Matlab is standard in computational neuroscience (and most disciplines) for drafting programs and for less computationally intensive analysis and modelling. Compiled languages are usually a better choice if you need to do something extremely intensive. R is, of course, standard for statistics, but I honestly do most of my analysis in Matlab.
As far as mathematics: A strong background in calculus, linear algebra, statistics, and differential equations is non-negotiable. If you're interested in the biologically realistic modelling of neurons and neural networks, than you really can't get your foot in the door without some familiarity with dynamical systems (I've been working with a fairly abstract model of pre-frontal neural clusters over the last few months, and 90% of what I'm doing involves non-linear dynamics). Beyond that, you can find a use for almost anything; knowledge of stochastic processes is extremely useful, and I've even managed to make use of some topology and analysis.