안녕하세요~
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Dear Professor (교수님 성함),
Good afternoon, professor!
My name is (작성자 이름), and I am going to study at (학교 이름) as an exchange student for upcoming fall semester and I am looking forward to taking courses in (학교 이름), including '(강의명)'.
Yesterday, I registered courses and was relieved to see that the schedule for lectures didn't conflict. But, suddenly I found out that there is a time conflict during exam week between two courses, and one of the two is (강의명).
From studyguide, the exam for (강의명) is going to be held on December 17th, 12:00-14:45, and the other course has an exam on the same day, from 12:00-14:00.
The thing is that I really want to take both classes. However, there is not much chance of solving this problem.
I don't know if there is going to be resit exam. Even if there is a make-up exam, I don't know if I could take it because I'm going back to my country on January 30th.
Therefore, I was wondering if it is possible to ask you could offer an alternative exam date.
Though I know you are extremely busy, I really don't want to miss out on these great opportunities. If you offer me the other date, I would be really honored and get incentives to study much harder.
I thank you so much for your time and consideration.
Best Regards,
(작성자 이름)
이렇게 썼는데 어떤가요......?