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.