In fact, perhaps all but one or two lecture topics will be self contained, so the main thing that you really need is mathematical maturity. Basically, if you are happy to get homework problems that say, ``Prove the following theorem,'' then you are in the right course; and if not, then not.
The normal prerequisite is an undergraduate course in automata theory, such as CS 301. You should be familiar with the basics of regular and context free languages, and the machines that accept them, though we will probably only explicitly refer to them in one or two lectures.
We will begin with a fast review of Turing machines.
See me if you want to discuss your background.