So I'm currently finishing up my last quarter of undergrad, but unfortunately I have to take a year off before starting grad school. My degree is in physics, but I've been far more interested in mathematical physics than anything I've taken in the past couple years and plan on going to grad school for math (should've double majored but it's too late for that now). I've taken the first part of abstract algebra (covered group theory) and real analysis, and my physics courses covered applications of complex analysis and differential equations.

Now, my question is, what would be some of the most important topics for me to study in the next year before grad school? I'm pretty sure finishing up abstract algebra and real analysis will be among the most important, but I'm open to any advice.

Thanks in advance.

  • $\begingroup$ From what I remember (and maybe depending on different countries), I would say that usually undergraduate program covers : abstract/linear algebra, analysis (basics : riemann integral, derivative, limits, taylor developpment, differential equations, etc... then lebesgue theory, probability, complex analysis, series and especially power series, Fourier theory), topology (basics : open/closed subset, metric spaces, density, compactness, connectedness, etc...) and topology together with algebra (Banach/Hilbert/Hermitian spaces, density results in linear algebra). I would say it is a fair start. $\endgroup$ – yago May 23 '14 at 9:02
  • $\begingroup$ The best people to ask are the people at your institution. $\endgroup$ – Gerry Myerson May 23 '14 at 9:21
  • $\begingroup$ I actually have asked people at my institution and have gotten extremely varied results. Only consistent answers I've gotten are algebra and analysis, and differential topology/geometry for some reason. But seems like those first two are where I should start. $\endgroup$ – Silynn May 23 '14 at 9:27

I would say something you should aim for if you want to understand mathematical physics is Lie theory (in particular Lie groups and their representations). This is a topic that you can get started on with fairly few requirements (by for example starting with the book by Brian Hall called Lie groups, Lie algebras and representations), and which will be a major topic in many areas of mathematical physics.

  • $\begingroup$ Agreed with Tobias. It is a cornerstone in quantum physics! +1 $\endgroup$ – user3001408 May 23 '14 at 9:07

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