Hello, I'm a rising Junior at UC Berkeley, and I'm in a bit of a dilemma for the upcoming semester. I'm a math major, and intend to go to graduate school to pursue a Ph.D in Pure Math, but am not sure about the best path to take. Right now, I've completed the upper division Linear Algebra (Friedberg, Insel, Spence), Abstract Algebra (Dummit/Foote), and Real Analysis (Baby Rudin) courses with A's in all of them, and am in the process of completing Elementary Number Theory and Complex Analysis. For the fall, I have the choice of either skipping Galois Theory and going straight into the first-year graduate Algebra sequence, or slowing down and taking the upper division Galois Theory class and waiting until my senior year to take the Algebra sequence. With the first option comes a potential opportunity to get way ahead of the curriculum and take more advanced graduate classes next year, and with the second comes more of an opportunity to explore other areas of math (set theory, logic, algebraic topology) at the undergraduate level and get a more solid foundation at the cost of not having any real graduate classes under my belt when I apply to grad school next year. I have tried to study field theory on my own, and have a relatively good grasp on it, but not near the level I would have, I think, after completing a course devoted solely to it. As someone who wants to potentially pursue some area of algebra as a specialization after my undergraduate years, which option would be more beneficial? Will the grad. course kill me? Do admissions officers look much more strongly on those who have a strong graduate background? Thank you very much!