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.
Show me a paper that explains "every bit of notation they will use"! ;P
(I understand there's a difference between "explaining" and "stringently defining", but I can't help thinking of the only book I know that actually tried to stringently define all notation: Principia Mathematica. If I remember correctly it took Bertrand Russel about 160 pages to define addition and prove that 1 + 1 = 2. :P)
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.