Differential equations, linear algebra, depending on the level some group theory won't hurt you. For linear algebra, I'm partial to the Friedberg Insel and Spence "Linear Algebra" textbook, although any good quantum mechanics book will have at least a cursory overview of linear algebra. The differential equations are things you'll probably see in your standard university course on the subject.
One of the problems of math in QM is the Dirac notation, where column vectors are denoted |z> and row vectors are denoted <z|, and the base field is complex. Even if you already know basic vector space math, that takes some getting used too.
the mathematics required for QM is not very different from those in E&M, CM or stat mechanics. A few new stuff though, especially operators, hilbert spaces and the like. But i think, don't start on QM if you don't have a good idea of classical physics.
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