
LaTeX
TSR Wiki > Study Help > Subjects and Revision > Subject Guides > Mathematics > LaTeX
LaTeX (pronounced Latec  the x is actually a chi symbol) is an electronic typesetter used mainly for technical or scientific documents but it can be used for almost any form of publishing.
LaTeX is not a word processor! Instead, LaTeX encourages authors not to worry too much about the appearance of their documents but to concentrate on getting the right content. For example, consider this document:
The purpose is not primarily aesthetics as with a word processor, but correct content.
LaTeX contains features for:
* Typesetting * Control over large documents containing sectioning, crossreferences,
tables and figures. * Typesetting of complex mathematical formulas. * Advanced typesetting of mathematics with AMSLaTeX. * Automatic generation of bibliographies and indexes. * Multilingual typesetting. * Inclusion of artwork, and process or spot colour. * Using PostScript or Metafont fonts.
LaTeX is built in to TSR. It helps enormously getting people to help you out if you format your mathematical queries using this method. Below are some basic commands to get you started:
Using LaTeX on TSR:
TSR currently has two LaTeX packages installed, one called TeXLive and an older one called MimeTeX. In terms of functionality and typographical quality the former is better, and this guide will assume you use TeXLive.
To use LaTeX on the TSR forums, simply enter the LaTeX code into [latex][/latex] tags.
e.g. [latex]x = 5[/latex] gives
Note Most, if not all, of the LaTeX commands on this page also work using the tags [tex] and [/tex] (which saves you quite a bit of typing if you're doing lots of it!) TeX is just the earlier version of LaTeX
Multiplication and division
If you need to use these symbols, use \times and \div respectively.
e.g. [latex]3 \times 5 = 15[/latex] gives , while [tex]4 \div 2 = 2[/tex] gives
Complex notation
Polar form
[tex]\langle r , \theta \rangle[/tex] gives
Plus or minus
Indices
If the exponent is more than one character long, then you have to use curly brackets (i.e. { and } ) This is the case throughout LaTeX.
e.g. [latex]x^{10}[/latex] gives
For square roots, you use the \sqrt command.
e.g. [latex]\sqrt 2[/latex] gives
e.g. [latex]\sqrt {b^24ac}[/latex] gives
If you want to take the nth root, use the \sqrt[n] command.
e.g. [latex]\sqrt[3]{1+x^2}[/latex] gives
Equals sign and inequalities
To get an equals sign, you simply use the ordinary = sign.
e.g. [latex]2^4=16[/latex] gives
For 'not equal to', use \not=
e.g. [latex]2^4\not=2[/latex] gives
For less than signs, we use <, and for greater than signs, we use >
e.g. [latex]2^4>15[/latex] gives
For 'less than or equal to' signs, we use \leq, and for 'greater than or equal to' signs we use \geq
e.g. [latex]5x+3 \geq 8[/latex] gives
As with the equals sign, the symbol for 'not less than or equal to', 'not greater than', etc. is just \not followed by the symbol (i.e. >, <, \leq, \geq).
e.g. [latex]5x+3 \not\geq 8[/latex] gives
For 'equivalent to' signs, we use \equiv
e.g. [latex]1+ \cot^2 \equiv \mathrm{cosec}^2[/latex] gives
Fractions
We use \frac{numerator}{denominator}.
e.g. [latex]\frac{1}{2}[/latex] gives
e.g.2 [latex]x = \frac{b \pm \sqrt{b^24ac}}{2a}[/latex] gives
For fractions which aren't squashed onto one line, use \dfrac{numerator}{denominator}.
e.g. [latex]x = \dfrac{b \pm \sqrt{b^24ac}}{2a}[/latex] gives
Brackets
To get brackets in LaTeX you simply use the parentheses you're used to using when typing Maths without LaTeX.
e.g. [latex](x+1)^2[/latex] gives
If you've got a huge expression with multiple brackets or roots, fractions, etc., you can get larger brackets, using the \left( and \right) commands.
