My school is offering a advanced mathematical methods classes next semester, taught by a supposedly world-renowned professor. Everyone to whom I've spoken, students and faculty alike, says he's an amazing teacher who gives you a unique education. However, here is the course description: My problem is that I don't have any context for the topics described above. While I'd certainly like to take a class with the aforementioned professor, I don't want to sink a lot of time into learning things that may or may not actually be useful. Is there anyone more familiar with these topics who could give me their take on them, particularly regarding how pervasive they are in various subfields of physics?