The "research portion" of my paper is mostly done, but I'm having trouble putting together my research. (Keep in mind this is at the undergraduate level). It's not so much that I don't know how to organize my thoughts; in fact, I've written a very detailed outline. I seem to have a two questions I'm wrestling with (I apologize if this is a tad long-winded)
The monotonous proof-theorem-proof-theorem style that essentially consists of a list of facts with no exposition seems to be most accepted. But will this really make my paper stand out? When I think about texts with proof-theorem-proof-theorem, I think of the color gray. If I try to be clever and witty, it could certainly backfire on me, but such papers are the most memorable papers I've ever read!
So what should the tone/style of my paper be?
I'm struggling very much with how detailed my paper should be. By no means am I writing a textbook, but I need to show the audience (namely admission committees) that I know what I'm talking about. On the other hand, I have a deadline! There's always this looming thought in the back of my head that says "But you can't leave that out!" when I debate if I should skip something just to speed up the process -- it's as if I have a hoarder living in my head. I have this same issue with considering how much background/prerequisite math I should include for the reader -- it is confusing, to say the least, writing to an audience that is more knowledgeable than the author. This is certainly very difficult for me to figure out.
So how detailed should my paper be?
I'd really like to hear feedback from professors and/or admission committees members. But, of course, feedback from anyone with research experience is appreciated!