Here's a quick list off the top of my head. On the left is a Quantum Mechanics concept, on the right is the math concept its related to.

* The Schrodinger Equation --> Differential Equations. Wave equation.

* Wavefunctions and Normalisation --> Probability Density. Differential Equations and Function continuity

* Bohr Model --> Algebra

* Bracket Notation --> Matrices, vectors, vector spaces, linear independence

* Operators --> Transformations, matrices, unitary matrices

* Commutators --> see operators! maybe a little algebraic field theory for motivation on why AB - BA is not necessarily 0.

* Eigenstates --> these are special wavefunctions. Eigenvalues and Eigenvectors

I recommend Paul Dirac's original Principles of Quantum Mechanics for a baptism by fire. He's the primary source for a lot of this stuff. He simplified a lot of the methods in QM with his Bracket notation.

Sorry if I missed something.