Lower Ranked Mathe PhDs - What do I need?

[UMGaines]

oops @ "Mathe"

Hey All,

I'm an economics grad student who has realized that the only reason I ever liked economics was the math. I started taking some proof-based courses on the side, did very well, and got hooked. I took the GRE with econ in mind, and my score isn't so great, but I'm much more into calculus and up than the GRE stuff. I'm slow with calculations, to be honest, and have to check everything for silly mistakes, even given understanding. For this reason, I'd like to avoid a retake if possible.

It looks like it's possible to get into some of the lower ranked programs with a 740 GRE Q per the new NRC data. The completion rates, however, bother me at a lot of schools. There are a LOT of programs that are not on the rankings that I'd imagine I could get into, at least some of them, that is.

Right now I'm in the first RA course and rocking it, and plan to finish a math BS over the next year with the usual: 3 piece RA, Abstract Alg, Matrix Theory, Complex Analysis, a Programming class (c++ or num. analysis), etc.

I'm looking at schools in urban areas like Texas-Dallas, U St. Louis, SMU, Alabama-Huntsville, etc. I'm not stressing over placing into an academic position if I go to a program like this, I'll be happy with other career paths if that's what I must do. I just want to get the degree and learn the math. I doubt I'll be impoverished with a solid econ MS under my belt.

Does anyone have any advice/recommendations? I'd like to avoid places with massive attrition.

Thanks!

Edited May 1, 2011 by UMGaines

[coffeeintotheorems]

What proof-based courses did you take?

I'm glad you like Calculus; I think everyone here does. However, higher mathematics does not in any way resemble what you did in calc. Before you even think about a degree in higher math, make sure you know and love Real Analysis and Abstract Algebra, two fundamental areas that tend to trip new students up. What do you know of these two subjects?

My advice is to worry less about "completion rates" and focus more on making sure you understand what you'll be getting yourself into. Also don't sweat the general GRE; it's middle-school math, you know. Just buy the official ETS practice book, take all of the exams under timed conditions, and work on your weak spots. You should make an 800 after that.

Edited May 1, 2011 by coffeeintotheorems

[UMGaines]

Ah, sorry, i typed "RA" instead of real analysis. I've done a little piddling on the side with Abstract Algebra and Topology, and am top of the class in the first Real Analysis class that I'm in right now, and I definitely love it.

I'm aware (and excited) that math is much different after calculus. The Analysis course has made me certain. I actually like the Analysis better than the computational calculus. Next semester is going to be the "Proving Grounds" now that I'm done with econ (all the stuff I've done so far has been on the side). I'll be taking Abstract and another Reals class in addition to two others TBD.

The advice on the GRE sounds good. The time part surprised me. All of the problems I worked were correct, just didn't finish :|.

Edited May 1, 2011 by UMGaines

[stansfield]

I don't think you have to love analysis and algebra, they are typically extremely dull but you have to do well in those courses for sure. I guess you might love algebra depends on the topics and the pace ie. some digression on quarternions and geometric group theory but there's nothing more tedious than real analysis.

[UMGaines]

I don't think you have to love analysis and algebra, they are typically extremely dull but you have to do well in those courses for sure. I guess you might love algebra depends on the topics and the pace ie. some digression on quarternions and geometric group theory but there's nothing more tedious than real analysis.

Good to know. Hopefully that means that if I'm finding Reals interesting, the others will be even more fun!

[coffeeintotheorems]

Ah, so that's what "RA" meant . If you're loving that course and understanding it, it sounds like you're well on your way. Congratulations! Also, when I said not to sweat the GRE, I additionally meant that it's the least important part of your graduate applications, at least in the sense that your ability to do middle-school mathematics quickly has little bearing on your success in a graduate mathematics program. It sounds like all you need is speed, which will come with practice. It's like Ben Affleck said about the Series 7 exam: "Don't worry, if you study you'll pass. And then you can start working on becoming a millionaire." (paraphrased very roughly from Boiler Room.)

I don't think you have to love analysis and algebra, they are typically extremely dull

I beg your pardon! And you call yourself a mathematician! I assume what you meant is that the analysis and algebra courses are typically extremely dull, due to a bad choice of text, a bad professor, or both. If that is what you meant, then I concur.

