Here are some notes on Compton scattering. And by 'notes' I really mean deriving the Compton equation, the photon and electron energies, etc., and not so much on the discursive side. They have not been heavily proofread yet, but I believe everything is substantially correct.
Consider this your mathematical guide for Compton scattering (chock full of goodies related to the homework), with your textbook filling in the basic background.
I would like to be able to keep up with notes on the same level as the blackbody notes for every topic, but it is unrealistic to do on the fly ... I'll provide what I can.