This is how The Senate plays Kassadin
Masteries: 9/0/21, as much cooldown as possible + 15% spell reduction.
Runes: Attack speed for red runes, max health for yellow runes, max mana for blue runes, split your quints evenly between these three
Items: STACK ROD OF AGES OH MY GOD.
Kassadin is a freaking beast when you stack Rod of Ages. It's far superior to any kind of pseudo-physical DPS. By the time you get your first Catalyst done, leveling up is basicly your way of staying in the battle, outweighting the need to get any health regen or mana regen.
By mid game, you're already a monster, only gaining momentum as you move into late game.
What a lot of people don't realize is the core of Kassadin's damage is done through stacking his teleport. With the disgustingly huge mana pool you get from Rod of Ages stacking, you can get teleport up to level 6 or 7, dropping 700 mana on a massively powerful bit of magic damage. Sure, teleporting in a way that saves mana is nice, but you need it to do damage.
Eventually you'll have more HP then your tanks and you'll be able to out-damage most of your casters. Oh and don't forget. Kassadin takes 15% less damage from magic. Toss that on your incredible escape abilites, disgusting mana pool, crowd slow and powerful silence. That's a nasty peice of work right there.