# Maths in SEQTA

Mathematical and scientific formulae in SEQTA are entered using LaTeX syntax. This is a quick guide to using LaTeX, adapted from this guide.

## Alternatives

If you'd rather not typeset expressions using LaTeX, consider exporting to an image from a tool like OneNote, Word, or Mathematica.

## Basic operators

The plus `+`

, minus `-`

, division `/`

, equals `=`

, less-than `<`

, and greater-than `>`

symbols have their usual meaning.

- To denote multiplication, use
`\cdot`

(a centred dot) or `\times`

for a × symbol.
- For less-than-or-equal-to, use
`\le`

; for greater-than-or-equal-to, use `\ge`

.
- To write a superscript or subscript, use
`^`

and `_`

, respectively. For multi-character super- and subscripts, wrap contents in braces: `x^{y+2}`

: .

## Fractions

Use `\frac{x}{y}`

to typeset fractions; the first value is the numerator and the second the denominator: .

## Roots, sums, integrals, limits

- For a basic square root, use
`\sqrt{ x }`

— whatever is between the braces will be encapsulated within the root: .
- For
*nth* roots, use `\sqrt[n]{ x }`

; for example, `a = \sqrt[4]{ x^8 + y^2 }`

: .
- The symbols for sums and integrals are
`\sum`

and `\int`

, respectively. To set limits, use subscripts and superscripts: `\sum_{k=1}^n k = \frac{n(n+1)}{2}`

: .
`\lim`

produces the "lim" symbol, and a subscript on this is the expression below it. For example, `\lim_{x\to\infty}f(x)=0`

: . In this example, `\to`

produces an arrow, and `\infty`

produces the "infinity" symbol. You can also use `\limsup`

, `\liminf`

, `\sup`

(supremum), `\inf`

(infinimum), `\max`

and `\min`

.
## Operators

Instead of just typing *sin*, *cos*, *tan*, etc., rather use `\sin`

, `\cos`

, `\tan`

, `\log`

, `\ln`

, `\exp`

, `\arctan`

. This ensures that the appropriate spacing is used.

## Greek letters and other special characters

To display a lower-case Greek letter, type it in lower-case with a leading backslash: `\epsilon`

, `\mu`

, `\delta`

, etc. For uppercase, capitalise the first letter: `\Epsilon`

, `\Mu`

, `\Delta`

.

## Parentheses

The symbol pairs `( )`

, `[ ]`

, `\{ \}`

(note the backslashes!) generate round, square, and curly parentheses at normal sizes. If you want your parentheses to grow appropraitely, precede the left parenthesis with `\left`

, and the right with `\right`

.

`\left| \sum_{i=1}^n a_ib_i\right| \le \left(\sum_{i=1}^n a_i^2\right)^{1/2} \left(\sum_{i=1}^n b_i^2\right)^{1/2}`

produces

.