This build is useful for all lines, but especially fore mid.

This build not prefered "only AP" style, but it contains moreover : Health, Mana, Mana Regen and Magic Penetration

I have 9 Greater Marks of Insight - because I need Magic Penetration
Next I have 9 Greater Seals of Clarity - because I still using "Q" and need Mana Regen
Then I have 9 Greater Glyphs of Force - because I need some Ability
And 3 Greater Quintessences of Potency - the same reason as Glyphs :)

My Masteries are focused on AP and HP

The "core" of this buld is Rod of Ages because it gains some HP and Mana, and other things prefer AP and Magic Pene

I focused on "Q" because I like its low cooldown and high damage - but you must be fast and tactical
Spell W i need only because it slows enemies and reduces their Magic Resist so I can spam spell Q
The second spell which I focused on is spell "E" but it devours to much mana
And the ultimate I improved when i could = LVL 6 , 11 , 16

Karthus most help team with his Wall of Pain - slows and reduces armor and magic resist

When Karthus meet some heap of minions only use "E" and it's done :)

Karthus can jungle too with his "Q" and "E" spells