How Can I Assess My Math Standing and Future Path?

[pob1212]

Hi all,

I'm a 3rd year undergrad at a top 20 university, not known for its math program, finishing up my degree in applied math and I've come to the conclusion that I behind in mathematical experience and ability when compared to other 3rd years undergrads at top math universities. The point of this post is for you to assess my current standing and offer guidance. Here's some background:

GPA ~ 3.7-8

Courses taken:
Multivariable Calc
Linear Algebra
Diffe Eq
Foundations
Numerical Analysis
Probability & Stat I

Courses to take:
Probability & Stat II
Partial Diff Eq
Optimization Theory

I have the option of getting a degree in applied math, but I'd have to take a year of real analysis and algebra, and a semester of complex variables and abstract vector spaces.

I have no research experience! (I know, bad)
I've also been the type of student who only studies math as it pertains to coursework.
I only decided last year (as a sophomore) that I wanted a degree in math. As for the future, I remain undecided. If I get the pure math degree (in addition to the applied), I perform very well in those courses, my mathematical ability improves greatly, namely with proofs, and I involve myself in research, then I'd consider myself capable of studying some area of pure math at the graduate level. Could be wrong...
I could also study something applied such as statistics...
Or I could not go to grad school and get some industry job

The point is, I'm behind the game and I don't know exactly what I want to do with math. However, I have decide my focus is math. Pure math is very attractive to me, but I'm currently weak in this area. I would very much like to go to grad school either way. I'd also like to get involved in an REU this summer and thought I could until I did a bit of research and found out how competitive they are, which sparked about an hour of self reflection and this post.

If you decide to respond, please do so honestly (I don't need sugar coated responses), and provide advice; its time for me to move forward. Again, where do I stand? what steps should I be taking? where am I lacking? etc...

Thanks a lot

 

[Pengwuino]

I don't even know what the point of this thread is. It sounds like you have a good idea of what you need to do already. Do you have any specific questions that focus on a certain part of this path you're attempting to take? Are you not sure you can get into a good grad school?

 

[pob1212]

Are you not sure you can get into a good grad school?

Correct. In short, I'm not sure I can make it in pure math given my current standing. I believe I have a better chance in an applied math graduate program, but even then I don't think I'd get into a good one.

I realize I have to nail each course from here on out and I need to get involved in research. Even if I do both I feel like I'm so far behind that I've missed the boat. I'm asking for thought and advice...

 

[Pengwuino]

Why do you feel you're so behind? You're only in your third year. It's not absolutely mandatory that you have research experience, and certainly not before your third year. Your GPA is fine and if you plan on trying to do research, you're fine. I think you may need to start thinking more about exactly what kind of mathematics you want to do because, if it's anything like Physics, you'll want to select your school based not on overarching ideas such as "applied" vs "pure", but on specific subsections of the field.

 

[AlephZero]

Apparently you haven't done any analysis courses (as opposed to calculus) so presumably that is not a prerequisite for the courses in your OP.

That would suggest those courses are aimed at how to use the math rather than a "deep level" understanding of it. As you said, you need some analysis (and possibly some abstract algebra as well) to be "up with the game" as a mathematician, either pure or applied, and you may need to fill in some theoretical gaps in your chosen subject if you want to do research in applied math.