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Undergrad level math courses are not as thorough as you might think due to the time compression needed to fit a topic into a semester. Learning fast is kind of the point. If you dive too deep you'll run out of time to get through all of the material and get poor grades.

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I would argue that this is highly dependent on the University/professor who is teaching you.

I've seen courses where we're taught next to nothing in terms of thoroughness and also courses that stick us neck deep in the subject, literally going from axioms to a complete, standard mathematical framework.

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