I guess you might love algebra depends on the topics and the pace ie. some digression on quarternions and geometric group theory

What about finite group theory? The Sylow Theorems, the Fundamental Theorem? Those are covered in every first-year sequence, and I find it hard to believe that you didn't find those topics fascinating. If nothing else, the connections to elementary number theory should pique the interest of any new algebra student; a failure to do so would mean he doesn't appreciate some of the more fundamental aesthetic nuances of higher mathematics and should run far, far away.

[UMGaines]

Ah, great. I'm definitely excited and want to get more into the discipline! After this summer I'm going full-time math, but will need to send out apps in December I assume after I get grades in the other math courses to get some meat on my app. I'm optimistic that I can get a very good letter of rec from my Analysis professor, and I suppose pick up the other two next semester if I do well enough early on in the course. I suppose letters from calculus profs aren't much good, or even intro to proofs.

[stansfield]

I'm referring to courses ofc, those fields are too broadly defined but the distinction is not important. and no I didn't find those fascinating and I definitely understood them but I never took the undergrad version of algebra analysis. there's absolutely no reason why you must be fascinated by these topics, they could be too elementary or too difficult or just plain dull depending on the person. or you could love them. some mathematicians never touch number theory. the most interesting math course I took as an undergrad was set theory from the philosophy department.

the important thing to communicate is that lack of interest in these 2 subjects should in no way dissuade one of pursuing grad school in math and correlates very weakly to ability or penchant for research. as Thurston said, some people are very fast on the uptake and burn out early while others are slower to absorb but do fabulous work later on once they find their niche.

[coffeeintotheorems]

the important thing to communicate is that lack of interest in these 2 subjects should in no way dissuade one of pursuing grad school in math and correlates very weakly to ability or penchant for research.

In any given are of higher mathematics there will be an initial tedious hump of abstraction that any new student will have to overcome, even when properly motivated. An unwillingness to force oneself through the difficult, boring, tedious groundwork of subjects like analysis and algebra is a bad sign and correlates very strongly to the tenacity required for graduate studies in pure mathematics.

(Out of curiosity, which courses did you take as an undergrad that made you love higher math and want to go more deeply into it? You mentioned logic; what else? I don't know much about ergodic theory--your field--but my understanding is that it requires a great deal of measure theory (analysis) as a prerequisite.)

Long story short, my message to the OP and those in a similar position is that you need to take, excel in, and enjoy some course of traditional higher math as a test of your fitness for graduate study. This course could be analysis, algebra, topology, geometry...as long as it is heavy on rigorous proofs. If you don't enjoy any of those subjects--several of which you'll have to pass qualifying exams in--then you're not going to succeed in higher math.

Edited May 2, 2011 by coffeeintotheorems

[stansfield]

I liked riemannian geometry, algebraic topology, ergodic flow, teichmuller dynamics. some parts of algebra was interesting like open problems in geometric group theory but it didn't do much for me overall. I also started number theory in high school without really a proper background so it was ruined for me and I didn't want to touch it anymore. Best math course all around was either that set theory course from philosophy or machine learning from cs with an eye towards geometry. those cores like analysis and algebra were pretty boring but I knew it was too early to judge, they are merely a temporary impasse one must overcome to delve into the good stuff.

either way I concede my path is rather unusual so you probably represent the mindset of the majority of math students.

[UMGaines]

Thanks everyone for the replies.

Just finished up my first real analysis class and I'm pretty sure I maintained straight As on every assignment/exam. That's a first for a math class. I guess I like proofs a lot more than computations.

[hubris]

My two cents: there is no reason to keep that low of a GRE score given the amount of time you have.

Speed and accuracy can easily be built up and so will your prospects.

[CauchyFan]

Alabama-Huntsville,

Whoa. This is where I go to school (and am a TA at now).

If you want to go to UAH you only need your scores to add up to 1500 (Q, V, and Analytic*100+200) and you don't need the Math GRE.

That said, UAH is an Applied Math school. We do have a couple of great analysts around (Functional Analysis), a couple of great combinatorics guys, and one of our new professors is an up-and-comer in the field of Random Matrix Theory, but in the grand scheme of things we don't have a pure mathematics program (only a PhD in Applied Math). Our main areas of expertise are Differential Equations (specifically dynamical systems), Numerical Analysis, and Probability/Statistics/Stochastic Processes. If your passion is in topology, algebraic geometry, group theory, complex analysis, or something like that, we don't really have anything for you.

However, if you want to work in industry, Huntsville is an incredible place to be and UAH is a very good school to go to. But if you want to go on to be a professor at some big school with a pure math program, you should probably go somewhere else.

Edited July 8, 2011 by CauchyFan