quick LaTeX guide

Note: The following is adopted from Andy Schultz's Quick LaTeX Guide.

Wikidot uses a markup language called $\LaTeX$ to generate properly typeset mathematics. Since you'll be posting to the forum and creating Wiki pages with serious mathematical content, it's good that you get some practice writing mathematical expressions in $\LaTeX$.

the basics

When you're in the editing panel, you can insert mathematical expressions within your text (i.e., "inline") by using the code

[$ your-mathematical-expression-here $]]

For instance, this sentence — which includes the equation $x^{2}+y^{2} = r^{2}$ — is typeset as

For instance, this sentence -- which includes the equation [[$ x^{2}+y^{2} = r^{2} $]] -- is typeset as

You can also have your mathematical expressions separated from the text and placed on their own line for emphasis. For instance, if you wanted to type


Here's some fancy mathematics that I don't really understand

(1)
\begin{align} \log \zeta(s) = s\int_{2}^{\infty} \frac{\pi(x)}{x(x^{s}-1)}~dx = \log \prod_{p} (1-p^{-s})^{-1}. \end{align}

Man, that's complicated!


then you'd use the code

----
Here's some fancy mathematics that I don't really understand 
[[math]] 
\log \zeta(s) = s\int_{2}^{\infty} \frac{\pi(x)}{x(x^{s}-1)}~dx = \log \prod_{p} (1-p^{-s})^{-1}.
[[/math]] 
Man, that's complicated!
----

more examples

Here are a few more examples that illustrate some of the mathematical notation we may want to use:

expression you want code you type
$n \in \mathbb{N} \subseteq \mathbb{Z}$ [[$n \in \mathbb{N} \subseteq \mathbb{Z} $]]
$\sum_{i=1}^n i^2=1^2+2^2+ \cdots +(n-1)^2+n^2$ [[$\sum_{i=1}^n i^2=1^2+2^2+ \cdots (n-1)^2+n^2 $]]
$\sqrt{2} \notin \mathbb{Q}$ [[$ \sqrt{2} \notin \mathbb{Q}$]]
$2\in \{2,3,4\} \cap \{1,2,3\}$ [[$2\in \{2,3,4\} \cap \{1,2,3\}$]]
$f:A\to B$ [[$f:A\to B$]]
$f(x_1)\neq f(x_2)$ [[$f(x_1)\neq f(x_2)$]]
$\{a_n\}_{n=1}^{\infty}$ [[$\{a_n\}_{n=1}^{\infty}$]]
$(f\circ g)(x)=f(g(x))$ [[$(f\circ g)(x)=f(g(x))$]]
$\frac{a}{b}+\frac{c}{d}\neq \frac{a+b}{c+d}$ [[$\frac{a}{b}+\frac{c}{d}\neq \frac{a+b}{c+d}$]]

Wikidot also provides a brief summary of how to include mathematical expressions into the wiki.

a few general comments

Here are a few things to keep in mind:

  • All wiki commands are of the form [[blah]].
  • All inline mathematical notation must be framed by dollar signs. That is, in the wiki, all inline mathematical notation is of the form [[$stuff$]].
  • All displayed mathematical notation (i.e., on its own line and centered) is of the form [[math]] math-stuff-here [[/math]].
  • All special symbols in $\LaTeX$ are of the form \some-command. Once you've used $\LaTeX$ enough, you can almost guess what the command is for a certain symbol.

For a list of some of the more common $\LaTeX$ symbols, see here. If you want to see a really, really, really long list of symbols, go here.

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