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Math italic d vs roman d
While preparing the article LaTeX teaching techniques, Lenore Horner for the 2011-1 issue the proofreader and author disagreed over the use of an italic d vs an upright or roman d.
Proofreader Calleecharan
[Horner] writes $ \frac{ds}{dt} $ on page 3. The differential operator "d" should be upright and not in italic.
Author Horner
I made the changes in the derivative notation because the argument that the derivative is an operation and so shouldn't look like a variable made sense to me. I later checked every single math and physics book on my shelves at home (I have another shelf-full at school that I keep forgetting to check) and not a single one of them - including the one by an author who had his wife write a font for the TRS-80 to properly typeset his book - writes the derivative in any way differently from the variable d. I guess LaTeX is out to change the way we write math in this case.
We asked a well-known math book publisher and TeX expert, Michael Spivak.
Should dx/dy have an italic d or a roman d? For centuries, of course, mathematicians have used an italic d. Then some standards committee or other decided it should be roman d, since italic letters are reserved for variables. As far as I know, $e^{i\pi}=-1$ is still written with an italic e and an italic i, but perhaps they were worried about Emerson's hobgoblin of small minds.
I believe the roman d flag is now carried by physicists and engineers, but don't know that many mathematicians who use it. I haven't yet seen a Calculus book that uses a roman d, though there's almost certainly an enthusiast somewhere who has written one.
Claudio Beccari cites the ISO standard for this (and also published an article on it in TUGBoat ten years ago):
The roman d (differential), the roman i or j (imaginary unit), the roman e (base of natural logarithms) must be typed in upright type by an ISO regulation, but it deals only with typesetting mathematics in Science and Technology. See the paper sp811.pdf http://physics.nist.gov/cuu/pdf/sp811.pdf issued by the NIST (National Institute for Science and Technology, the successor of the US National Bureau of Standards).
The ISO regulations, I must underline, deal only with Science and Technology, not with pure mathematics, and mathematicians are not bound to such regulations. It applies to physicists, engineers, chemists, and others dealing with measurable sciences. (Of course, mathematics is a science, but the term science used by the regulation implies sciences that deal with measurable physical quantities). The underlying ratio legis is that physical quantity symbols should not be confused with symbols that do not represent quantities; furthermore, physical quantities have similar symbols, where d, i and e are used very frequently for diameters, distances, diffraction indices, electric current, electron charge, and the like. The italic physical quantities should not be confused either with the units of measurement that, again, must be in upright type, and not italic, slanted, or oblique forms.
As a university engineer and professor I published using mathematics during the whole length of my research career, and I find these regulations very wise and very convenient to use in practical situations, as well as the obligation to use roman type in subscripts and superscripts that do not represent physical quantities or mathematical entities, so that the i-th element of a succession of voltages should be $V_i$ while the input voltage should be $V_{\mathrm{i}}$.
I underline that the ISO regulations apply to Science and Technology, so the use of, say, upright or italic d for the differential depends on the field where that symbol is used; roman type is compulsory in Science and Technology, optional in pure mathematics.
Since the proofreader is an engineer he recommended the roman d. Mathematicians apparently almost always use the italic d.
The author is a physicist and chose to use the italic d. Now this all makes sense ... or does it?
Displayed equations
After the article LaTeX teaching techniques, Lenore Horner was published we received the following comment:
Ross Moore 2011-09-20
One extra thing that I do is use \tfrac{1}{2} so that the fraction looks nice, even in displays, where otherwise it can dominate an expression (as in one of your early examples).
Horner 2011-10-11
I have to disagree with Ross. See attached examples and pedagogical discussion of why using universal small halves in displayed equations doesn't make sense. What it comes down to is that I agree with LaTeX default choices on appropriate sizing within expressions and disagree with Ross's suggestion to override those defaults.
Redefining LaTeX math commands
Juan Luis Varona 2011-09-20
Comment on Speedy LaTeX on the Mac, Lenore Horner
In general, it is not a good idea to redefine TeX commands. But sometimes it is a very bad idea. For instance, redefining
\renewcommand{\[}{\left[}
\renewcommand{\]}{\right]}
because in this way you cannot use
\[ formula \]
Note that
\[ formula \]
Is not the same as
$$ formula $$
although it seems similar (for instance, you can not to use \qedhere with $$...$$).
Horner 2011-10-21
Juan Luis makes a good point that redefining has dangers. In this case I think the advantages outweigh the dangers, although I do see that I should not have recommended $$ $$ as the replacement for \[ \] but rather either \begin{equation*} \end{equation*} or \begin{align*} \end{align*} since $$ $$ (I think) triggers TeX on which displaymath, equation, and align are built but is different from all of them. Personally, I prefer the align environments over the equation environments since I don't have to change the environment if I need to add extra lines of math later. Because I can insert any of the options with the same number of key-strokes and it makes sense to put the opening and closing statements of the displayed math on their own lines, there is no disadvantage in editing to using the longer forms. However, the longer \left( \right) or \left[ \right] necessary for most sets of parenthesis in an equation make editing and proofreading the equations themselves much harder for me. Sample of math redefinitions
Missing chess piece
Luis A. Dissett 2011-10-21
In Distractions — Some chess problems created in LaTeX the solution to "Additional chess problem 2" reads: "If it is white’s turn, then white plays 1. 0-0 and, irrespective of what black does, mates with 2. Rd4d1."
However, black can escape by 1. 0-0 Kd4-d5 2. Re1-d1 Ke6.
A black pawn is missing on e6.
