Sentences in graduate level writing should not end with prepositions. From Merriam-Webster: “A preposition is a word—and almost always a very small, very common word—that shows direction (to in "a letter to you"), location (at in "at the door"), or time (by in "by noon"), or that introduces an object (of in "a basket of apples"). Prepositions are typically followed by an object, which can be a noun (noon), a noun phrase (the door), or a pronoun (you).”
“The most common prepositions are at, by, for, from, in, of, on, to, and with. Other common prepositions are about, above, across, after, against, along, among, around, because of, before, behind, below, beneath, beside, between, close to, down, during, except, inside, instead of, into, like, near, off, on top of, onto, out of, outside, over, past, since, through, toward, under, until, up, upon, within, without.”