# Writing Tex Notation

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## 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:

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


A more practical application could be:

Question:

 "Add together all the numbers from 1 $\ldots$ 38.
What is an elegant and simple solution to this problem?
Can you create an algebraic function to explain this solution?
Will your solution work for all numbers?"


Answer: The question uses an even number to demonstrate a mathematical process and generate an algebraic formula.

 Part 1: Part 2. Part 3. $1. \ 1 \ + \ 38 \ = \ 39$ $2. \ 2 \ + \ 37 \ = \ 39$ $3. \ 3 \ + \ 36 \ = \ 39$ $\ldots$ $19. 19 \ + \ 20 \ = \ 39$ $\therefore x \ = \ 39 \ \times \ 19$ $\therefore x \ = \ 741$ An algebraic function might read something like: $t = (1 + n) \times n/2$ Where t = total and n = the last number. The solution is that, using the largest and the smallest numbers, the numbers are added and then multiplied by the number of different combinations to produce the same result adding the first and last numbers. The answer must depend on the number, $\frac{n}{2}$ being a whole number. Therefore, the solution will not work for an odd range of numbers, only an even range.

Source: Tex Tutorial