e.g. [latex]f(x) = 3x^2\left(1+\frac{2x+1}{x^22} \right)[/latex] gives (compare with [latex]f(x) = 3x^2(1+\frac{2x+1}{x^22})[/latex] which gives
Square brackets and curly brackets can also be used. For example, [latex]\displaystyle \int_1^2 \{x^2 + 1\} dx = \left[ \frac{x^3}{3} + x \right]_1^2[/latex] gives
Normal text
When writing within TeX tags, it is assumed that any letters denote variables, and hence are italicised. If you want the letters to be written normally (for example, if you are quoting units), use the \mathrm{} tag. The \text{} tag can also be used to perform this function on TSR.
e.g. [latex]\mathrm{hello}[/latex] gives (compare with [latex]hello[/latex] which gives )
For spaces, use "\ ".
e.g. [latex]\mathrm{With\ spaces\ without spaces}[/latex] gives
and [latex]v=1.2\text{\ m/s}[/latex] gives
Subscripts and superscripts
Superscripts are exactly the same as indices  we again use the ^ command.
e.g. [latex]\mathrm{Cl}^[/latex] gives (Note that you could also use the [sup] [/sup] tags instead though.)
For subscripts, we use the _ command.
e.g. [latex]x_1+x_2+x_3 = 5[/latex] gives
Sigma notation
To write sums, we use the \sum command.
e.g. [latex]\sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1) [/latex] gives
To make the first and last term appear above and below instead of to the side, use \displaystyle.
e.g. [latex]\displaystyle\sum_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1) [/latex] gives
Alternatively use \limits to add limits while keeping the size of the text the same.
[latex]\sum\limits_{i=1}^n i^2 = \frac{1}{6}n(n+1)(2n+1) [/latex] gives
To write the mean of x, xbar, use the \bar{x}. E.g.
Differentiation
Again, we use \frac{}{} to write dy/dx.
e.g. [latex]\frac{d}{dx} x^2 = 2x[/latex] gives
For f'(x), simply write it out normally within LaTeX tags.
e.g. [latex]f'(x)[/latex] gives
For partial derivatives, use \partial instead of d.
e.g. [latex]\displaystyle \frac{\partial}{\partial x} x^2y = 2xy[/latex] gives
Integration
For the integral sign, use the \int command.
e.g. [latex]\int 2x\ dx = x^2 + C[/latex] gives
For definite integrals, use the commands for subscripts and superscripts.
e.g. [latex]\int^2_0 2x\ dx = 4[/latex] gives
Again, like with sums, the \displaystyle command makes integrals look nicer:
e.g. [latex]\displaystyle\int^2_0 2x\ dx = 4[/latex] gives
Modulus sign
Use  for the modulus sign.
e.g. [latex]\sqrt{x^2} = x[/latex] gives
or \lvert and \rvert (in case you don't have a  key on your keyboard)
Factorial
Use the exclamation mark like normal.
e.g. [latex]4! = 24[/latex] gives
n choose r
[latex]^n\mathrm{C}_r[/latex] gives
Or, you can use the \binom command:
[latex]\displaystyle \binom{n}{r}[/latex] gives
You could also, if you wanted, write it as a vector(see below).
Greek Letters
Write \x where x is the written form of the Greek letter (i.e. alpha, beta, gamma, ... , omega).
e.g. [latex]\theta[/latex] gives
If you want the uppercase Greek letter, write the first letter as a capital.
e.g. [latex]\Delta[/latex] gives
Some Greek letters look identical to their Roman equivalents, and so are not provided; e.g. for lowercase omicron, simply write o.
Infinity
To insert the infinity symbol, use \infty.
e.g [latex]\displaystyle\sum_{i=1}^{\infty} \frac{1}{i^2} = \frac{\pi^2}{6}[/latex] gives
Trigonometry
[latex]\cos \theta[/latex] gives
[latex]\sin \theta[/latex] gives
[latex]\tan \theta[/latex] gives
[latex]\sec \theta[/latex] gives
[latex]\mathrm{cosec} \theta[/latex] gives
Alternatively, [latex]\csc \theta[/latex] gives
[latex]\cot \theta[/latex] gives
For the trig functions exponentiated, use ^ after the trig function and before the \theta (or whatever you're using).
e.g. [latex]\sin^2 \theta + \cos^2 \theta=1[/latex] gives
To write 'degrees', you could use the \circ command.
e.g. [latex]\sin 30^{\circ} = \frac{1}{2}[/latex] gives
Logarithms
Use some of the previous commands.
