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I'm wondering what type of university you were at that let you write a final. The most flexibility given to grad students in introductory courses I've seen is, at most, to write a quiz or two. Most don't even let you write homeworks.

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Actually, at my department (a "top-10" school for CS), for each course we TA, we're expected to write at least one problem set and come up with at least one question for each exam given. There are also half-courses on intro to Unix or intro to C++ that are taught entirely by grad students.

I suspect the OP was teaching an intro-level course, designed to get freshmen up to speed on basic linear algebra, filling any gaps they might have had in their high school curriculum.

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