Wizard Spellbook when Starting at a Higher Level

[Celeden]

So, I'm having a player start as a level 3 Wizard soon. I presumed that they'd have spells known as follows:
- Level 1: 6 1st Level Spells
- Level 2: 2 1st Level Spells
- Level 3: 2 2nd Level Spells (or a combination of 1st and 2nd)

Giving a total of 10 spells known. Since I don't think Wizards have the ability to swap on spells as they level like Sorcerers do, he'd be stuck with those 1st level spells. However, they wanted to take mostly 2nd level spells and only a couple of 1st, thinking that it'd be different starting at a higher level.
I've enforced the rules as I saw them so far, but if I'm wrong I'd like to sort it out. Is this how it's supposed to work?

[Cybren]

If they really want more spells known you can just give them opportunities via loot. What's their rationale? They just want those spells more?

[mgshamster]

You got the right of it. A wizard starts with six 1st level spells and then gets two more spells each level that must be no higher than their highest level casting slot.

In addition to that, he can use his starting money to purchase more spells per the rules for adding spells. You can find these rules in the Spellbool sidebar in the wizard class. It's 50 GP per spell level of the spell. So if he wants to start with more 2nd level spells, it's 100 GP each. Page 114.

From there, the DMG has rules for starting with more money at higher levels if you want to use that. Page 38. For his level, though, it's still normal starting equipment. This may be the time to use the alternate starting money rules in the PHB, found on page 143 (first page of chapter 5). Or you can just give him some extra cash if you want, as you're the GM. Or not. :)