Mages are considered to be fairly underpowered in the game, and I agree that you are indeed not a demigod when you roll a mage character. Not being a demigod does not, however, mean that you are underpowered.
Skyrim gives mages a huge advantage in fact if you are willing to take the opportunity to learn the new rules a mage needs to live by.
First; you need to make a very important choice; Bretan or High Elf?
Bretans enjoy a resistance to magic, a power to absorb magic, and a higher than normal magical aptitude. High elves on the other hand get a magicka regen power, 50 bonus magicka and a high magical aptitude.
Step one: No stamina. None. Do not put a single point into stamina. Yes, this will mean you can’t run far or carry a lot of loot, but it also means you have more points for your important stats, Magicka and Health.
Keep your magicka and health about even with each other. They are equally important. Magicka keeps your spells going, and Health keeps YOU going.
Step two: Ditch your robes. This is probably a bit of a shocker for some people who are used to other games; but heavy armor does not give you any casting penalty. The only purpose robes have is to make you LOOK like a mage.
Enchanting can give heavy armor exactly the same bonuses as robes have, but the armor actually protects you. You will need to level up your enchanting to be able to get strong enchantments on your equipment, but it’s for the best to be able to raise your heavy armor skill early on as well.
Now that you are outfitted for the job, there are a few tips for combat it’s self.
Tip 1: Tap channeled spells. Damage is very slow to register in this game. it seems as though for channeled spells there is a maximum speed which the health meter will fall to zero regardless of the damage they took. Many enemies die from just a puff of double-flame, but will need 2-3 seconds for their life bar to realize that they are dead.
As far as flames goes, it seems that it’s bonus damage does not register in a steady attack either; but tapping the spell repeatedly does more damage with each tap. Tapping rather than holding often can save you a LOT of magicka.
Tip 2: Be your own tank. Invest in heavy armor perks. Invest in alteration as well. If you chose Bretan, and take all three levels of magic resistance in the alteration tree, as well as max out your heavy armor bonus in the perks, your damage resistance to both physical and magical attacks will be insane.
Tip 3: Flame Atrinoch is your friend. Not only will it keep your enemies busy, but it does not give you any conjuration experience. This means you can learn the spell to use as a panic button, without fear of pushing your level up in a branch of magic you don’t often use.
Tip 4: Become a werewolf. Sometimes you will encounter enemies with either an insane level of magic resistance, or immunity to your spell of choice. Being a werewolf can seriously cover your bases there. As a werewolf, you won’t accidentally boost your single handed skill, but you will be able to basically bully even the strongest enemies in the game. I have heard a sprinting power attack can ragdoll a giant. Personally, I’ve used it on a troll and found it stays down a long time.
If you follow these tricks, you will be well on your way to making a truly powerful mage who has none of the mage’s typical weaknesses.