In the scientific manuscripts I edit, certain deviations from the generally accepted typographical conventions for mathematical text crop up frequently enough that I thought I would discuss a few of them in this post. First, let’s look at some of the basic conventions:

- Single-letter symbols for variables, physical quantities, and physical constants are set in italic type: for example,
*V*for volume and*h*for Planck’s constant. - Multiletter variable symbols, mathematical constants, trigonometric functions, mathematical operators, numerals, punctuation, and fences are set in roman type: for example, cmc for critical micelle concentration, π, sin, and Δ (difference), δ (small difference), and d (infinitesimal difference).
- Superscripts and subscripts that are themselves symbols for variables or physical quantities are set in italic type, whereas superscripts and subscripts that are abbreviations are set in roman type: compare, for example,
*C**p*for heat capacity at constant pressure and*K**i*for inhibition constant. - Mathematical operators functioning as verbs or conjunctions are set with a space on each side (e.g.,
*n*= 25 and 6.022 × 1023), except when they are used in subscripts or superscripts (e.g., a*n*+1). One exception is the slash (/), which is usually set without spaces:*x*/(*y*–*z*). - Mathematical symbols used as adjectives are set without a space between the symbol and the number: for example, a pH of <5.
- Functions set in Roman type should be preceded and followed by a space unless the argument is enclosed in fences: compare, for example, sin
*θ*and ln(2*x*).

Let’s look at some sample equations illustrating the departures from convention that I see most frequently. How many can you find in the following equation?

*Ni* / *N0* = exp (–*ΔEvib* / *kBT*)

where *Ni* is the number of molecules in vibrational state *i*, *N0* is the number of molecules in the lowest vibrational state, *ΔEvib *is the energy difference between the two vibrational states, *kB* is the Boltzmann constant, and *T *is absolute temperature. Here’s my revision:

*Ni*/*N*0 = exp(–Δ*E*vib/*k*B*T*)

I deleted the spaces around the slashes and the space after “exp,” and I used roman type for the subscripted numeral “0,” for the subscripted abbreviations “vib” and “B” (for “vibrational” and “Boltzmann,” respectively), and the Δ symbol. Note, however, that I retained the italics for the subscripted “*i* ” because it’s a variable. Here’s another example. The ozone depletion potential of chemical *i,* (*ODPi*) is given by

*ODPi = ki**τ**i**/kr**τ**r*

where *ki* and *kr* are the rate constants for the reactions of chemical *i* and a reference chemical with O2, and *τi* and *τ**r* are the atmospheric lifetimes of chemical *i* and the reference chemical. And the revised version:

ODP*i = ki**τ**i**/k*r*τ*r

Multiletter variables such as ODP*i* should not be italicized; nor should the subscripted “r,” which stands for “reference.” Whether or not you italicize Greek-letter variable symbols such as *τ* will depend on what style guide you are following. *Scientific Style and Format* suggests that they should be italicized, as does IUPAC. In contrast, *The ACS Style Guide*, although it does not provide any explicit guidance, shows Greek-letter variables in roman type*.*

For more information on typography for mathematical copy, have a look at the following references:

Coghill, Anne M., and Lorrin R. Garson, eds. *The ACS Style Guide: Effective Communication of Scientific Information.* 3rd ed. Washington DC: American Chemical Society, 2006. pp. 210–223.

Council of Science Editors.* Scientific Style and Format: The CSE Manual for Authors, Editors, and Publishers.* 7th ed. Reston, VA: Council of Science Editors, 2006. pp 158–167.

IUPAC. “On the use of italic and roman fonts for symbols and scientific text.” http://old.iupac.org/standing/idcns/italic-roman_dec99.pdf. Accessed July 20, 2012.

IUPAC. *Quantities, Units, and Symbols in Physical Chemistry.* Prepared by Ian Mills, Tomislav Cvitaš, Klauss Homann, Nikola Kallay, and Kozo Kuchitsu. 2nd ed. Oxford: Blackwell Science, 1993. Available at http://old.iupac.org/publications/books/gbook/green_book_2ed.pdf. Accessed July 20, 2012.

Swanson, Ellen. *Mathematics into Type.* Updated edition. Providence, RI: American Mathematical Society, 1999.

Thank you for posting this article. It is clear and useful.

May I clarify with you about the correct typographical convention for oscillation frequency? Which one of the following entries is correct?

(a) fo. f is in italic. o is the lower case English alphabet ‘o’ in non-italic subscript.

(b) fO. f is in italic. O is the capital letter ‘O’ in non-italic subscript.

(c) f0. f is in italic. 0 is the number zero in non-italic subscript.

It seems that (c) is used most of the time in the internet, including the IEEE journals. But I would think that the small letter ‘o’ should be used instead of the number 0. It is because ‘o’ stands for oscillation.

And capital letter ‘O’ would appears too bit for ω_O (\omega_O)

Thanks.

It seems to me that italic

fwith a subscripted non-italic (Roman) zero is the conventional symbol for fundamental oscillation frequency, and then higher harmonics are indicated byf1,f2, etc (subscripted numbers). So I think that (c) is correct. Does that make sense?