You've stated you want to play a Mage and you're getting advice on how you should use a sword. As long as you play on moderate difficulty levels and choose the right perks, as well as use Destruction spells that isnt resisted by hostiles (Frost on Nords, etc) you will be fine. If you use a mix of all magic, like a mage would do, it may even become too easy.
*sigh* There are all types of mages. A mage doesn't just have to use spells. What I am saying is that one should focus on other schools of magic before destruction. I play level 81, master difficulty, and I regret putting perks into destruction, when they would have been better off being placed in, say, restoration, illusion, or a combat skill. People are saying that I am incorrect in my opinion that destruction is not worth it, meanwhile I have invested in dual casting, and placed a perk in augmented flames. Now, I could have increased my fire damage by another 25%, but that wouldn't really be worth it. In tougher battles, my sword (which does 336 damage per swing with my armor effects/enchantments) can kill boss level creatures in as little as 10 swings (based off of an Ancient Dragon). A fully charged, two handed fireball, would have a tough time killing even a Dwarven Master Centurion in that many hits. On top of that, doing so drains my magicka incredibly fast (I did not invest in the perks to decrease the cost per spell). Although it may seem counterintuitive to tell a person who wants to be a mage to use a sword, if he is anything like me, it would most likely help out in the end. You can focus perks on other schools of magic, such as conjuration, or put perks into alteration to buff your magic resistance, which is what I did. Even in Oblivion, where you could actually make your own spells, most people, myself included, found destruction not to be worth it. The same, for me at least, is especially true in Skyrim, where you cannot even really level up your destruction damage to meet an enemy's level. The reason as to why I am telling him this is so that he doesn't get completely overwhelmed at a higher level. If he wants to play a pure mage, then he can thrown my advice right out the window. If he is open to the idea of using magic to bolster other areas, such as combat or stealth, then this info might be useful to him.