You should know the basics of algebra and analysis: matrix manipulations, determinants, vector spaces, derivatives, integrals, differential equations; at least to the point of understanding what they are. A basic general physics course of the kind served to most undergraduate science students in first and second year would be rather helpful too, as most of our examples will assume a certain understanding of the world around us (not too much though: it's OK not to remember the value of Planck constant). To this extent you should brush up on introductory classical and quantum mechanics and introductory classical field theory (electromagnetism).
Regarding programming and general computing skills, a certain degree of experience is expected. You should have been exposed to POSIX and some basic POSIX tools: you should know how to manipulate POSIX files and directories and how to edit and compile programs. If you are a Windows-NT user, you can obtain GNU tools from www.cygnus.com - these provide a fairly adequate level of POSIX compatibility and cost nothing.
If you are a Linux user, your computing skills are high enough.
If you have only ever used a Macintosh or Windows-95, do not despair. You can learn all that you need in one afternoon. If you are a fast learner. It's not that hard.
Familiarity with, even a mastery of, GNU Emacs will serve you well in this course.