How to play a mage in Skyrim

Sort and simple answer is yes! My second character is based around this build. I am currently level 32 and I am quite enjoying it. I rarely use equilibrium as I rarely run out of magicka and when I do I have a loooot of potions from hoarding them around.

At the moment I am dual casting apprentice level destruction - and yes this more than enough to kill frost dragons. maybe it takes a few more hits but it staggers dragons (not Alduin) and I am waiting till my enchanting is 100 so I can make my destruction free and not waste anymore perks. I use rune spells and conjuration (fire, storm and dremora lord) regularly to give me a tactical advantage.

Early game I'd suggest having a follower but not really that necessary later on.

I used restoration perks to increase my magicka regen by 50% so I can use atronach stone. i use arch mage's robe, morokai's mask and self enchanted amulet and ring for giving more magicka+magicka regen. So I suggest doing college of winterhold quests asap. Right now I have around 430 magicka and 410 health.

Hope this answers your question though I am a month late :p

Edit:

I will put up my character build here and edit it every so often if it helps:

• level: 35 (atronach stone)
• Enchanting - lvl 100 (and I always use grand souls for enchanting my gear)
• Destruction - lvl 90
• conjuration ~ lvl 86
• alteration - lvl 33 (I am including this as this is the next skill I will try to develop)
• gear: orcish armor (destruction+alteration), ebony helmet (destruction+alteration), ring (destruction+conjuration), amulet (destruction+conjuration), ebony gauntlets (magicka+something nice). So this makes all my destruction cost 0 magicka.

I tested this at the last part of the main quest-line

from the point where you enter Skuldafn.

It works rather well, would work better with some (crowd) control spells eg. paralysis from alteration, or some illusion spells etc.

You don't have to restrict yourself to any one class, furthermore racial bonuses are completely irrelevant compared to an average character's abilities.

2 races stand out with their racial bonuses, though: high elves and khajiits.

High elves have a +50 bonus to mana, the only racial bonus that raises a primary stat (health, mana, stamina), which is very helpful for any character that is going to do magic, even as a secondary activity, as it frees up 5 level ups' worth of points to be invested into something else.

Khajiits have unlimited nightivision, the only other way of getting nightvision is becoming a vampire (in vanilla, anyway), and a bonus to unarmed damage (22 vs 10 for argonians and 4 for everybody else), which can only be raised by wearing heavy gauntlets and have the appropriate high-tier heavy armor perk or by wearing/disenchanting Gloves of the Pugilist. It certainly makes fistfights less tedious.