| Quote #1
This separation from his spellbooks had been a real problem for Harry, because his teachers at Hogwarts had given him a lot of holiday homework. (1.7)
Little details like this highlight not only how awful the Dursleys are, but also how divided Harry is – he essentially exists in two worlds. We'd wager that if he attended a Muggle school, his aunt and uncle wouldn't go so far as to lock up his books for the summer.
| Quote #2
"What are you taking Muggle Studies for?" said Ron, rolling his eyes at Harry. "You're Muggle-born! Your mum and dad are Muggles! You already know all about Muggles!"
Hermione's philosophy on education seems to be to learn as much as you possibly can about every subject. And that even applies to subjects you already know a lot about – there's always more to learn. Hermione's emphasis on the importance of "point of view" here is thematically significant too (see the time travel adventure, which is all about gaining new perspectives on events).
| Quote #3
"But everyone knows that," said Hermione in a loud whisper. Professor Trelawney stared at her.
We really love the hardcore, rule-breaking Hermione that comes out to play during this book. Her reaction to Trelawney shows us that while Hermione respects authority (certainly more than her BFFs do) she doesn't respect it blindly. Some "authority" figures, like Trelawney, clearly aren't deemed worthy of respect.