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Introduction to graph theory
Published in Karthik Raman, An Introduction to Computational Systems Biology, 2021
Figure 2.2a shows Euler's sketch derived from the map of the city. Figure 2.2b is, essentially, the first graph that was ever created! Note the mapping of nodes and edges, as land masses (or islands) and the corresponding bridges. However, it is not a simple graph, given that it has parallel edges running between the same pairs of vertices. Also, Euler never drew it in this form, in 1735. Nevertheless, it is easy to paraphrase Euler's 1735 solution (see references [3, 2]) in modern graph theory parlance, namely in terms of the number of nodes with odd and even number of edges! Paths that begin and end at the same vertex of a graph, passing through every single edge in the graph exactly once, are now called Eulerian cycles, in honour of this solution of Euler. Figure 2.3 shows some simple examples of graphs with and without Eulerian paths. Finding Eulerian paths in graphs has more far-reaching consequences than solving the recreational mathematics problems of Figures 2.2 and 2.3, notably in modern biology, for assembling reads from a next-generation sequencer [4].
The potential of recreational mathematics to support the development of mathematical learning
Published in International Journal of Mathematical Education in Science and Technology, 2019
Peter Rowlett, Edward Smith, Alexander S. Corner, David O’Sullivan, Jeff Waldock
It is clear that recreational mathematics can be useful in education in several ways, including for engagement, to develop mathematical skills, to maintain interest during procedural practise, to challenge and stretch students and to make cross-curricular links. In undergraduate mathematics, recreational mathematics can be used for engagement with standard topics and for extra-curricular interest such as via the Maths Arcade. There are also opportunities to develop important skills that we expect of graduate mathematicians, including around problem-solving and communication. The explicit link between the benefits of recreational mathematics in education and the skills expected of graduate mathematicians is not made in the literature surveyed.