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.