges, which can be oriented or unoriented according to educational tasks. This allows not only to show the structure, but also to conduct its detailed analysis. One of the key advantages of Maple is the ability to create interactive and dynamic visualizations of graphs. The system supports changing the graph parameters in real time and demonstrates the reflection of these changes, which gives students an understanding of the internal interaction in the structure. The use of animation contributes to clarity when demonstrating algorithms for working with graphs, such as breadth-first or depth-first traversals, search cycles, or solving routing problems. This allows you to create experimental training modules where students can conduct research, test hypotheses, and observe the behavior of mathematical structures in a dynamic mode. This approach activates creative potential and stimulates deeper assimilation of the material. Along with the construction, Maple provides a developed analytical toolkit for studying the structural characteristics of graphs. Using the system allows you to calculate various parameters, such as vertex degrees, path lengths, and cycle definitions, which are basic indicators in graph theory. The system also supports the identification of specific types of subgraphs, such as trees or covers, which is useful in teaching discrete mathematics and its applied aspects. The use of functions for finding optimal routes, minimum covers, and other optimization problems is especially important, as it allows you to consider not only static but also applied aspects of graph research. These opportunities are fundamental for developing practical skills important in the mathematics teaching profession.