If you haven't seen a lecture from Donald Knuth's lecture series on trees, I suggest watching this video. Every year, at the end of the fall semester at Stanford, Donald Knuth gives a lecture on trees, a sort of Christmas tree lecture series. In honor of this, I've decided to give my own Christmas tree lecture, though my treatment will be much less advanced than Knuth's. Instead, I will focus on the basics.
This week I'll cover some fundamental properties of trees. Some of these properties I will prove during the episode; while others I will leave for you to attempt. I'll present a proof sketch of each property to make each proof easier to digest. I still recommend reviewing proof by contradiction and other useful proof techniques.
One technique covered will be finding the diameter of a tree. There are two well-known techniques for finding diameters. But why do they work? Tune in to find out!
See you live! (time, stream, channel)