Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
this is how i build my amumu..
first i'll get tears of the goddess for mana cap
then the boots
rod of ages for mana/hp/AP
rylai for hp/ap/slow
frozen heart for armor/mana/cooldown reduction/slowing atkspd could help a little as well
deathfire grasp for AP/cooldown reduction
then build archangel's staff from tears for AP/mana cap/magic def
you could jungle early with this build as well
ghost and flash is for running and jumping in/out.. in case you missed your bandage..
40% cd reduction is very helpful for your ulti.. you can have it down to about 70-80 sec i guess.. i forgot.. lol! then try to get the blue buff for more reduction and mana regen.. with this, you can cry all you want.. with some good damage and tanking ability..
or if you want to stack your despair with sunfire capes then you could remove the tear of goddes in the late game as you already have a lot of mana.. with that you'll have more life and passive damage per sec.