There is relatively little mathematics required for a typical first year chemistry course beyond what most will have studied at school.
A solid understanding of algebra, trigonometry and diffrentiation/integration is necessary. More advanced topics which may be useful include partial derivatives, solving simple first and second order differential equations, solving partial differential equations, group theory, Fourier transforms.
Appreciation of group theory in particular is important for a good understanding of spectroscopy and quantum mechanics. A good (but difficult!) introduction to this topic with suitable examples is Chemical Applications of Group Theory by F.A. Cotton. For the other mathematics you might find Mathematics for Engineers and Scientists by Alan Jeffrey useful, although there are lots of other texts which cover this sort of material well.