# Writing Tex Notation

## Using TeX Notation with the UVLe Tex filter

Go to Course Administration > Filters and make sure that the Tex Notation is ON

## Superscripts, Subscripts and Roots

Superscripts are recorded using the caret, ^, symbol. An example for a Maths class might be:

 $$4^2 \ \times \ 4^3 \ = 4^5$$
This is a shorthand way of saying:
(4 x 4) x (4 x 4 x 4) = (4 x 4 x 4 x 4 x 4)
or
16 x 64 = 1024.

$4^2\\times\4^3\=4^5$


Subscripts are similar, but use the underscore character.

 $$3x_2 \ \times \ 2x_3$$

$3x_2 \ \times \ 2x_3$


This is OK if you want superscripts or subscripts, but square roots are a little different. This uses a control sequence.

 $$\sqrt{64} \ = \ 8$$

$\sqrt{64} \ = \ 8$


You can also take this a little further, but adding in a control character. You may ask a question like:

 $$If \ \sqrt[n]{1024} \ = \ 4, \ what \ is \ the \ value \ of \ n?$$

$If \ \sqrt[n]{1024} \ = \ 4, \ what \ is \ the \ value \ of \ n?$


Using these different commands allows you to develop equations like:

 $$The \sqrt{64} \ \times \ 2 \ \times \ 4^3 \ = \ 1024$$

$The \sqrt{64} \ \times \ 2 \ \times \ 4^3 \ = \ 1024$


Superscripts, Subscripts and roots can also be noted in Matrices.

## Fractions

Fractions in TeX are actually simple, as long as you remember the rules.

 $$\frac{numerator}{denominator}$$ which produces $\frac{numerator}{denominator}$ .


This can be given as:

 $\frac{5}{10} \ is \ equal \ to \ \frac{1}{2}$.


This is entered as:

 $$\frac{5}{10} \ is \ equal \ to \ \frac{1}{2}.$$


With fractions (as with other commands) the curly brackets can be nested so that for example you can implement negative exponents in fractions. As you can see,

 $$\frac {5^{-2}}{3}$$ will produce $\frac {5^{-2}}{3}$

 $$\left(\frac{3}{4}\right)^{-3}$$ will produce $\left(\frac{3}{4}\right)^{-3}$  and

 $$\frac{3}{4^{-3}}$$ will produce $\frac{3}{4^{-3}}$

 You likely do not want to use $$\frac{3}{4}^{-3}$$ as it produces $\frac{3}{4}^{-3}$


You can also use fractions and negative exponents in Matrices.

## Brackets

As students advance through Maths, they come into contact with brackets. Algebraic notation depends heavily on brackets. The usual keyboard values of ( and ) are useful, for example:

  $d = 2 \ \times \ (4 \ - \ j)$


This is written as:

 $$d = 2 \ \times \ (4 \ - \ j)$$


Usually, these brackets are enough for most formulae but they will not be in some circumstances. Consider this:

 $4x^3 \ + \ (x \ + \ \frac{42}{1 + x^4})$


Is OK, but try it this way:

 $4x^3 \ + \ \left(x \ + \ \frac{42}{1 + x^4}\right)$


This can be achieved by:

 $$4x^3 \ + \ \left(x \ + \ \frac{42}{1 + x^4}\right)$$


A simple change using the \left( and \right) symbols instead. Note the actual bracket is both named and presented. Brackets are almost essential in Matrices.

## Ellipsis

The Ellipsis is a simple code:

 $x_1, \ x_2, \ \ldots, \ x_n$


Written like:

 $$x_1, \ x_2, \ \ldots, \ x_n$$