I've decided to pursue introductory quantum mechanics as an independent study next year at my high school, and I am looking for a good textbook. Specifically, I would like a book that does not limit the math it uses to describe concepts. I'm familiar with multivariable calculus, differential equations, and linear algebra, as well as some basic concepts of abstract algebra. With that in mind, I'm looking for a book that rarely, if ever, sacrifices the formality and mathematical rigor of the topics covered for the kind of intuitive, conceptual presentation that glosses over important subtleties. The ideal book would also not require extensive prior understanding of physics; I have only learned as much as is taught in AP Physics C, and I plan to study pertinent material, like waves, that was not part of the curriculum but is essential to quantum mechanics. So let's suppose my experience by the time I start quantum will be at most all of the material covered in a sizable first-year physics textbook with calculus (specifically, University Physics by Young and Freedman).
In short, I am looking for a book that will cut me some slack with prior physics knowledge but not with prior math knowledge. Any ideas?