e.g. [latex]\ln x^k = k \ln x[/latex] gives
and [latex]\log_a x^k = k \log_a x[/latex] gives
Dots
[latex]x_1+x_2+\cdots[/latex] gives (i.e. central dots)
[latex]x_1+x_2+\ldots[/latex] gives (i.e. dots at the bottom)
[latex]\dot{x}[/latex] gives (i.e. dot above x)
[latex]\ddot{x}[/latex] gives (i.e. two dots above x)
Matrices and Vectors
For a bold letter, you could use normal text and make it bold (e.g. [b]i[/b] gives i), or if you wanted to use LaTeX, use the \mathbf{} command.
e.g. [latex]\mathbf{i}[/latex] gives
The \vec{} command can also be useful.
e.g. [latex]\vec{AB}[/latex] gives
To write a vector or a matrix, you could use either of the pairs
 \begin{pmatrix} \end{pmatrix}
 \begin{bmatrix} \end{bmatrix}
 \begin{Bmatrix} \end{Bmatrix}
 \begin{vmatrix} \end{vmatrix}
 \begin{Vmatrix} \end{Vmatrix}
 \begin{matrix} \end{matrix}
which enclose the matrix/vector in ( ), [ ], { },  ,   and nothing, respectively. Between these \begin{} and \end{} commands, enter the coefficients of the matrix/vector row by row, separating coefficients on the same row with & and separating rows by \\.
Examples:
[latex]\begin{pmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{pmatrix}[/latex] gives
[latex]\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{bmatrix}[/latex] gives
[latex]\begin{Bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{Bmatrix}[/latex] gives
[latex]\begin{vmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{vmatrix}[/latex] gives
[latex]\begin{Vmatrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{Vmatrix}[/latex] gives
and
[latex]\begin{matrix} 1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9 \end{matrix}[/latex] gives
For vectors, simply write a matrix with only one column:
[latex]\begin{pmatrix} x \\ y \\ z \end{pmatrix}[/latex] gives
Arrays
Sometimes, it could be useful to lay out what you write nicely in a table. For many cases, the \begin{matrix} \end{matrix} commands will suffice for this, but a little more control is offered by the \begin{array} \end{array} commands.
When using this, you need to decide beforehand how many columns you want to have, and include a string of letters, one for each column, enclosed in {} directly after the \begin{array} command. The letters indicate what alignment you want of the entries in that column, l for left, c for centre, and r for right.
e.g.
[latex]\begin{array}{rlc} n & n^2 & n^3 \\ 3 & 9 & 27 \\ 4 & 16 & 64 \\ 11 & 121 & 1331 \end{array}[latex]
gives
You can have horizontal and vertical lines in your table. For a horizontal line, use the \hline command , and for a vertical, put a  in the list of column alignments.
e.g.
[latex]\begin{array}{rlc} n & n^2 & n^3 \\ \hline 3 & 9 & 27 \\ 4 & 16 & 64 \\ 11 & 121 & 1331 \end{array}[latex]
gives
Arrows
e.g. [latex]\Rightarrow[/latex] gives
e.g. [tex]\not\Rightarrow[/tex] gives
e.g. [latex]\rightarrow[/latex] gives
e.g. [latex]\Longrightarrow[/latex] gives
e.g. [latex]\longrightarrow[/latex] gives
e.g. [latex]\mapsto[/latex] gives
Arrows can point left by replacing "right" with "left", or they can point both ways by replacing "right" with "leftright".
e.g. [latex]\longleftarrow[/latex] gives
e.g. [latex]\Leftrightarrow[/latex] gives
Logic Symbols
Other
[tex]\displaystyle\underbrace{10^2 + 14^2 + 18^2 +\cdots}_{41\text{ terms}}[/tex] gives
[latex]\lim_{x\to 0}[/latex] gives
[latex]\displaystyle\lim_{x\to 0}[/latex] gives
Sets
[latex]\subseteq[/latex] gives
[latex]\nsubseteq[/latex] gives
[latex]\mathbb{P}[/latex] gives
[latex]\mathbb{N}[/latex] gives
[latex]\mathbb{Z}[/latex] gives
[latex]\mathbb{I}[/latex] gives
[latex]\mathbb{Q}[/latex] gives
[latex]\mathbb{R}[/latex] gives
[latex]\mathbb{C}[/latex] gives