What classes are needed for a rigorous understanding of quantum mechanics?

[blindconsole]

I want to relearn QM within a rigorous mathematical framework. What classes should I take? Off the top of my head, I expect that I'll need to know functional analysis and group theory. What else?

 

[John Creighto]

I want to relearn QM within a rigorous mathematical framework. What classes should I take? Off the top of my head, I expect that I'll need to know functional analysis and group theory. What else?

I bought a book recently from Chapters, "The Mathematical Principles of Quantum Mechanics by Derek F. Lawden" for only 30$. I believe it is exactly what you are looking for. It is the size of a small novel and it will build up the mathematical principles of quantum mechanics from the ground up. It even has some stuff at the end of the book on relativistic quantum mechanics.

 

[HallsofIvy]

As to what classes you should take, certainly Linear Algebra would be necessary. Probability, surely.

Since you are talking about taking classes, I assume you are in a college now. Talk to people in the Physics department!