I've got the Skyrim legendary edition on the way right now and am wanting to play a strict magic user. How viable is it on Master or Legendary difficulty?

You will need a follower and loads of magicka, otherwise it's no worse than on expert, things just take (even) longer to kill.

if you also take conjuration, you should have no problem (at least on master). i would not recommend destruction as only offensive school though.

if your thinking of only using destruction http://youtu.be/1zNdw4DaUM8 but if your going to use all the magic school then that's a little more reliable.

-zero cost

-dual cast+impact

-specialize in a element and wear one of the three dragonpriest masks frm the DB DLC. (they give 25% more damage)

-use conjuration or followers as distractions

other than that, well if you up the difficulty all you are doing is making the battles longer (more enemy health or somthing). So there's not really any point unless you want to have really long battles.

Ive played a mage on Master with no issues. I will add that destruction was used as a secondary skill (next to conjuration) with 100% cost reduction so it was really nothing to fling unlimited duel cast fireballs at a giant or whatever. But to answer your question, yes it is viable if you plan accordingly.

Conjuration, Illusion, and followers scale with difficulty, so they become more powerful while Destruction becomes relatively weaker. But it's possible to play as a mostly Destruction mage on Master (though around level 42 Destruction starts to scale down relatively even more).

You'll be kiting a lot if you don't make use of Conjuration or followers, but it's doable. IMO, it's tedious and not very fun, but you can complete the game.

I just played a pure mage build (high elf) on Master. I concentrated perk points on Illusion, Alteration, and Destruction. I increased magicka and health around 5:1 and never invested in stamina. I didn't use followers, conjuring, any physical or bound weapons or armor.

Start the Mages College quest around level 10 and get the Archmage's robes.

Illusion goes a long, long, way at lower levels while you build Alteration (use the 'skin' spells: oak, stone, ebony). Once you get the Alteration Paralyze spell, everything becomes much easier. By the time Illusion gets to 90 and the spells work against undead and Dwemer machines, you're almost overpowered. I saved eight perk points, a ton of filled soul gems (used the Soul Trap spell, no soul trapping weapons) and got to 100 in Enchanting in one push from around 48 (got to 48 by disenchanting all items from loot that provided new enchantments, never bought stuff from vendors). Once you can enchant your own gear, the cost of destruction magic drops to about zero and magicka regeneration is practically instant. I retired the character around level 45.

It was a very fun build, good luck!

Like the poster above said Legendary damage reduces the damage you do but it does not reduce the damage followers, summons, raised creatures or frenzied enemies do so illussion and conjuration scale really well and are totally viable. If you are playing Legendary you can use destruction on top of illusion and conjuration and just pretend that your destruction magic is what is actually damaging opponents.

Viable for what?

I've used pure mage builds on master without too much issue. I've struggled with characters using destruction as a primary damage skill on legendary, however. Conjuration is a huge help, as its damage/magicka is much more efficient than destruction. That can get you by until you can either level up your enchanting or increase your magicka pool to 10000000 so you can dual cast expert spells

The spell 'Ignite' is your best friend