# [texhax] derivatives and integrals: math operators

Phil Parker phil at math.wichita.edu
Fri Aug 7 04:41:46 CEST 2009

On 08/06/2009 at 10:20 PM, Reinhard Kotucha <reinhard.kotucha at web.de> wrote:
>On 6 August 2009 Phil Parker wrote:
>
> > On 08/06/2009 at 03:58 PM, Nat?rcia Fernandes <natercia at eq.uc.pt> wrote:

> >>Math operators should be typeset in upright letters and also have
> >>a special spacing.  So shouldn't the "d" of derivatives (or
> >>integrals) be set with upright letters, since both are
> >>mathematical operators?
> >
> > Neither is a mathematical operator as far as mathematicians are
> > concerned, and we also don't set all operators upright -- only
> > certain ones.

>Hmm.  I always thought that everything except variables is written upright.
>There might be different conventions, but are there any rules?

"Limit-like" and "trig-like" operators and functions are set upright. For
example, lim, sin, log, ker, and tr. That's a rule.

Most operators named with a single letter are set italic. For example, a
(pseudo)differential operator P, a linear transformation L, a selfadjoint
operator A, etc. That's a convention, not a rule, but very few would dare
violate it.

Operator-like things (e.g., functors) that have multiletter names, such as
Spec, probably tend to be upright most of the time. But one may create an
exception if one is naming a new operator and wishes to do so. This is just a
guideline based on what most of us tend to do.

>  There was a
>similar discussion a few years ago.  I don't remember the details, but I
>remember that someone told me that he has a book published in 18?? in the UK
>with "d" typeset upright.

Examples do not prove theorems. English maths didn't catch up with everyone
else until almost C. 20 -- the Newton-Leibniz debacle crippled them for 200
years.

> > The convention you mention is one adopted by some physicists,
> > engineers, and other users of "applied" mathematics for reasons
> > with which most (if not all) "pure" mathematicians either just do
> > not agree or regard as plain wrong.

>What are the reasons...?

I don't know. I've heard many different ones from many different physicists,
sometimes more than one per physicist. Those in a specific area tend to agree
on how it's done in that area, but it varies widely from area to area.

Since we create the stuff, we get to make the rules, conventions, guidelines,
etc. Perhaps they want to change it so they can feel some sort of ownership of
it when they use it. (Who knows? I'm not a psychologist! But I suspect it's
more to keep us from reading physics too readily: we haven't paid our dues,
and physics is a lot easier to understand with advanced math than with
elementary math [a.k.a. "the hard way" or Phys 101 way].)

Another physics quirk is to write \int dx\,f(x) instead of \int f(x)\,dx as we
do. That just creates unnecessary confusion, especially in elementary (as in
Calculus III) double and triple integrals.

And THE most annoying physics quirk is to use \otimes (tensor product) for
\times (set product). That's just plain stupid.

--
Phil Parker
--------------------------------------------
URL http://www.math.wichita.edu/~pparker/
Random quote:
Confidence is the feeling you have before you understand the situation.