Math Graduate Course vs. Stronger Foundations

[Mews]

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!

 

[micromass]

Well, what graduate algebra courses are we talking about here??

I have no doubt that you could handle the grad courses with having seen Galois theory. But field theory and Galois theory can become fairly important at a point (especially algebraic geometry), so having seen Galois theory can really be a bonus. In fact, I expect all math majors to take Galois theory at some point, if only for general culture.

So if I were you, I would just take the Galois theory, and leave the grad courses for later. Or you could self study Galois theory too! In either case, make sure you know it.

 

[Mews]

This would be the basic graduate algebra sequence, taught out of Lang, and they will cover Galois Theory again, but I'm guessing pretty quickly...

 

[jetforcegemin]

Why not register for 114 and 250A and then dropping one based on how comfortable you feel with 250A? Also, did you take 113 or H113?

 

[transphenomen]

I do not know if your school supports this, but you could audit the lower class while taking the upper class. That way you do not need to do all the work of the lower class if you do not have enough time.

 

[Mews]

I took regular 113. I will probably try going to both classes for a little while, but should I feel behind if I feel like I cannot handle the graduate course? I'm really not sure how high the bar is set in terms of getting into math Ph.D programs...

Thank you all for your advice thus far!

 

[micromass]

I took regular 113. I will probably try going to both classes for a little while, but should I feel behind if I feel like I cannot handle the graduate course? I'm really not sure how high the bar is set in terms of getting into math Ph.D programs...

Thank you all for your advice thus far!

All depends on why you can't handle the graduate course:

If the graduate course starts of with things you know nothing off and which you still have to take a course in, then this is not so bad. Just taking the appropriate courses should do it.

However, if it appears that the course goes to fast and you are unable (or unwilling) to put time into it, then this is a bad sign.

 

[jetforcegemin]

Most of the people who I know that took 250A without 114 took H113 so you might be a bit behind. I've finished my requirements for the math degree and I had quite a bit of trouble when I was enrolled in 218A because the prereqs were severely understated and the pace was extremely quick which forced me to eventually drop the class. I would definitely have a backup plan since there is a very real possibility that you just aren't prepared yet. If you have any questions about specific math courses at Berkeley I suggest you ask at the Uc Berkeley subforum at college confidential. There are quite a few math majors there that would be able to answer your specific questions.