I worked off of Mahdu Sudan's lecture notes and spent 8 fifty-minute lectures and still required a considerable amount of hand waving.
This year I used slightly less than 6 fifty-minute lectures with much less hand-waving based mostly on Irit Dinur's new proof of the PCP theorem. The six included a lecture by Jaikumar Radhakrishnan on expander graphs on a day I was out of town. I departed from Dinur's writeup in two ways:
- I used Radhakrishnan's version of Dinur's gap amplification argument.
- I used the proof that NP has a PCP using a polynomial number of coins and a constant number of queries in Sudan's notes (Lecture 3, Part II) instead of the long-code test in the appendix of Dinur's paper.
If the students already know expander graphs, the proof takes half as much time as before. Thanks Irit. But still that one lecture proof of the PCP theorem remains elusive.