With my other character dead due to a save corruption,I decided to start making spinoffs of him,how his life may have gone if things had went differently. I've never done a pure mage before,so while I'm very excited,I'm a little lost. He's a hotheaded mage who learns for the sake of learning,and strives to be the best.I use destruction accompanied with alteration and illusion. Any other tips for this?

make sure you master more then one type of magic, I tried a pure pyro mage build... ended up having to learn other types of magic when a lot of the time my fire just blew stuff around the room while the enemy shrugged it off with a laugh. So make sure you specialize in fire, frost and lightening. Doesn't hurt to use illusionary weapons as well. Only problem with those is they share your weapons skills which if you have one, makes illusion weapons almost useless. Unless you use illusion weapons a lot in which case that will improve your weapons skills.

Learn how to dodge amd run around.

Abuse Magicka potions

Carry a dagger (or something, but Mages in-game tend to always have a dagger) around just in case you have no way to use magic at all or want to administer posions like weakness to magic or an element.

do not waste time with the master level destuction spells, they are a waste of time and magicka

Learn to love the spells right below master (like incinerate)

Welcome to the family. Welcome to the enlightened, young one.

You've been enlightened from brutish or cowardice life.

For offensive develop your destro and conjuration. At low level use conjuration to distract enemies while you attack them with destro.

Use 3:1 ratio for magicka:health.

Conjuration is a necessity for any practitioner of the arcane, especially a pure mage. Need someone to take the heat? Pop a Flame Atronach.

Are your enemies too great in number, and you need 'em to chill out? Frost Atronach is your dude.

If you want to add real shock-value to your battles, then toss a Storm Atronach in the midst.

Or maybe you're just lonely? Don't worry, the Dremora Lord's throaty smack-talk puts the AYYYYYYY in "companionship," and subsequently a fiery demonic greatsword into the bellies of your enemies. i pray to the gods you have mercy on me for these unholy puns

...aaaaaand i guess you can raise dead people if you want

Since you wont be using any other skills besides magic, I'd say focus on at least 4 schools, plus Enchanting and/or Alchemy if thats your kind of thing. Personally I stray away from Illusion. Too boring, too simple (besides invisibility), and by and large, useless on a lot of enemies.

I suggest adding Conjuration to your list. Whenever your skill is high enough to summon Dremora Lord's.. you're good for any situation. They're the closest I usually have to a follower. I love 'em.

Of course, there are exceptional NPC's you can revive with Dead Thrall. And I think there is a perk that even allows you to heal them.. but I'm not sure.

Be patient in the early levels with your pure mage when it can seem quite difficult and you will be rewarded later in the game with incredible power. As others have suggested here conjuration is a very good idea if this is your first pure mage, antronachs are good for crowd management and the twin perk is good at later levels. When I play pure mages I go with a 1 health, 5 magicka and 0 stamina ratio which seems to work perfectly for my characters.
Make sure you take advantage of the terrain and try to attack where possible from distance as the pure mage is a glass cannon and should try to avoid all "up close and personal" battles where possible. A follower is a good idea first time out to give you some breathing space while you get used to the style and I would recommend maybe Mjoll, although the choice is yours obviously. Best of luck with your play through, I think the pure mage style is by far the most challenging and rewarding and would highly recommend is. Stick with it and I'm sure you will enjoy it.

Here are a few links to help you out. I only play as a sorceress, my twist on a mage.

http://www.gamesas.com/topic/1483118-tips-for-playing-as-a-mage-noob-to-tes-and-skyrim/page-2

http://www.gamesas.com/topic/1481463-never-actually-made-a-mage/

http://www.gamesas.com/topic/1482616-mage-surviving-against-multiple-enemies/

The main thing to have fun while you are blowing everyone to pieces.

If you are to do a pure mage, take either Altmer (+50 magicka and can regenerate magicka faster with his daily) or Breton (daily power allows it to absorb Magicka). That's the best advice I can give you. Oh, and get a weapon that drains magicka and do not neglect Restoration. That's basically a must. Also, if you have Dawnguard, join the vampires and do the sidequests until you get the one about the Rings of Blood Magic. Equip the Ring of the Erudite and you get even more of that stuff.

No,the character is based on a khajiit.And since I enjoy learning for the sake of knowledge,I don't think joining the evil corrupt vampires is a good idea.

Better than being a miserable pile of secrets.

