Archangel's Staff x2 (400 + 1000 mana, 25 mp5, 45 AP + 3% mana = AP)
Why?
good mp5 regen for mid game
you can last longer in team fights and recall less often
more mana you have the more powerful you become
2 of this item gives you 6% mana = AP

Mercury's Treads (25 MR, Enhanced Movement 2, 35% Reduced C.C.s)
Why?
increased survivability

Rabadon's Deathcap (155 AP, all AP increased by 30%)
Why?
can double your AP
messes the other team up for a bit when your DPS is doubled
E.X. you have 250 before deathcap, after deathcap 250 + 155 = 405 * 30% = 526.5 AP

rod of ages (450 HP + 180hp, 525 mana + 200 mana, 60AP + 20AP)
Why?
increased HP for survivability
increased mana for longer fighting and increases AP (Archangel's Staff)
increased AP also
math with death cap and 2 Archangel's Staffs
725 * 6% = 43.5 AP
43.5 + 80AP = 123.5 AP
123.5 * 30% = 160.55 AP after 10 mins
Zhonya's Hourglass (50 armor, 100 AP, Active: invulnerable and untargetable for 2 secs)
Why?
armor and active for survivability
100 more AP helps too (130 AP total with death cap passive)

this is how i play heimer
earthfother_06-08-11_21-02-08.lrf
need LoL Replay to watch

june, 26, 2011
Frozen Heart changed to Zhonya's Hourglass
For better survivability

aug 06, 2011
item added Kage's Lucky Pick (25 AP, 5g per 5sec)
why?
more gold, has little set back on build early game
sell building secound Archangel's Staff