Gah... I am seeing so much fail at the point of AP zilean. Yes, glacial shroud is good, but for SUPPORT zilean. Also, someone said that survivability is more important than damage on zil, so why is it that every set is not running MERCURY TREADS. I cannot stress this item enough for zilean. IF YOU ARE NOT STUNNED, YOU CANNOT DIE. Mercury treads need to be on every zilean build, no questions asked.
As far as items for lots of damage, I start with Tome+Pot, turn the tome into Kage's, for money and AP, then buy Tear of the Goddess, then (usually) Mejais Soulstealer, then Fiendish Codex, then my Mercury treads, then turn the tear into archangel's staff, then deathfire's grasp. Then, if my mejais is not maxed, I will by haunting guise, then zhonya's ring.
My runes are Blue: MPen, Yellow: Mana Regen/5, Blue + Quints: Flat AP. Its pretty powerful being able to do 160 level 1, or 450 with a double bomb level 4 (I level speed before rewind, it saves more lives and gets more kills than an early double bomb would)
@the person who was saying zilean can't deal damage as AP, what do you say when the bombs are doing 1000-1200 and getting TWO of them every 3 seconds? I think 800 dps is nothing to laugh at, especially when it is splash damage and hits at range 650.
Also, to the person above me. Igite is a must on AP Zilean... if they have 4 seconds before they die, you do not want them healing during that time. Also, the 10 ap from the mastery is brutal early game.