The runes Bring extra gold into play which is needed for this very expensive build. The mana boosts help with both Ryze's natural AP bonus and the Seraph's Embrace.

These are pretty straight forward. AP offensive and mana utilities. The utilities spell boost is for a temporary health boost and flash cooldown.

The first thing you should buy is a tear of the goddess. B back when you can buy it. It will begin to charge the Tear/Archangel/Manamune passive. Get boots. You can instead get Ionian Boots Of Lucidity. When and which enchantment you buy is up to you. Turn the Tear into an Archangel Staff and buy another Tear.
SPECIAL ****
What will happen is when you buy the Staff is that all the mana you earned on the Tear will transfer over to the staff. It will also appear on the new Tear but will not be added to your mana. When you max the mana bonus the Staff will transform into a Seraph's Embrace. The Unique Passive bonus mana will be turned into item stats allowing a new Unique Passive of the same type to take effect. The new Tear will reset it's bonus mana to 0 and begin to recharge. The end result is 3000 bonus mana and 3% of all mana into AP.

Prepare the next staff by upgrading the current Tear and buying another. At this point you should have an Embrace, an Staff, a Tear, and boots. Buy the Will of the Ancients for a little sustainability.

After preparing for continuous charging build the Rabadon's Deathcap. It's passive gives a much greater AP boost than another Staff/Embrace. Also, even with Ryze's rapid fire Overload it takes 60 mins to charge the 3 in this guide, maybe more.

Be sure to grab Overload first because it has the fastest cooldown. It may sound stupid but it is a good idea to fire away at minions when ever possible. Remember that each time you use abilities you get some mana back immediately and increase the amount of damage it will do next time.

I chose these spells because this is a glass cannon. Jumping in to start a fight probably destroying one or more enemies and then respawning is quite more effective than a heal.

Pros
Huge amount of damage
Huge amount of mana to draw from
Spell Vamp heals large chunks at a time
Continuously increasing power
Big Damn Shield
Cons
Large amount of gold required
Long time to full charge
Nothing to reduce squishyness other than the Big Damn Shield