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I am a math major who will be a senior in my undergraduate career. I will be applying to graduate schools in mathematics.

I still have not decided which courses to take in my senior year. So far, I have taken most of the undergraduate math courses, including real analysis, complex analysis, abstract algebra, and advanced linear algebra. I am certainly going to take topology (2 quarters) and differential geometry (1 quarter), and possibly probability theory (2 quarters) next year, but I might also be able to take additional class, so I am debating whether to take the graduate-level analysis sequence or the second-year physics sequence.

It probably makes a lot of sense to take the graduate analysis sequence (3 quarters) if I am planning to go to a graduate school in math. The textbook for this course is Big Rudin (of course!). I really enjoyed my analysis classes (both real and complex) here, and I think it would be wonderful to learn more about it. It would also help my chance of getting into more selective graduate schools as well. However, while I did enjoy analysis, I wasn't really a superstar in my classes--while I did get A's in my complex analysis sequence, I only did reasonably well in my real analysis sequence (B+/A- level), so I'm not so sure if I would be able to handle a graduate level course. Furthermore, I will be preparing my thesis through my senior year, so topology and thesis might be enough for my senior year. I did, however, talked to a few professors, including the one who I had for real analysis, and the one who will be teaching the graduate analysis next year, and most of them seemed positive about that idea, except for one.

Now, some of you might be wondering why in the world I would ever want to take a physics class. I took a first-year physics in my sophomore year, but I was only semi-interested in the subject back then, so I didn't study physics further. But recently, I took a seminar course that studied a little bit of nonlinear dynamics and quantum physics (It wasn't really like a physics class, since the seminar was also accessible to non-science majors... so no heavy math was involved), and I thought the topics were very interesting, which made me regret for not studying more physics. So I thought that while it is too late to major in physics now, I can at least learn a little more so that I can study physics during my free time, or even better, consider studying mathematical physics in grad school (warning: I don't really know what this is; I only mentioned because it involves "math" and "physics"). The first quarter of the second-year physics sequence that I'm considering to take discusses modern physics (i.e. special relativity, light, quantum mechanics, atomic and nuclear physics), and the remaining two quarters will discuss thermodynamics and statistical mechanics. If I'm lucky, I might be able to get a minor in physics, but that's not really necessary.

So yeah, I was wondering what people on here think about this. It's too bad that they are both offered at the same time, because otherwise I would try out both of these courses during the first week and stay in the one I feel more interested. Ask me if you have any question about my background.

Thanks