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Syntax is about trying to understand how we generate all the sentences we do in English. We learn basic generalizations, rules, etc.
The ultimate goal is to build a roadmap of how language is generated. Specifically, arrangements that actually make sense.
It's difficult to explain without going into further detail, but imagine it like analyzing a computer algorithm that no one designed because it just developed through evolution, and then trying to guess how the algorithm is written. Every time you think you figure it out, someone says, "but what about this sentence?" and then you have to change everything around again.
Also every step of the way we weren't actually taught how to do the assignments until we already did them (and got them wrong pretty much). So they had us do first, learn later. And the class is 3 days a week, with an assignment being handed out & due every class. And you can't bullshit it either, you have to actually think about it and show that you've thought about it.
So yeah, it's been nuts.