Advice for Applying to Math PhD Programs with Limited Research Experience

[AMH]

Hello,

I am currently a Junior at an average state university with a not particularly well known math department. I'm pretty set on pursuing a Phd in math (my interests lie primarily in numerical analysis and PDE's), and would like advice on which programs would be realistic to apply to.

Background:
GPA: 3.95 (math GPA: 4.00 - but again, not from strong math department)

Upper Level Coursework: Linear Algebra 1 &2, Intro Analysis 1&2, Abstract Algebra, Applied Math 1 &2 (using David Logan's text), Probability Theory, Numerical Linear Algebra, Numerical DE's, Software Applications

Will take grad courses in Numerical Analysis, Real Analysis, and Topology next semester, as I've nearly exhausted the interesting undergraduate courses.

GRE: Q: 169 V: 160 W: 4.5 (Haven't taken the subject test yet)

Research: Very little. Did an REU in PDE's last summer. Won a small mathematical modeling competition. Hope to get involved with faculty during my senior year.

I'm considering staying at my undergrad institution for an extra year to complete a masters degree in mathematics and complete a master's thesis. Of course, I've consulted with professors regarding this decision, but have gotten mixed feedback. Some think I should apply for a couple top schools, others have recommended a more conservative approach. Where do you think would be reasonable to apply for a 'reach' school? Safety? Would a masters bolster my application (particularly if this led to more serious research)?

All advice welcome and appreciated!

 

[Dr. Courtney]

http://colleges.usnews.rankingsandr...ges/rankings/national-universities/top-public

Did your school make this list? About where are they ranked? A 3.95 GPA from a school in the top 30 is much different from a 3.95 GPA from a school in the top 100 is much different from one that is unranked.

I am of the opinion that students benefit much more by a change of scenery in grad school.

http://grad-schools.usnews.rankings...ools/top-science-schools/mathematics-rankings

Odds are if you are at a top 100 school now, you can jump into the top 20 for grad school, but I would apply to at least four schools, with at least one in the top 50 as your backup plan.

 

[mathwonk]

The grades and GRE scores look good. Since I don't know your school I don't know how its name will impact admissions. But most schools have faculty members who themselves attended excellent schools for undergrad or grad school, hence they know talent at the highest levels and can write a letter which will compare you to not only the best people from your own school but also to people at better schools. So a lot depends on what those letters say. I do not know what grad schools you aspire to, but there are a lot of programs out there with excellent faculty in them, even ones not close to the top 20. This is because there is a very strong competition for faculty jobs and there has been for decades now, with people coming here from all over the world to work here. Moreover your list of courses does not strike me as containing much in the way of advanced work, so I think you would be very out of your depth in terms of preparation at a very top school. At top places the students have often already taken a good deal of graduate work which you have not. So I think you will get into a good place and hopefully one that is at the right level for your background, not greatly beyond it, and of course not below it. I am a retired research faculty member from the university of Georgia in Athens, GA, and have served as the graduate coordinator there, as well as taught many graduate courses. Although not a top ranked place we had undergrads go to excellent programs and also had grad students perform very well afterwards. E.g I once taught graduate algebra to a class including a high school student who afterwards went directly to Berkeley grad school, bypassing college altogether. There are opportunities at many places, it mostly depends on you.

One thing I missed in your list of courses is advanced calculus, where you learn the inverse and implicit function theorems, and change of variables in integration. That is a very important course. If you have had it test yourself a little by whether you can state the implicit function theorem. Maybe even deduce it from the inverse function theorem, and then also prove the inverse function theorem. Don't feel bad if you cannot, since I think I have never had a graduate class that even knew the statement of this theorem well enough to use it. I finally learned to review this theorem in grad classes I taught where it was used, rather than taking it for granted. I recall that when I was at Harvard in the 1960's the definition of a math major for an undergrad was to take "advanced calculus and any other 6 classes".By the way if you want to clarify what level your math dept is in, here is an old ranking by the AMS, showing UGA as in the top 104 but not the top 48: my point is that roughly top 100 is pretty good. UC Davis and Amherst are in there for example.

http://www.ams.org/profession/data/annual-survey/groups_des

 

[AMH]

I appreciate both responses! I agree that I most likely wouldn't survive a top Phd program, but hope to attend a school where the majority of graduates continue on to research positions in academia. I think top 20 would likely be a stretch (my school has sent multiple students to top 5 schools, but it's fairly rare), but may apply just on the off chance that I get lucky. Based on several conversations as well as your responses, I think my target programs would fall into the (rather arbitrary) 'top 30-50' range. Of course, research is a much larger consideration than rank.

My main motivation for considering staying at my current school for a masters degree is that I could get funding for it. I don't think this would greatly influence where I ended up applying to for a Phd program (I still wouldn't apply to 'top 10' schools), but I think this could make the transition to serious research easier. Also this would only take an extra year and could help narrow down research interests.

Mathwonk, I can state the Implicit Function Theorem, but only because one of my professors went off on a tangent about it during a lecture a week or so ago. Also, Advanced Calculus is called 'Introductory Analysis' at my school.

Dr. Courtney, my school is on that list.