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1) I have taken classical mechanics but the course didn't cover Lagrangian and Hamiltonian mechanics, that's covered in a course named classical mechanics II. With my remaining hours, I have to choose between this or Solid State Physics or upper level math. I know that this level of mechanics will be covered in a grad class mech course but I feel a bit afraid about not seeing it before that. Any recommendations?

2) I've taken all required math courses + an upper level linear algebra course but nothing else beyond that. I've learned a lot of other math from physics classes and my advisor recommended to take more physics than math as "you'll learn the math you need there". This summer I'm signing up for probability & statistics and a mathematical methods course (PDE's basically) and I'm also taking a graduate Mathematical Physics course in the Fall. However, I feel like Complex Analysis (the grad math physics course presumably covers this) is mentioned and used a lot in physics and was also contemplating Differential Geometry as I'm taking general relativity and feel it could help further understand the subject which I want to continue studying in graduate school if possible. Are the courses I've mentioned enough or not?

3) Research with a professor is eating up my remaining hours, which is good and bad at this point. We can choose how much academic credit we want to get for research work and it'll count as an advanced elective. Of course, I can always choose to get little (1 or 2 hours) or no credit for it on paper and still participate but I'm under the impression that having strong hours on this will look great when I apply to graduate school. Can anyone enlighten me on this?

All of this is in preparation for graduate school in physics. I want to have a good working , and broad, knowledge from my undergraduate studies. Sorry for the long post but my advisor really sucks and doesn't talk much. Thanks for the help in advance!