I hope you all can give some helpful advice. Unfortunately, no one around me seems to be able to answer in a reasonable way.
I'm interested in persuing mathematical physics in Grad school. Currently, I'm an undergrad sophomore, and my current interest is in application of representation theory to Quantum Field Theory. I'm also interested in string theory. Basically, physics that is theoretical enough that most physics departments wouldn't be the right place to research it. But luckilly, many top schools have math departments with programs in mathematical physics.
Ideally, I'd like to get into a toptier school, like Princeton, Harvard, or MIT. I come from a second tier state school, the University of Oklahoma. I'm far ahead of the program, having taken almost exclusively graduate classes in my second year, including an introductory course on QFT and the basic Ph.D. qualifying courses in math. I'm pretty sure my application will be seriously considered despite the school I come from. I also have a decent shot at a Goldwater scholarship this year.
I've been accepted into a rather prestigious physics internship over the summer at Fermilab. The internship, however, is in accelerator physics, which is not exactly what I'm specializing in. Certainly, I'm interested in it, or I wouldn't have applied. I have to decide by this Friday whether or not to take it. The various REUs I applied to have all not gotten back to me. Personally, I'd be perfectly happy taking this internship, but I fear that it would put me too far on the physics side of things to be considered for a math Ph.D. I've spent the last 3 years working at Princeton Plasma Physics Lab with the theory department, so this would make 4 years of research in theoretical physics, and very little in math. I'm involved in a small research project in the math department, quite related to representation theory and string theory (algebraic knot theory), but this will probably only yield a single publication.
My question then, is this: Will an applications committee at, for example, Princeton, treat an internship in theoretical physics with any regard, if my area of interest is mathematical physics? Would an application to such a committee by a person with several published papers in physics, but none or only one in pure math, still be considered?
tl;dr: Should I accept an internship that is interesting and tangentially related to what I want to research, or should I refuse it and wait to see if anything better opens up, and how would it affect a grad school application at a competative school?
Math Summer 2010 Dilemma
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 qinwamascot
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Math Summer 2010 Dilemma
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Re: Math Summer 2010 Dilemma
It sounds like what you really want to do is a math REU, but you're afraid that if you pass up the physics internship you might not get one and then you'll be left without summer plans. The first thing I would try is contacting the REUs you applied to and let them know your situation. Tell them you have to say yes or no to this summer internship soon, but you really want into their REU and do they know if they will be able to accept you. This may increase your chances, and may solve your dilemma for you. If that doesn't work, you could try finding out what happens if you accept the summer physics internship now, but later want to back out  there may be no delicate way to find this out, however.
As for your main question about how an REU compares to the Fermilab internship for grad school applications, I'm afraid I can't help you with that one.
As for your main question about how an REU compares to the Fermilab internship for grad school applications, I'm afraid I can't help you with that one.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson

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Re: Math Summer 2010 Dilemma
You could also try calling up the Graduate Admissions people at the schools you're looking at and asking them.
Re: Math Summer 2010 Dilemma
I hope you figured out whether to take the Fermilab gig. I had a similar dilemma this summer  accept the Harvard Center for Astrophysics (with the theory project I really wanted to get my hands on) or accept an internship doing Optics in Paris at l'Institut d'Optique. Still interesting, but not exactly where I want to end up. I ended up taking the one in optics. Seriously, how many times will I get paid to spend a summer in Paris?
These are just my thoughts. At places like Princeton or MIT, your application would hold much more weight in theoretical physics than math, and I'd be willing to bet that the math department would just forward your application on over to the physics people. However, this isn't necessarily a bad thing. Physics theory at a top tier school is incredibly difficult to get in to. I know several physicists with applications as impressive as yours who have been rejected, for whatever reason. With your strong math background, however, and several publications in theoretical physics, you're pretty much guaranteed an in. Even from a secondtier school.
If you were to apply in math, however, you're running up against a lot of math purists. Your application is still strong, but consider the program of study for a math Ph.D. Two foreign languages in your first two years there, so you can prove you're sufficient in translating the works of dead Frenchmen. A lot of math courses outside your field. Limited RA funding, since you're going for a niche field against a lot of equally qualified applicants, so you'd probably end up with a TA. Depending on your funding, you might not get to do the research you want until your second or third year. You'll find that most of the theoretical physicists at the top tiers are mathematicians at heart anyways, and QFT and representation theory lie right in that niche which is in with mathematical physicists right now. So you'd get to do the kind of research you want, and most likely right away.
To sum it up: I think your application would be very strong going to a theoretical physics department, and you'd be doing the same research either way.
Michelle
P.S. I'm in the running for the Goldwater this year as well. We should hear soon, right? Good luck.
These are just my thoughts. At places like Princeton or MIT, your application would hold much more weight in theoretical physics than math, and I'd be willing to bet that the math department would just forward your application on over to the physics people. However, this isn't necessarily a bad thing. Physics theory at a top tier school is incredibly difficult to get in to. I know several physicists with applications as impressive as yours who have been rejected, for whatever reason. With your strong math background, however, and several publications in theoretical physics, you're pretty much guaranteed an in. Even from a secondtier school.
