This lecture was the first lecture on network flow. The lecture had been given last year using activities, so the activities were already present in the lecture. (Last year's starting point was a little bit later in the lecture, so there had been more activities planned). This year, the lecture started with quite a few definitions before getting to the first activity. The reason for using Tablets was to have students do the first activity - to work a non trivial example. I wasn't that thrilled about the other activities in advance - although the second one did work out well in having students work together.
The first problem was to find a maximum flow in a moderately complicated graph. The goals were to ensure that students were familiar with the problem, and were challenged by an example. The problem had been designed so that it took a little bit of work to find the solution: so that the first choice did not give a maximum flow. The problem was also designed so that the maximum flow did not saturate the source or the sink.
This problem was the right level of difficulty: the majority of the students did find a flow of size 65 after some search. When discussion the solution, I asked if there could be a flow of size greater than 65 - one student argued that a particular node would be blocked - showing that there was some wasted capacity leaving the source. A second student argued that the minimum cut was 65. Introducing the minimum cut through an example the students had played with worked very well
This activity was to find a pair of augmenting paths in a graph. Before the activity augmenting paths had been defined - including a discussion of augmenting against the flow. There were two paths in this example - one simple augmentation, the other augmenting against the flow. There was a lot of discussion between students, explaining the augmentation process to each other, and all solutions submitted were correct - so there wasn't much need to explain the answer. This activity worked very well with students sharing tablets.
The final activity was to have a student draw a residual graph, after being given an example. This activity was probably unnecessary, and too easy. The concept is simple enough that it is not necessary for students to work through an example for reinforcement.
