In understanding the derivations, a strong calculus background is desirable. You should also be familiar with multivariable calculus because partial differentiation is useful when studying the wave nature of particles; differential equations when studying Schrodinger,etc...
The text book I used was Physics for Scientist and Engineers with Modern Physics, 7E by Raymond Serway and John Jewett, Jr. Chapters 39-46 deal with quantum mechanics and modern physics. It's a great text.
Another good text in understanding Quantum mechanics on a more advanced mathematical level would be Quantum mechanics : a conceptual approach by Hendrik Hameka.
Also, I would suggest reading In Search of Schrodinger's Cat by John Gribbin. This book is great for those who want to know more about the history and progress of quantum mechanics.