Here's one I think is probably 101 level for others here, but what is the difference between a multidimensional scalar and a vector? I'll gratefully read through any reference you can link to.
Whether something is 101-level or a difficult thesis topic often depends on your point of view. Different fields seem to define scalars differently, with the physicists sometimes arguing that the mathematicians have got it all wrong: http://imechanica.org/node/15857
On a related note, I was tremendously impressed with the quality of discussion at imechanica.org. At a glance, it may be the best example of a well-functioning online community that I've ever seen.
Great part:
"They should not call the elements in the number field F scalars. These elements already have names: they are called numbers. And we physicists and engineers need the word scalar to name some other objects. Mathematicians, like physicians, should at least learn to do no harm. "
A vector belongs to a vector space, which implies certain algebraic rules relating it to other vectors in the space (http://en.wikipedia.org/wiki/Vector_space is probably enough reference). A multidimensional scalar is a more general data type, as any or all of the vector axioms can be relaxed or eliminated.
