Offensive magic is mainly DESTRUCTION. When that fails you are going to have a hell of a time surviving no matter what school you use.
I agree with this too, Destruction is underpowered.
but again, if you use all your schools of magic you'll survive.
another idea you can use is to make poisons that makes the enemy weak to a specific spell.
I know you're going to think "well that's not what a pure mage does" that's what I thought too. But, and it is a stretch, but in Skyrim you have to accept it,
DON'T use a dagger as a weapon. ONLY use it to apply a poison that makes your enemies weak. THEN, after they're poisoned use your destruction spell.
for example: I like frost spells. I use a poison that makes enemies weak to frost magic, I hit them once with my dagger, then I put it away and light up with my frist based magic. The same applies to Fire, and shock.
also, you can't really make yourself speciliaized in one form of destruction.
Shock- use on other mages
Fire- use on undead, frost atranochs
Ice- use on humans, fire atranochs, animals
@Nightshade Assassin: is there a detect life-spell? I thought they got rid of that. Also, if you're using UESP, don't. The UESP is not accurate at this time as the game is brand new and thus will take a while to finalize any theories, strategies, or basic info.