Scott Aaronson has just published a new book about quantum computing. According to the nice introductary comments the author himself has written to his book here (scroll down to the second half of the article if you only want to learn about the book), it should explain and introduce both the physical and mathematical concepts quantum computing is based on.
Maybe reading this book can help studentsstudents in choosing the appropriat mathematical and phyics lectures to be heard in what reasonable order to finally being able to do research in quantum computing too.