My new playthrough is going to be a pure mage but I've never done that before. I've only ever played Combat/Stealth classes like Agents or Scouts. So anyone have any tips for playing a pure mage on master? Also I'm debating my back-up weapon. Mace, War Axe, or Sword?

You could use Conjuration's bound weapons as weapons when things in a fight gets rough. They can become pretty powerful if you get the right perks. You will be able to use more magic and rely less on actual weapons.

Use more than just destruction: a Mage with just one school of magic is like a warrior without armor. Destruction alone is a very difficult playstyle - I'd suggest using illusion or conjuration as well as destruction.

As for backup weapons: a 'pure' Mage would likely use a dagger, nothing more. It'd be a last resort, probably enchanted. Swords, maces and axes would likely be too difficult for a mage, who'd likely be inexperienced with weapons.

Focus on magicka - don't worry about health or stamina. A larger magicka pool = a stronger Mage.

Why master, you do not need to prove how 1337 or leet you are. Anyhow conjuration is useful and you will need alteration for stoneflesh etc. Restoration is a yes, illusion is good croud control. When you want a physical weapon use bound bow or sword spell.

Know how every time you level up you can increase magicka, well I did every single time until I was 81. With enchantments and naturally high magic I have 1110 magicka, and 234 percent regen.

Take advantage of all the schools and discard any back up weapons. A pure mage won't need them. You get really powerful.

I am doing the same thing just not on master. I figured destruction was the way to go but after reading all these posts I feel like I'm doing it all wrong

Read my comment in this thread for destruction advice on master - http://www.gamesas.com/topic/1398249-i-want-to-be-a-destruction-wizardcan-i/

The rest of the schools are quite self-explanatory, do you plan on being a vampire?

Yes but later down the line when I decide to do Dawnguard on that playthrough.

for a backup weapon i'd use the bound blade, its cheap to cast, and when perked is does pretty meaty damage (for no smithing upgrades) i'd actually focus on conjuration, destruction, and maybe some healing. Also get a follower who can eat troll punches...cause if not trolls will eat your face. I hardly ever get hit with a companion and summon blocking for me, and you just step back and launch fire at whatever is attacking your crew.

Also would recommend alchemy and enchanting, you'll be a potion addict for the first half of the game, and you'll hopefully enchant a lower cost set to help with the insane spell cost of high end spells.