I always have trouble working out which spells magic-user characters can and cannot learn. It's a horrendous bookkeeping mess. However, I like the idea that not every magic-user will know sleep, charm person, etc. but will have some of the wonkier spells, like fool's gold and write.
To make the bookkeeping a bit easier, I went up and wrote up a sheet listing every magic-user spell in the player's handbook with a little box next to each spell. The idea is that if the box is checked, the spell is in the character's spell book. Cross off any unknowable spells.
LINK HERE - download it, otherwise it's nearly unreadable.