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Feb 5, 2011 at 21:40 comment added KConrad As far as the Fourier transform is concerned, I think it is beneficial for students to be aware that there are different conventions and know the effects this can have (I don't mean memorize the effects, but realize it alters things here and there). This becomes particularly noticeable when you do Fourier analysis on R^n and not just R, where I think the way different conventions behave justify why inserting 2*pi into the exponential part of the Fourier integral is, notationally, the simplest convention.
Feb 5, 2011 at 5:15 comment added Theo Johnson-Freyd The convention OP asks about absolutely matters. One way to see that it matters: the different choices give different algebras in characteristic $p$ (one's more like polynomials, the other like divided powers).
Feb 4, 2011 at 20:00 history answered Dan Lee CC BY-SA 2.5