AP Quintessences: 15 AP is good early game, simply just better then anything else for quints.

AP Per Lvl Seals: 18+ AP at level 18 helps.

MR Per Lvl Seals: 32 at level 18, makes you tankier against magic damage, switch these out for flat armor if against an AD Midlaner

Magic Pen Glyphs: 9 flat magic pen, you have some tankiness, and damage, now you need to get that damage through. Flat pen is great for that.

Raise Morale isn't very important so we max it last, maxing Parrley and Remove Scurvy allows us to max our heal and damage at relatively the same time well putting points in Cannon Barrrage when possible.

Lets discuss all of these.

Spirit Visage: HP, Stronger Oranges, and MR, good against fed AP champs.

Zhonya's Hourglass: Armor and AP, get seeker's arm-guard early game against AD midlaners and turn it into this.

Frozen Mallet: Massive Slow, AD Damage, and HP? No, don't get this, you want AP.

Hextech Gunblade: AD, AP, Lifesteal, and Spellvamp, with an awesome active? Haven't tried this but it might work out awesomely.

Sorc's Treads: Flat magic pen isn't better then CDR on GP imo.

Trinity Force: Lich Bane is a better sheen item with magic damage, which is what you want to deal.

Rod of Ages: Nice scaling HP, Mana, and AP, might be good to replace Liandry's Torment.

Rylai's Crystal Scepter: AP and Health is good, sadly this item's slow doesn't proc on Q's, but might be good if your playing more ult focused.

Wit's End: Not exactly a horrible idea, adds 42 magic damage to Q and basics along with having MR and attack speed.

WotA: Spellvamp does not proc on your Q, this is not a good idea.

Deathfire Grasp: You aren't a burst champion, but this item might work out if you use it on someone pre-ult and with a Q, this active itself will probably end up doing more damage then your Q.

Frozen Gauntlet: Lich Bane is better, get Zhonya's if you need armor.

Malady: Viable just like Wit's End, adds magic damage, shreds MR, and has attack speed.

Were going to go over every mastery from left to right.

Offense:

Summoner's Wrath: 5 AP & 5 AD can be helpful in a fight when opening with ignite. Definitely worth 1 point.

Sorcery: 4/4 for 4% CDR, with the build well discuss farther down this gets us to 39% cool-down reduction (out of max 40%. Really helpful for Q spam with Lich Bane, orange's spam, and cannonballs.

Havoc: Lets look at what increasing damage by 2% can do, lets say one of our cannons balls late game deals 250 magic damage through MR to a champion. 2% of 250 is 5, 5 more damage won't make to much difference, but there's 25 cannonballs, that's 125, not to much looking at the around 7000 magic damage we do over all with our ult, but this also adds damage to our Q, Lich Bane, Basics, and all the damage we output.

Arcane Knowledge: 8% Magic Pen is really helpful prior to void staff.

Mental Force: 3/3 for 6 points of AP is really nice, thats 4.8 more damage on Lich Bane+Spellsword, 6 more hp from oranges, and 1.2 more damage on every cannon ball.

Spellsword: This is essential, you 100% have to have this. GP lacks magic damage early game, and just has useless AP, this takes 5% of it and adds it as damage to his Q and basics, once you have Lich Bane you will be dealing 80% AP as damage on Q's.

Archmage: 4/4 for 5% Increased AP. Lets say we have 500 AP, this gives us 25 more AP, not a lot but worth 4 points, this kicks in late game mostly.

Executioner: This is like Havoc except 5% bonus on targets below 50% HP, a decent bonus of damage making sure no one escapes your Q spam.

Defense:

Durability: Some more health per level, gives you tankiness late game making you harder to burst.

Hardiness/Resistance: Some flat tankiness for lane, take Hardiness against AD Midlaners, or Resistance against regular AP Carries.

Utility:

Summoner's Insight: Reduces cool-down on flash.


Discussion of other masteries:

Lets start with Offense, there's nothing else there taking that's worth while. Moving Summoner's Wrath is a good idea if not using ignite or exhaust. What about Defense? Diving more into Defense isn't a bad idea if your against a really bursty midlaner or your team doesn't have a really good tank. With utility there's really nothing worth diving for here, mana regen, mana, move speed, cdr, improved recall, etc. That stuff really won't end up helping us as much as points in other places.

Pros:

Massive Lane Sustain

Massive Damage on Ult

Global Presence With Ult

Remains a Decent Dueler Early Game

Naturally Tanky, Doesn't Feed Lane Because Oranges

Cons:

Blue Dependent for Orange Spam

Lacks Poke Damage on Q

Passive Lane/Not Gonna Get Fed Easily

When playing AP GP use ult from your lane to get assists, secure kills, and save peoples lives.

In teamfights just put your ult down and watch people die, well using your Q to poke and buffing everyone with your E.