EJMT Abstract

Graph Theory is known as a difficult topic at the intersection of mathematics, data mining and computer science. Although graphs are theoretical constructs studying arbitrarily complex relationships between objects, their interdisciplinary real world applications are numerous. In addition, students are becoming more familiar with computer technologies, and nowadays there is a wide range of free software packages and technologies allowing to bridge the gap between theory and practice in the context of graph theory. The first objective of this paper is to propose some ideas and use cases of how to make teaching graph theory more understandable and interesting, and the second is to highlight its relationships with other STEM disciplines, including algebra, statistical analysis, big data and software development, adhering to the concept of context-based learning. Our idea is to show students different examples of how certain notions studied in theory can be represented as a graph and visualized using simple computer programs, and also to encourage them to perform their own experiments. As examples, we consider the graph of numbers and their prime factors, given the upper bound; the visualization of a permutation group; simple random graphs and networks of financial time series. These examples were given to a small group of graduate students in computer science as homework projects, but we believe that they can be adapted for a wider audience. Furthermore, we discuss why these graphs are interesting for educational purposes and how to stimulate students’ imagination and creativity in terms of context-based and project-based learning. The examples given in this paper are formalized from a mathematical and graph-theoretical point of view, and suitable for students who have at least basic knowledge in programming and early-undergraduate level of mathematics.