For a pure mage don't forget to invest heavily into enchanting early on. Enchant small things to build the skill up so that you can enchant your robes & clothes. Plus you can take staves (& staffs) to take as back up. That and take scrolls.

Alteration for mages armor I'd also important.

The best advise Is what Resident said earlier. Invest, practice and master each school so you can be a more well rounded Mage.

I build Mages that only have 100 Health, every level up goes into Magicka. I only invest in Cost Reduction Perks in Destruction, because of the Spell Cost, and Alteration because all of the Cost Reduction Perks from Novice to Expert are required for the benefits like Magic Resistance, Spell Absorbtion, and Stability.

If My Mage wears Robes and Clothing, then I will get the Mage Armor Perks. If My character is a Hybrid build, Mage Armor is useless and gets nullified by Dragonhide.

I try and get Destruction up to Adept as quickly as possible to take advantage of the Cloak Spells on all of My Mage based characters. A Cloak will allow a Mage to focus on a tougher Opponent that will kill the Mage in One hit while ignoring a lesser opponent that is closer.

I prefer to use Shock, and Chain Lightning is My characters favorite Spell. I do not use Followers that can be harmed by the AOE of Adept Spells, and often visit Apocrypha just for the Perk to allow Followers to not be harmed by My characters Spells and Shouts.

Wouldn't Conjuration render followers redundant?

I have found that non-hostile NPC's do not (seem) take damage from Shouts and Spells with the Perk from Apocrypha. I have not had problems using Chain Lightning and Cloaks near NPC's after getting the Perk. I really need to try Stormcall in a town.

EDIT Stormcall in a Town is a bad idea. NPC's do not take damage, but the Shout does counts as an assault. A Follower will defend themselves when NPC's do become hostile. I also usually remember to use an Apprentice or Expert Spell to avoid Friendly Fire

The more the merrier i say.

Antronachs don't carry stuff for you and every good mage needs a pack mule especially with their lack of stamina.

yup!! There's nothing more badass then rolling with like two companions who summon there own followers and then conjur yourself two extra back up its one of those feeling!

If you are going to wear any armor at all, then forget the alteration. I personally do not use it. At the beginning put all your points into magicka. When you are starting out and use the flame spell, do not just put out a constant flame. If you do, you will run out of magicka quickly, and it will take a while to build up again. Set the enemy on fire, then quit the spell. Set the enemy on fire, and then quit the spell. Keep repeating until the enemy is dead. Doing it this way makes your magicka build up faster and you will not be using it all in one blast. Hope that made sense.

You will also want to pick up conjuration for helpers. Use the same element for helper chosen or you could kill off your conjured helper. A frost atronach is immune to frost, so forth and so on. Also, the bound weapons are good and poisons can be applied to them.

Keep a backup sword just in case. One of the first things to do is go to the college, as when you first get there you get spell for only 30 gold. Then you get a free bed and storage until you get your own, and you get a decent set of robes and a hood to help you out. If you go on the first quest, make sure you are at least level 5/6, and during the quest you will also get a ring that adds to your health and an amulet that has cost reduction. You will also level up at least 2 levels during the quest. All the spells for all the schools can be purchased from the people at the college.

I always play as a sorceress, my twist on a mage, and I never put points into health, for I have never needed them. For the first 15 levels all my points go into magicka for the more magicka your character has, the more spells you can fling. Later I put points into stamina for the plunder I want to carry for I have no followers.

A "hot-head" character would like fire, so take the dual casting perk with the impact perk. It will cause an enemy to stagger every time they are hit with a dual casted fire spell. Take the quiet casting perk in the illusion tree so enemies will not hear you casting that spell. Take the Aspect of Terror perk also, as it adds 10% damage to your fire spells. One of the destruction perks causes fear, and because it does, it gains the bonus from the illusion tree. Also make sure you take the Augmented Flames 2 perk. I only use frost on fire dragons, and I very seldom use shock spells. Some people like frost and shock, but I do not use them hardly. If you get into a bind with enemies, a dual casted flame cloak will help very much in dropping them down.

If you intend to sneak and use a conjured bow, then take the first perk in stealth, then take the deadly aim perk for it gives 3x as much damage while in sneak. I also take perks in the restoration tree only for the necromage perk, as it grants extra damage on all spells while fighting the undead. It includes drauger, vampires, etc. It also gives bonuses such as a spell with a duration will last 50% longer, and spells with a magnitude are 25% stronger. Destructions spells will do 25% more damage with this perk, but again, only toward the undead.

Hope all this helps.