One of the main challenges in mathematics writing is that the format of the text, not just the text itself, conveys precise meaning:
v (bold) is a vector (a quantity with size and direction) or a matrix
\(v\) (italic) is a variable or symbol, in whatever alphabet (eg Latin, Greek)
v (text typeface) is the letter vee
To ensure that your meaning is accurate, you must follow these rules:
- Use italics, bold, underline and other formatting correctly.
- Use 1-letter symbols where possible, because multiplication is often shown by juxtaposition – that is, \(xy=x×y\) and not the single variable \(xy\).
- Use upright text for mathematics expressed in abbreviations or whole words.
- Be consistent in your notation. For example, a vector may be written v (bold), v (bold and italic), \(\vec{v}\) (italic with an arrow) or one one of several other ways; use the format prescribed by the publication. If you have discretion, choose 1 form of notation and be consistent.
Never:
- italicise mathematical functions with long names, such as sin, cos, log and tan
- italicise brackets, operators (eg +) and so on
- italicise labels that are not variables (eg the minimum value of \(x\) is \(x_\mathrm{min}\), where min is not italic but \(x\) is).
The limiting value of the absolute value of \(x-1\)as \(x\) approaches 1 from below:
$$\lim_{x \rightarrow 1^-} \left| x-1 \right| = 0$$.
[The variable \(x\) is the only character in italic.]
An integration from the minimum to the maximum value of some variable, \(t\):
$$v=\int^{t_\mathrm{max}}_{t_\mathrm{min}} -i\omega^2 f\left( x,t \right) dt$$
[Labels ‘min’ and ‘max’ are not in italic, whereas ‘\(dt\)’ is (do not write it ‘\(\mathrm{d}t\)’, with roman d, italic t). Function \(f\left(x,y\right)\) is italic, as is \(i\) (\(i = \sqrt{-1}\)) and Greek letter omega, ω.]
If quantities are given long names – words or acronyms – use roman type to match the discussion in the body text. Ensure that spacing is correct between terms and around mathematical symbols such as = and +:
Calculation of annual population growth:
APG = (births – deaths) + NOM
where APG = annual population growth, NOM = net overseas migration
Mathematics uses some unusual typefaces, often for specific purposes:
Blackboard or double-strike bold is used to denote number sets. That is, all the examples of certain types of numbers:
- ℕ is the set of natural numbers (positive integers, and usually zero); 1, 2, 3, 56, 234, etc
- ℤ is the set of integers, positive and negative; 1, 3, −67, −456 678, etc
- ℝ is the set of real numbers; 1.2, 3.14159, π, −45.0, etc
- ℂ is the set of complex numbers, \(C=A+iB\) where \(A\) and \(B\) are real numbers and \(i = \sqrt{-1}\).
Other typefaces you may see include calligraphic (eg ℋ) and fraktur (eg ℌ). Follow the conventions in your subdiscipline.
In general, avoid entering mathematics as formatted text directly from the keyboard. It may be irritating to enter a single variable as an equation, but doing so will guarantee that the character looks the same in the running text as it does in the equations.
