A pure mage is not a viable character in Skyrim.
The magic system in Skyrim is abysmal. Unlike melee, where even with no stamina and no ability to do power moves, you can still swing your weapon. With no magicka, you can't do anything as a mage except run.
The spell costs are not even high, they are stupendously stupidly high.
Beyond the fact that cloth has no armor value and enchanting stinks as bad as it did in Oblivion (yeah, the ability to put one buff on a piece of armor..yay), which makes pure mages take a horrible beating compared to a character even in light armor. A mage will be out of magicka right after the fight starts, and carrying around 200 magicka potions is not a viable means of trying to go on as a mage character.
Finally, removing spellcrafting from the game just adds insult to injury to those of us who wanted to play a mage, Bethesda. You could have made a vastly improved spellcrafting system (even though the one in Oblivion was pretty good as it was, especially after adding the Supreme Magicka mod) but instead, you pretty much guaranteed no one will be able to play a mage in Skyrim, and if they even decided to suffer through some how (god mode for the win I guess) why bother when, without spellcrafting, the magic system is boring by default.
Oh yeah, on top of all that, thanks for putting in all the little stories about npc mages researching this spell or creating that spell. Seems the npcs can do it, but the players can't.
Can't wait til mods start rolling out to change all this mage abuse. However, it would be a helluva lot better Bethesda, if you put out a patch to add spellcrafting and reduce the grossly high magicka costs of simple spells, let alone the higher end spells. Evidently some "savant" at Bethesda thought a mage could actually kill 5 bad guys when only able to cast enough spells that can actually kill ONE bad guy. Better yet, I want someone at Bethesda to make a mage, use only the spells in the game, and just try to kill a giant and his pet mammoth on your own. Let me know how that works out for ya...
By the way, to reiterate, I'm talking about "pure" mages here, not battlemages.
To end, no I'm not nerd raging, no I'm not frothing at the mouth (any more than normal) no I'm not even shrieking a little bit. This was my discovery of creating a mage and trying to play him, and subsequently deleting his worthless carcass.

Ok, ok, explain how, in what universe, the magic system is possibly improved? You have less spells that cost more magicka than ever to cast and no spellcrafting at all, so go ahead and explain that, if you would