So we all know about how awesomely Detect Life boosts your Alteration, but, dang, that spell eats magicka like nobody’s business, so you can never hold it all that long…
Enter the Secret of Arcana exploit.
The Secret of Arcana, if you’re unfamiliar, is one of the powers you can select from the Black Book Filament and Filigree (available in Kolbjorn Barrow at the end of the Unearthed quest, through the Dragonborn DLC). Basically, the effect of this power is that spells cost no magicka for 30 seconds. This is a hugely beneficial power, especially for a warrior type who probably doesn’t have a very big pool of magicka to draw from, so higher-end spells are just impossible without that 30 seconds of free spellcasting.
However, there’s a bit of a work-around here. Yes, for 30 seconds, using the Secret of Arcana, spells cost no magicka. BUT, if you cast a continuous-effect spell (like Detect Life) and hold it, it’s going to keep right on costing 0 magicka until you release it. Doesn’t matter if it’s 30 seconds, 60 seconds, or 10 freaking minutes. As long as you hold that spell, it’s going to keep right on going.
Long story short, go to someplace well-populated like Solitude, activate your Secret of Arcana, then cast and hold Detect Life for as long as you want, and just watch your Alteration zoom right up.
As my characters tend to be more warrior-types that don’t have much use for Alteration, I find this most handy when I’m looking to speed to the next level in pursuit of a particular perk. Or a few, actually.
(Detect Life spellbooks are rare, but if you go to Treva’s Watch and do the Infiltration quest for Stalleo, he’ll give you a Detect Life book as a reward regardless of what level you are)
On a completely unrelated leveling note, I always try not to buy training in skills that I actually use. It sounds counter-intuitive, but if your character is primarily a one-handed swordsman, your one-handed is going to max out without any help. If all you wear is heavy armor, your heavy armor is going to max out by itself. Your light armor, on the other hand, isn’t going to increase at all. So you may as well pay to boost those unused skills - doing it this way is also a lot easier on the pocketbook.
Both are handy methods, I’ve found, for getting the maximum advancement out of my characters.