[AUCTeX] \frac and \ddot key bindings

[Ryan Krauss]

I am a new AucTeX and Emacs user.  AucTeX seems really cool and I am
excited about it.  I am an experienced LaTeX user and former vim user.

I use \frac{}{} and \ddot{} a lot and I see them on the Math menu in
Emacs, but there is not a math mode short cut for them.  I have poked
around a bit, but I don't see how to define my own math mode short
cuts for them.  I think I used `/ for \frac in vim, but it seems to be
assigned to \not.  I am pretty new to Emacs, so I could really use
some elisp lines to copy and paste into my .emacs file for these two
as examples.
(If these short cuts already exist, can you please tell me what they are).

One other thing that troubles me: the LaTeX environments menu doesn't
have an entry for \begin{equation}.  Is there a short cut to create an
equation environment?

Thanks,

Ryan