I'm a third year physics student, and I need help with a decision. I have the core physics classes done, and some math (calc, 2 semesters of analysis, linear algebra, group theory, topology), as well as 4 months of research experience and a publication (of which I'm not the main author). My goal here is to be able to enter a top PhD program in mathematical physics. Option 1 - Graduate this winter. I'd graduate with the core classes you'd expect from any 4-year physics degree; 2 courses in quantum mechanics, subatomic physics, E&M, thermo, etc, without much extra stuff. On top of the math mentioned above, I'd also have a bit more algebra, as well as a class on Lie groups. I would then work during the Summer doing research in algebra, and enter a masters program in mathematics, in Lie theory and mathematical physics next Fall. I would then enter a PhD program somewhere else, again in mathematical physics. Option 2 - Graduate in 2 years. On top of everything from option 1, I would have an extra 16 months of research experience, as well as about 12 extra courses, in topics such as nuclear physics, more advanced QM, as well as manifold analysis, measure theory, more algebra (linear, abstract, lie), differential geometry/topology. Enter a masters/phd program after that, in mathematical physics. So basically, I'm wondering if it's worth it to do those extra years of undergrad courses, getting more experience and taking a few extra classes, or if it's better to enter grad school now, and take those extra classes there. In option 1, would the university where I would apply for a PhD care about my undergrad coursework (beyond the GPA and other general details) if I already have a masters? Would they care about having an extra 16 months of undergrad research on top of a masters, as opposed to someone with just a masters? Any help would be appreciated.