Is Vector Calculus useful for pure math? I have the option to take a vector calculus class at my uni but I have received conflicting opinions from various professors about this class's use in pure math (my major emphasis). I was wondering what others thought about the issue. I appreciate any advice.

The answer depends on your interests, and on the place you continue your education.  In some areas in the world, PhD's are very specialized so any course that is not directly related to the subject matter is not necessary.  One could complete a pure math PhD and not know vector or multivariate calculus.
However, this is increasingly rare; more and more PhD programs are following the American model, expecting their graduates to have some breadth of knowledge in addition to the specialized skills required for the PhD thesis itself.  Such programs would consider a lack of vector calculus a serious deficiency and may not even consider your application into any math PhD program, pure or applied.  Certainly this is the case at most universities in the U.S.
