Although this concept of a purely AP Amumu is superficially viable, if you look at the way he plays in game, you will see this is not the case. AP 'Mumu is a fairly expensive build... Due to his weak early game, this is a major issue. He is simply out-harassed and thus gains far less gold.
Amumu is meant to be a tank. He has amazing armor, and great skills for preventing damage to teammates through the use of his ultimate, and stun.

I can't give this a thumbs up, and get a full night's sleep, yet at the same time, I cannot give it a thumbs down as I can see this took a lot of time.

EDIT: Needs moar CDR, otherwise you sit there with your despair up, looking like an idiot with nothing else to cast. i.e. Singed.