I am taking an abstract algebra course and I am really interested about the topic. So much so that I spend most of my time reading supplementary materials. I consequently know a lot more theorems than the ones covered in class.
In a recent quiz, I used a theorem in one of my proofs that was not mentioned in the lecture since. My professor gave me partial marks for my answer for the reason that we didn't cover this theorem in class even though the proof was completely valid! I can't really see where he is coming from. How would someone be able to use a theorem correctly if he doesn't know its proof? I was quite baffled by his comment.
Do you agree with this?
EDIT: The professor just Emailed me and said that after thinking for a while, he decided to award me the full mark for the question. He also mentioned that he didn't want discourage me from studying the subject (since he saw most of my previous quiz grades were full marks) and I was passionate about it, but kindly requested that I include any proof for a theorem that I cite from now on in his exams. He also sent a broadcast message to the whole class indicating this.
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