How to prepare for graduate school in mathematics?

[Fisicks]

Hi,

I am a sophomore and I recently dropped Graduate Complex Analysis. I was just missing something. The solutions to the questions on the problem set were not capable of being formed by me. This being said, I am wondering if it is still possible for me to attend graduate school for mathematics. Forget prestigious schools, will I still be able to do a Ph.D. in mathematics at any graduate school when it comes time?

I have taken these upper division
intro. to abstract algebra - A
advanced calculus I/II - A/A
intro. to topology - A
linear algebra - A
I am currently taking
field theory
number theory
set theory


My whole plan was to go to grad school and not being able to keep up in grad complex kinda made me question this. Looking for some advice.

Thanks for your time.

 

[deluks917]

Where do you go to school (Top 5, Top 10, etc)?

 

[Number Nine]

It seems to me that you don't have much experience with analysis, let alone complex analysis, which may be your problem. I'd say either enrol in a few real analysis courses or self-study over the summer. Do you have any experience with complex variables?

 

[Fisicks]

University of Maryland,

and yeah I had no complex analysis experience except the usual 1 year undergrad course in real analysis.

Also, I plan on doing a REU this summer if this factors in. I applied to 13 places.

 

[micromass]

Did you take any rigorous analysis classes yet??

You're only a sophomore, so you're not really expected to be able to do graduate classes yet. I suggest you take an undergrad complex variables class. Maybe you can handle the complex analysis in your junior/senior year??

 

[micromass]

University of Maryland,

and yeah I had no complex analysis experience except the usual 1 year undergrad course in real analysis.

Also, I plan on doing a REU this summer if this factors in. I applied to 13 places.

What were the topics of your real analysis class and the grad complex analysis class??

What was difficult about the complex analysis? Can you give us a problem you struggled with? What did you find hard about it?

 

[Choppy]

How did you get permission to take a graduate class as a sophomore?

This sounds to me like a clear case of jumping into a class that you were not ready for. Taking graduate level classes is really only something you should consider if you're a senior, and you really aren't being challenged by courses at your own level. In graduate classes the problems are supposed to be mini research projects - directed at students who have the time and background to dedicate to solving them. Just having the introductory course under your belt isn't necessarily the only prerequisite. You need to have a certain level of understanding of the field as a whole.

By no means does struggling at this point mean that you are not capable of completing a PhD. It does suggest however, that you have some academic maturing to do - there's nothing wrong with that.