The previous talk in the series is here. The next talk in the series is here.
This is the first video where the course gets down to some actual mathematics. It is quite basic, but introduces ideas that will be used in several places in more sophisticated arguments later on.
We start with the average of a random variable lies between its minimum and its maximum, then consider double counting. Finally, we discuss trees, Euler’s formula, and the number of edges in a planar graph.
This video was produced by Tim Gowers as part of his Part III course at the University of Cambridge. Printed notes for this course are available here.