You should learn what the concepts mean instead of judging the names associated to them. We call something a Ring to avoid saying "a set with two operations which behave in a certain way [...]" every time we refer to it.
Real maths is done either in books or papers, where the authors explain every bit of notation they will use. This is not the case in online resources, which is indeed a bad practice... But hey, don't blame maths for that.
And regarding the "understanding maths in terms of computer programs", sure that's possible to do with _some_ topics, but you just can't expect a computer to represent _every_ concept you'd like.