If you were to apply in math, however, you're running up against a lot of math purists. Your application is still strong, but consider the program of study for a math Ph.D. Two foreign languages in your first two years there, so you can prove you're sufficient in translating the works of dead Frenchmen. A lot of math courses outside your field. Limited RA funding, since you're going for a niche field against a lot of equally qualified applicants, so you'd probably end up with a TA. Depending on your funding, you might not get to do the research you want until your second or third year. You'll find that most of the theoretical physicists at the top tiers are mathematicians at heart anyways, and QFT and representation theory lie right in that niche which is in with mathematical physicists right now. So you'd get to do the kind of research you want, and most likely right away.
To sum it up: I think your application would be very strong going to a theoretical physics department, and you'd be doing the same research either way.
Michelle
P.S. I'm in the running for the Goldwater this year as well. We should hear soon, right? Good luck.
 qinwamascot
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 Joined: Sat Oct 04, 2008 8:50 am UTC
 Location: Oklahoma, U.S.A.
Re: Math Summer 2010 Dilemma
Thanks for the advice everyone. I did end up taking the position at Fermilab after Cornell REU rejected me. I still had a few math REUs left, but Cornell was the big one. So far, my advisor at Fermilab seems to be quite willing to conform to my interests, so I'm hoping to still have a relatively strong application to math grad schools and to have some fun over the summer. But for now, I'm leaving my options as open as possible. Notably, I got two offers to do research in pure math next semester, one of which I've accepted and another of which I'm still considering. Hopefully, I'll get my name on at least a couple of math papers next year.
Everything there's true, but I've found that (at least so far) I've enjoyed math classes more than physics classes. If it comes between doing work in theoretical physics outside my interests or in pure math outside them, I'd enjoy math, but not nearly as much physics. I've never found a math subject I disliked (except applied statistics, but that's more my fault for taking a lower division class in it), but my interests in physics seem to narrow every year. Classes in AMO and condensed matter (taught by theorists) have confirmed for me that not all physics is fun, even if I'm good at it.
Also, I consider myself somewhat of a math purist even if I'm in mathematical physics. When my physics professors skip steps in proofs (like assuming a certain limit satisfies some continuity property), I finish the proofs in my notes anyway. My physics notes are always written in definitiontheoremproof format, and I tend to use math notation everywhere except on graded assignments. So I feel like I'd fit in more in math than physics.
Goldwater results are supposed to come out by "late March", which includes only tomorrow. There are two possibilities: either we hear about it tomorrow, or resuts are late (in which case they will have emails from me and hundreds of other anxious undergrads in their inboxes come Thursday)
If you were to apply in math, however, you're running up against a lot of math purists...So you'd get to do the kind of research you want, and most likely right away.
Everything there's true, but I've found that (at least so far) I've enjoyed math classes more than physics classes. If it comes between doing work in theoretical physics outside my interests or in pure math outside them, I'd enjoy math, but not nearly as much physics. I've never found a math subject I disliked (except applied statistics, but that's more my fault for taking a lower division class in it), but my interests in physics seem to narrow every year. Classes in AMO and condensed matter (taught by theorists) have confirmed for me that not all physics is fun, even if I'm good at it.
Also, I consider myself somewhat of a math purist even if I'm in mathematical physics. When my physics professors skip steps in proofs (like assuming a certain limit satisfies some continuity property), I finish the proofs in my notes anyway. My physics notes are always written in definitiontheoremproof format, and I tend to use math notation everywhere except on graded assignments. So I feel like I'd fit in more in math than physics.
P.S. I'm in the running for the Goldwater this year as well. We should hear soon, right? Good luck.
Goldwater results are supposed to come out by "late March", which includes only tomorrow. There are two possibilities: either we hear about it tomorrow, or resuts are late (in which case they will have emails from me and hundreds of other anxious undergrads in their inboxes come Thursday)
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Re: Math Summer 2010 Dilemma
I've been feeling increasingly despondent regarding my chances in the Goldwater as the date grows ever later. But I guess they're just slow in getting out the notifications  check online, I've heard they usually post a press release there before winners get notified by mail.
If you have a strong interest in most math and very little interest in physics, then definitely don't apply to physics programs. Basic prerequisite to surviving grad school is making sure you're interested in what you're going for.
If you have a strong interest in most math and very little interest in physics, then definitely don't apply to physics programs. Basic prerequisite to surviving grad school is making sure you're interested in what you're going for.
 qinwamascot
 Posts: 688
 Joined: Sat Oct 04, 2008 8:50 am UTC
 Location: Oklahoma, U.S.A.
Re: Math Summer 2010 Dilemma
I've been feeling increasingly despondent regarding my chances in the Goldwater as the date grows ever later. But I guess they're just slow in getting out the notifications  check online, I've heard they usually post a press release there before winners get notified by mail.
I've been feeling exactly the same. TBH I'm far more anxious right now than I ever was with college admissions or anything else. If they don't tell us tomorrow I'll probably start breaking out into spasms (I'm exaggerating, but not a lot).
If you have a strong interest in most math and very little interest in physics, then definitely don't apply to physics programs. Basic prerequisite to surviving grad school is making sure you're interested in what you're going for.
I'm interested in physics, but only in a very small area of it. I'd still go to grad school in physics, and definitely make the best of it, but I much more see myself going to grad school in math. If I do turn out to have a more physicsoriented grad school application, I'd probably apply somewhere like UChicago, which tends to have strong collaboration between math and physics via the Fermi institute.
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