There's basically a few standardized item builds for amumu mostly mentioned above me
(All builds start with philo's > ninja tabi...or boots of choice)
-AoE damage/Mixed defense
Sunfire
Sunfire
Banshee's Veil (Or if you choose, Force of Nature, but i highly prefer banshee's)
Guardian Angel
-AoE slow/damage / mixed defense (but not as much armor as above)
Sunfire
Rylai's Scepter (1.5s slow with every tantrum or bandage toss is nice, more AP, and HP to boot)
Banshee's Veil (Or if you choose, Force of Nature, but i highly prefer banshee's)
Guardian Angel
-Heavier damage while still getting good hp/mana but armor/MR come way later
Rod of Ages
Rod of Ages (or skip #2)
Rylai's Scepter
Guardian Angel
Banshee's Veil (Or if you choose, Force of Nature, but i highly prefer banshee's)
basically....you can use offshoots of any of those 3 core builds and you rarely can go wrong because of how versatile and amazing amumu is =P