# 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

.