Re: Science Department / department
NOT A TEACHER
I'd capitalize it. Let's say, that I attend a college and study at The Department of Computer Science. "The Department of Computer Science" is the name of the department I study at and there's no other department of the same name in the school. In that case, I think it should be capitalized as I wrote it. Similarly with movie or book titles, for example "The Da Vinci Code", "The Lion, the Witch and the Wardrobe". Or if I work in marketing in a company, the department where I work is very likely to be called "Marketing Department" (as it's the only department of that name in the whole company).
Please note that I'm not a teacher.