Amumu was one of the first champs that I bought, and I always loved him. But I always built him tanky-jungle (how he's supposed to be), but one day (a year later since i bought him) I started checking out his ap ratios, and I started to wonder... "could it be that this little fellow could be a freaking mage??"
I started my reasearch on the internet, but all the builds I found were still super tanky, so I decided to start experimenting. Many games later, I finally built my own Amumu AP, with wich I really appreciate playing, even in rankeds. You will see when you play him (spoiler allert - 1000 damage with E with 2.5 sec. cooldown). Well, I hope you guys enjoy playing with this build has much as I do.

If you lose lane, don't worry, just start roaming, do a little of the jungle, ask for ganks, go help out mid, try to get those hidden free kills...
And if you are positive and you already have the 3 first main items, don't be afraid of 1v2, you're damage should already be enough to take anyone down (just don't miss your Q) - that's the wonderful thing about AP Amumu.
Oh, and if you really get confident, stacks never hurted anyone :P