Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
About the build.
I believe Sagasus Ryze Guide is just about perfect. For everything ryze related go there!
I just have a few differences that I feel are superior.
Personally I believe rod of ages to not be worth getting and I always rush veil and glacial shroud as the boost they give you is of the uttermost importance, the defensive boost is just way too effective.
ROA is a good item don't get me wrong but so many other items are more useful on Ryze.
I also believe rylais can just about be included in the core part of the build, being able to control targets with the slow adds so much more utility to ryze.
Late game I switch out Sorcerers for Mercury's and substitute the mana resist by getting a void staff. But most games don't last this long.
All this being said some items are situationally more useful which are all explained in Sagasus Ryze Guide.
I use movement speed qunits over health/insight/mana mainly because being faster then most opponents is extremely useful, allowing you to poke and get back with great efficency.
It is a toss up between armor, mana and MRp18 glyphs, all have there uses. Armor for Defensve, mana for more damage and mana regen for..regen.. I tend to find that regen is not useful enough to help ryze, by the time I use all my mana its time to go back and buy my next item or everyone is dead.
I feel that flash and ignite are the most useful, I don't need ghost with rylai's and my movement speed and flash gives many gimic kills and ignite just gives you more power.