Do I need to lower my expectations?

[Tavanio]

I'm heading into my final year studying math, and am planning on going for a PhD.  I'm hoping to get into top tier schools like CMU, UChicago, or MIT, but I'm not sure I have a real chance.  I've kept a 3.97 GPA, but my school is a small midwestern university so I don't know if the lack of a reputation will make that mean less.  On the general test I got 165 Q and 162 V, so only on the bottom edge of what they're looking for.  I don't have any REUs or research experience outside of classes and thesis.  On the practice subject tests I've taken I've gotten roughly 60th percentiles, so again not the greatest.

 

However, on the positive side I'm likely going to have very strong letters of recommendation, and have been able to take grad level courses.  I've been the TA for Real Analysis last year and this year, and have presented my thesis at a math conference.  I don't know if that's enough, though, so I'm not sure if I should give up on the top tier and look towards slightly less ambitious schools.  Any insight would be greatly appreciated.

Edited August 7, 2015 by Tavanio

[isilya]

Get more research experience this year!!!!! That is the number one.thing you can do to improve your application. You might want to improve your Q more since you're applying to math programs, but do not prioritize that if it means doing less research.

[Tavanio]

Would research this year help?  I'm planning on submitting my applications as soon as I can, so early October once I get my subject test score.  That would only be a month or two into any research I'd have done, so I don't know if I could list it on my application.

[Chai_latte]

Well, it's not about listing it (you can definitely list it).  It's about the skills you acquire as a result of the research, like critical thinking or various programming languages.  After two months, you've barely gotten your feet wet.  So, that's not going to help.  

You mentioned a thesis in your original post.  That thesis did not require original research?  If it did, be sure to emphasize that research and the number of semesters you devoted to it...it counts.  

If you only did thesis research for 1-2 semesters, I would not apply in October if I were you.  You probably do have what it takes for the schools you mentioned.  But, without a good amount of research behind you, you'll have a hard time demonstrating that to adcoms. 

[MathCat]

What kind of math? I wouldn't consider CMU a tip-top math school in general. I guess it might be in your area.

 

I know that in pure math it seems that it's generally not expected that you have truly original research as an undergrad - it's simply not accessible. Even very top schools like Stanford explicitly state that they do not require or even expect you to have research experience.

 

It's very hard for us to guess if you stand a chance, because I think your LORs carry a lot of weight and we obviously can't know what they say. I think your lack of research experience doesn't help, but may not be a deal breaker (especially since you do have thesis experience). I would talk to your LOR writers about your applications and see what they think. In any case, don't consider ranking alone, but also how well they fit with your research interests and whether graduates get the kinds of jobs you're after.

 

edit: Also, there is no real benefit to applying early unless the school has rolling admissions. Most places won't start looking at applications until the deadline has passed. And you won't get your subject test score until late October if you write it in September.

Edited August 8, 2015 by MathCat

[Chai_latte]

@ MathCat- I don't mean to hijack the thread, but I'm curious.  If you guys don't do original research, what do you do?  Projects?  Lit. reviews/seminars?  How about applied math folks?  They do the kind of research that a science person typically thinks of, right?  

 

@ OP- I totally rescind my "advice".  I didn't realize that math was so different!

[MathCat]

@ MathCat- I don't mean to hijack the thread, but I'm curious.  If you guys don't do original research, what do you do?  Projects?  Lit. reviews/seminars?  How about applied math folks?  They do the kind of research that a science person typically thinks of, right?  

I'm speaking in broad generality here, as a disclaimer...

 

The main issue is accessibility. In pure math, an undergrad often wouldn't even have the background to understand an original problem, let alone going about solving it. If they can, there's probably going to be a lot of supervisor involvement. Something like taking a paper and slightly generalizing or translating results is more likely - for example, maybe a paper focuses only on results about spaces satisfying certain conditions, but the proofs could be easily modified to extend to a slightly larger class or something.

 

Basically, after completing an undergraduate degree in math, you've still hardly seen anything. There's a fair chance you've never even seen an introductory course in any of your professors research areas. If you have, it was probably in your final year. Thus, it's hard to get any "real" research experience during your bachelors. I did little research projects throughout my degree - mostly they were tackling some little, basic case of some problem. Even then, most of the time was spent learning the background, and then the actual "research" was just tackling one specific situation. None of this was publishable. It's kind of like doing a directed reading course in a way. It was only in my final year that I was able to tackle something that could be publishable.

 

This is contrasted with something like statistics or applied math, where you can undertake a completely original project by applying the techniques you know to a new problem. It's also easier to be a research assistant if there is data to analyze. In pure math, it's generally about proving things, not computations or data analysis.

 

edit: As far as lit reviews go, it's quite possible an undergrad could spend a semester learning enough background to understand one paper. And one semester might not even be enough, depending on the paper!

Edited August 8, 2015 by MathCat

[Chai_latte]

@MathCat- I see...thanks for that.  I've seen undergrad and MS applied math research and assumed that pure was the same way.  But, now that I think about it, your points are good/common sense.   

[Tavanio]

What kind of math? I wouldn't consider CMU a tip-top math school in general. I guess it might be in your area.

 

I know that in pure math it seems that it's generally not expected that you have truly original research as an undergrad - it's simply not accessible. Even very top schools like Stanford explicitly state that they do not require or even expect you to have research experience.

 

It's very hard for us to guess if you stand a chance, because I think your LORs carry a lot of weight and we obviously can't know what they say. I think your lack of research experience doesn't help, but may not be a deal breaker (especially since you do have thesis experience). I would talk to your LOR writers about your applications and see what they think. In any case, don't consider ranking alone, but also how well they fit with your research interests and whether graduates get the kinds of jobs you're after.

 

edit: Also, there is no real benefit to applying early unless the school has rolling admissions. Most places won't start looking at applications until the deadline has passed. And you won't get your subject test score until late October if you write it in September.

 

The area I'm interested in is mathematical finance/financial engineering.  From what I understand, CMU is definitely tip-top there.  They're the only school I've found so far that lists Mathematical Finance as an area of research for a PhD.  I'm also working through a book by a professor there as an independent study.

 

Thanks for the tip on early applications: I thought that rolling admissions was standard.  I think I'll still try to apply as soon as I can, assuming my GRE score is decent.

 

I'm speaking in broad generality here, as a disclaimer...

 

The main issue is accessibility. In pure math, an undergrad often wouldn't even have the background to understand an original problem, let alone going about solving it. If they can, there's probably going to be a lot of supervisor involvement. Something like taking a paper and slightly generalizing or translating results is more likely - for example, maybe a paper focuses only on results about spaces satisfying certain conditions, but the proofs could be easily modified to extend to a slightly larger class or something.

 

This is contrasted with something like statistics or applied math, where you can undertake a completely original project by applying the techniques you know to a new problem. It's also easier to be a research assistant if there is data to analyze. In pure math, it's generally about proving things, not computations or data analysis.

 

edit: As far as lit reviews go, it's quite possible an undergrad could spend a semester learning enough background to understand one paper. And one semester might not even be enough, depending on the paper!

 

Yes, this is exactly what my thesis was: the original paper proved a result for general Rⁿ, but was extremely complicated and my proof was a more understandable version for R².  I did have another decently sized research project for an econometrics course (I'm econ/math double major) that was completely original but was just statistical analysis.  I don't think that financial math is applied math since it's very theoretical, but I could be mistaken.

[MathCat]

I know nothing about financial math, so I've got no specific advice there, sorry.