Josh M Foster
Developer
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Well, there are two numbers that answer that question. I'm going to answer assuming you're a specialist wizard, as the question indicates.
As for how many you know, you know every cantrip, except the ones from your prohibited schools, and 7 first level spells of your choice. None of those have to be from your school, but you really want at least 1 to be.
As for what you can cast each day, the wizard class table on page 80 if the core tells you your base.
3 0th and 1 1st level spell. To that you add a bonus spell for your school. This spell must be from your chosen school.
Finally you add bonus spells from intelligence. 19 gives you 1 bonus 1st level spell.
So, final tally: You know all 0th level spells (cantrips) except the ones from your two prohibited schools and 7 first level spells, which can be from any schools.
You can memorize 3 cantrips each day, but you can cast them as often as you like.
You can memorize 3 first level spells each day, one must be from your chosen school. If you memorize a spell from a forbidden school, it counts as two spells.