Talk:Stokes' theorem

Level of abstraction

Stokes' theorem is a good example of a piece of mathematics that can be treated on many different levels.

I'm very much in favor of the following structure of the articles: first give the simplest (and least exact) formulation, as for instance can be found in physics books or elementary math texts. (What I call the vector analysis formulation of Stokes' theorem comes from Jackson Classical Electrodynamics). Then proceed in increasing rigor, until finally only a few specialized mathematicians can understand the notation. I understand that rigorous notation has its use, not only because it is compact, but also because it contains all conditions under which the theorem is valid, excluding all pathological cases (those which the average physicist, or applied mathematician would never think of).

I make a point of this, because it is a perpetual cause of quarrel at our big neighbor's place. Our neighbor has many mathematics articles that I cannot read, not so much because of the math content, but because of the advanced notation. So, I say: CZ is not paper, there is room for formulations at all levels. The only criterion is that the formulation must be common in textbooks, either undergraduate or graduate, physics or math. --Paul Wormer 09:04, 11 July 2008 (CDT)