How do I enter groovy typeset mathematics, images and code?

This site is here to facilitate mathematical and computational discussion. As such, it is often nice to format your questions and responses as nicely as possible - including typeset mathematics, images, and code as appropriate.

Sections and other formatting

Textual entry into discourse is based on Markdown - a lightweight markup language that makes formatting relatively easy. To start this particular section, for example, I simply entered:

## Sections and other formatting

Creating a bulleted list is as easy as indenting with asterisks. To get this:

• First item
• Second item
  • A sub item

Just type this:

* First item
* Second item
  * A sub item

And code like the above is entered by indenting four spaces.

To create typeset mathematics, simply enter a LaTeX snippet. For example, to generate this:

$$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi},$$

I simply typed

$$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi},$$

You can do inline as well. Thus, to generate $f'(x) = -2xe^{-x^2}$, simply type:
$f'(x) = -2xe^{-x^2}$.

How do I type set brackets in math mode? In LaTeX, I can simply type \ { \ } in math mode. That doesn't seem to work here. If I type \$ \ { a \ } \$ I get $ \ { a \ } $ with no set brackets.

Whenever you're having problems like this on Discourse, try the double slash. So, if I type $\\{a\\}$, I get $\{a\}$.