Lego lectures

I've been pondering the matter of lecture notes of late, and Luca's announcement of his new set of notes prompted me to write this.

Here's what often happens to me. I'm looking to either hand out or prepare an outline for a lecture (or set of lectures) on topic X. Under the principle of (code) reuse, I go hunting for lecture notes that I can link to. I'll often find three or four examples of almost what I need, but either there'll be background information that I have to provide links for as well, or maybe the treatment isn't quite what I wanted.

It seems to me that what one needs are Lego lectures (this is the term coined by my colleague Matt Might when I described my solution to him). My inspiration for this idea comes from reading Dexter Kozen's book on complexity theory.

So what are Lego lectures ?

• One set of notes, a few pages or less, on a SINGLE topic. Very focused, and usually one main theorem. In Kozen's complexity notes, each lecture is (almost) one main result in complexity theory.
• As little referencing of prior notes as possible, and notation declared when needed. 

The idea is that if you have a collection of lego lectures on all topics, you can cobble together a class on a topic relatively easily, and give it your own angle.

I've probably written only two lego lectures in my life: one on tail bounds, and one on the FFT. But they have turned out to be immensely useful, and get reused all the time. I think that from now one I'll model my lectures notes on the lego principle.