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*Australian manual of scientific style *Start communicating effectively

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),(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.*v*

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.

If you have a choice, choose your fonts carefully.

In physics, we might see the formula:

\(F = I l B \sin \theta\)

where *\(I\)* is a current in a wire, \(l\) is the length of the wire and so on.

In a sans serif font, this becomes:

*F* = *IlB* sin*θ*

There can be 2 problems here. First, in many sans serif fonts we cannot easy distinguish capital I (eye) from lower-case l (el). Second, many sans serif fonts do not include a set of mathematical symbols. The Greek theta (*θ*) will then be taken from a serif font and may not match the other characters visually.

Some formulas use the Greek letter nu (*ν*). Depending on font, this may look like a *v* (vee).

**Reminder. **Choose your notation carefully. For example, some Greek letters are too similar to their Latin equivalents and must be avoided unless convention demands their use. Such pairs include nu (*ν*) and *v* (not to mention upsilon, *υ*), iota (*ι*) and *i*, and omicron (*ο*) and *o*. Many Greek capitals are the same as those in English (eg capital alpha = A).

Always format symbols the same in running text as in the equation:

We can write

$$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

where a = 2, b = 3 and c = 1. [wrong – a, b and c are roman]

where \(a=2\), \(b=3\) and \(c=1\). [correct – \(a\), \(b\) and \(c\) match the equation]

Always use the correct mathematical symbol, not a convenient keyboard equivalent. In Microsoft Word or Google Docs, this usually means using the symbols menu or the menus in your equation editor. Most symbols can be entered by typing a code and then Alt+x – see Special symbols in Microsoft Word. A keyboard equivalent may look acceptable in your current font, but not in the final production font. It may also be mathematically incorrect. This table includes some examples, but there are many more.

Character | Alt+x code |
---|---|

Minus sign: A hyphen (-) is not a minus sign (−); nor is an en dash (–). In Word, the equation editor should put in a minus sign when you type a hyphen (if text is styled as math) |
2212 |

Multiplication sign: The letter x (ex) is not a multiplication sign (×); nor is an asterisk (*) . In fact, * has a specific meaning in mathematics that is different from simple multiplication |
00d7 |

Angled brackets, ⟨like these⟩, are not ‘greater than’ and ‘less than’ signs, <like these> |
27e8 (left) 27e9 (right) |

Prime symbols: Quote marks are not prime symbols (′, ″ and ‴) |
2032 (single) 2033 (double) 2034 (triple) |

Degree symbol: A superscript letter o (oh) is not a degree symbol (°) |
00b0 |

Plus or minus: The combination +/- (or +/−) is not a ‘plus or minus’ symbol (±) |
00b1 |

Comparisons: Repeated ‘less than’ (<<) and ‘greater than’ (>>) symbols are not the same as ‘much less than (≪) and ‘much greater than’ (≫). Similarly, do not use a combination such as ‘=<’ for ‘equal to or less than’, use the correct symbol (in this case, ≤). Combinations such as ‘=<’ and ‘!=’ may be used when quoting computer code, but that is a different subject area |
226a (≪) 2264 (≤) 2265 (≥) |

Proportional to (∝) is not the same as the Greek letter alpha (α) |
221d |

Approximately equal to/similar to: A tilde, ~, is not an ‘is approximately equal to’ sign (≈), nor it is an ‘is similar to’ sign (∼). In some fonts, the tilde will look like the latter, but in others it will be very different. |
2248 (≈) 223c (~) |

Mathematical writing very rarely uses the obelus (division sign, ÷, Alt+x code: 00f7). Division is usually indicated by writing as a fraction or using the solidus (a type of forward slash; Alt+x code: 2215). The slash (technically a ‘virgule’) on your keyboard is nearly always acceptable.

To avoid confusion, plurals of symbols usually take an apostrophe:

… all the *x _{i}*’s in Equation 2 …

although in many cases, the singular form can serve as a plural:

… all the *x _{i}* in Equation 2 …

Use your ear – try reading out loud to find the best way.

**Special symbols in Microsoft Word**

Writing mathematics often requires inserting non-keyboard symbols. Here is a brief guide to doing just that.

Word provides 4 main ways of inserting unusual characters:

- Search for them in the Insert Symbol dialog. If using the equation editor, you can use its menu of characters as well.
- Some symbols can be inserted by holding down Alt and typing a number on the keypad, then releasing Alt. For example, typing 0215 while doing this gives ×. If it does not work, try changing your NumLock setting.
- Almost any available symbol can be inserted by typing its (hexadecimal) code then highlighting the code and hitting Alt+x. You can find these codes by using the Insert Symbol menu:
- Type the code – for example, 00b1.
- Select the code (by mouse or keyboard) and hold down Alt and x at the same time.
- Release Alt and x, and the character should be inserted (in this case, ±).

- Create and use a keyboard shortcut.