Our course was titled Netzwerke und Komplexe Systeme (Networks and Complex Systems) and rather than going too much in depth in one particular area we covered a broad selection of topics, as we wanted to give students an overview and also an idea of how different disciplines approach complex phenomena. We discussed pure Mathematics topics as the colouring of graphs, algorithmic discussions as the travelling salesman problem, social network analysis, computational neuroscience, dynamical systems, and fractals.

A network of the former monastery in Rossleben, where the summer school was held. The students created the network themselves. To parallelise the task they split up into four groups, each covering one level of the building. They then used this network to simulate the spread of a contagious disease, starting at the biological lab (A35, in red).

A couple of thoughts on what went well and which parts might need improvement for further of such events:

• We did a questionnaire before and asked the pupils some questions like “Do you know what a vector is?” and also concerning their motivation to join the course. This was very helpful in getting a rough idea about their knowledge level.
• We gave them some material to read before the course. In retrospective, it probably would be better to give them something to read, as well as, some problems to solve, such that the learning outcome is clearer and more effective.
• The students gave presentations on topics we choose for them based on their answers to the questionnaire. The presentations were good but a lot of students overrun the allocated time because they were very enthusiastic about the topics.
• The students were also enthusiastic about the programming exercises, for which we used Python and the NetworkX library. One challenge was the heterogeneity in programming experience, this made the splitting up into two groups, beginner and advanced, necessary.
• In contrast to courses covering similar topics at university-level, the students did not have the necessary mathematical background for the more complicated aspects of network science. Accordingly, it is better to choose less of these and allocate time to introduce the mathematical methods, for example, eigenvectors or differential equations, beforehand.
• The students very much liked hand on exercises, for example, the creation of random networks of different connection probabilities with the help of dice or the creation of a network of the floor plan of the building in which the summer school was held, as shown in the Figure.

It was great fun to introduce the students to the topic of network science and I strongly can recommend others to organise similar outreach events! You can find some of our teaching materials, including the worksheets and programming exercises in the original German and a translated English version, online. A paper describing our endeavours is under review.

Four Erdős–Rényi random graphs as generated by the participants by rolling dice. A twenty-sided dice was used for the probabilities p = 1/20 and p = 10 and a six-sided dice for p = 1/6 and p=1/3. This fun exercise allows the discussion of degree distributions, the size of the largest connected component, and similar topics for ER random graphs.