Alright AP Amumu probably isn't the most viable build, at least for ranked games. But it is a very fun champ to play and you can really catch people off guard with the burst he can put out. AP Amumu requires skill and good decision making to be successful.

Pros:
- Great Burst
- Crowd Control
- Good Ganker
- FUN!!
Cons:
- Almost worthless during down time.
- Not completely but somewhat ult dependent.

Basic ap runes:
Pretty interchangeable but I use.
Greater Mark of Insight
- Always need magic pen.
Greater Seal of Replenishment
- Mana regen is a good choice imo. Despair is constantly draining mana.
Greater Glyph of Focus
- Shorter CD on spells is helps reduce down time.
Greater Quintessence of Insight
- Again magic pen.

Masteries I use for almost all AP champs.
"Switching clarity and ghost out if not using those masteries of course."

Sorry, don't have time to finish atm but will add more info and possibly throw some gameplay videos in here. Enjoy.