[...] a particular math symbol is troubling me it's a plus sign within a circle.
Any Ideas???
Usually $\displaystyle G \oplus H$ denotes the direct sum of $\displaystyle G$ and $\displaystyle H$. ($\displaystyle G$ and $\displaystyle H$ being two groups or two vector spaces or...)
There is no one meaning for $\displaystyle \oplus $.
I have seen it used in many, many different ways.
The best you can do is to follow your textbook/instructor.
A definitions should have appeared there.