TITLE: Is arrow notation for vectors "not mathematically mature"?
QUESTION [93 upvotes]: Assuming that we can't bold our variables (say, we're writing math as opposed to typing it), is it "not mathematically mature" to put an arrow over a vector?
I ask this because in my linear algebra class, my professor never used arrow notation, so sometimes it wasn't obvious between distinguishing a scalar and a vector. (Granted, he did reserve $u$, $v$, and $w$ to mean vectors.) At the same time, my machine learning class used arrows to denote vectors, but I know some other machine learning literature chooses not to put arrows on top of their vectors.
Ultimately, I just want a yes or no answer, so at least I do not seem like an immature writer when writing my own papers someday.

REPLY [9 votes]: In my experience, $\overset{\rightharpoonup}{v}$ and $\mathbf{v}$ are used more often in science and engineering (even at the research level).  This explains why they are often used in lower division mathematics courses, since at this point most of the class is not a mathematics major. As you proceed through mathematics, you begin to see vector spaces like real numbers and function spaces, and it makes less sense to think of vectors as "different" from the other things you're working with. Once you start hearing the word "module" enough, the notation has almost completely disappeared. The only exceptions I have seen are in differential geometry and applied math. I don't think the notation is so much mathematically immature as it is associated with "spatial" thinking.