Mathematical Physics graduate programs?

[Ryan007]

I have a master's in physics. I'm looking at PhD programs, but I really don't want to take the same courses over and take comprehensive exams (or the damn GRE). I managed to squeeze in a few math classes before I finished. I would like to do research in physics, but from a more math-heavy angle. I want to take more math courses as well as advanced physics courses. I've been studying computation on my own lately. Computational skills would be beneficial for the private sector; I'm not pursuing a career in academia.

I've been looking around but I can't find flexible math/physics PhD programs. Math and physics departments are usually very distinct and separate. Their structures haven't changed in ages.

Any suggestions for grad programs? I would also consider schools outside of the US.

 

[Ryan007]

No new ideas.

 

[heatengine516]

Indiana University Bloomington offers an actual degree in "Mathematical Physics"

http://www.math.indiana.edu/graduate/mathphysics.phtml
http://www.indiana.edu/~iubphys/research/mathmatical.shtml

I wouldn't get too hung up on the title of the degree though. There's probably at least one professor in the math or physics department of a research oriented university that does research that would be considered mathematical physics. It's a very broad term. Start by looking at schools close to where you live that you could easily visit, look at the faculty pages of the math and physics department and see if any of them are doing research you might be interested in. I would speculate that most people who do mathematical physics just got a degree in either math or physics but did research in an area of mathematical physics

 

[Ryan007]

Thanks for the info. I've seen this program before, but upon a second look it seems pretty good.

The advantage of a official degree program in mathematical physics is the recognition by the advisors that one's research straddles both fields. On the other hand, a program that is 100% pure math oriented will emphasize proofs, while a program that is 100% physics oriented will have too much of the usual hand-waviness. Also, time will be allowed for coursework in both math and physics, rather than a curriculum in entirely one field and independent study in the other.

My original plan was to get a job, pay off my debts and build some savings. But after 9 months of constant application-sending, I'm giving up. A PhD as plan B isn't a good idea but I have to do something. I've been studying through MOOCs but that will only take me so far.

 

[artfullounger]

Have a look at international programmes. Particularly in the UK, they don't require the GRE and don't usually have qualifying exams like they do in the US (typically you go more or less directly into research, getting your PhD in 3-4 years) and it can be fairly cross disciplinary (depending on the supervisor's and department research interests).

Cambridge have a theoretical/mathematical physics research ongoing in both their Maths and Physics departments, and similarly Imperial College, London have a similar range in their Physics and Applied Mathematics departments. Also Oxford recently launched a Mathematical and Theoretical Physics masters programme to complement the Part III Maths at Cambridge and Quantum Fields & Fundamental Forces programme at Oxford. Naturally these are pretty selective however, but may be worth a look.

At a slightly less elite level, Exeter has a decent theory group, but it's much more computationally oriented from what I gather. Southampton have a HEP group which has at least some links with CERN (they send 1 final year undergrad there to do a year long project each year). Additionally the Maths department at Southampton only does fluids and relativity on the physical side of research so anything else would be under the purview of the physics department in theory. Also Edinburgh has a somewhat recent mathematical and theoretical physics programme in the Higgs Centre which offers masters and doctoral degrees. Southampton and Exeter don't have masters in these areas/at all and Cambridge only has the two Part III MASt programmes on the taught side. Imperial has a nmber of utaught and research masters. All offer doctoral programmes however.

Off the top of my head I think CalTech, Harvard and Princeton have pretty maths-y programmes last I heard (depending on your research group anyway) in the US, but your mileage may vary.

 

[Ryan007]

Speaking of schools, should I even bother to apply to places like Oxford? I think they would send me an email warning me not to apply, before I even push the "send" button!

 

[artfullounger]

Speaking of schools, should I even bother to apply to places like Oxford? I think they would send me an email warning me not to apply, before I even push the "send" button!

Only you can really answer that. I mean fundamentally there's no harm in applying outside of any application fees, but you haven't given any indication of how well you did in your previous studies to gauge by otherwise :P

You have a master's, so provided you averaged at least a 2:1 equivalent minimum (~3.2+ GPA I guess? LSE has an equivalency chart somewhere for UK to US marks) you would fulfil the minimum requirements I believe. That said a lot of people applie to the PhD programme with a 1st and get rejected so, it depends on other factors too. Having some research experience (at a minimum some kind of undergraduate project/thesis) is probably implicitly required, and having any publications will greatly improve your application I imagine.

 

[Ryan007]

Thanks for the advice/info. My undergrad GPA was ~3.8 and my master's GPA was ~3.6 (lowered due to some B's that I got in the upper division math classes that I took). I did a pretty good research thesis in theoretical solid state physics. I may publish something based on it soon. I like deep/creative thinking but I detest memorization (thus not a fan of the GRE). I'm also constantly studying things on my own, for whatever it's worth.

The thing is, my classmates from this year and previous years had better qualifications and still had a hard time getting into PhD programs. Everyone got in somewhere, but then again most people applied to 10-20 schools.

I'm not so concerned about getting in. I'm much more concerned about moving somewhere and not making it through (hence the apprehension about comprehensive exams). Much of my fear comes from a traumatic experience that I had after high school. I moved to the opposite side of the US and lasted only a few months at a very prominent school. I hated the dramatically different environment so much that I couldn't make it through one semester. I ended up getting my BS from a local state school that is much less prestigious, though I did get a good education. I had a similar experience after my BS. I went to a nearby university for a master's in electrical engineering. I quit that program because I hated the department and I didn't like engineering. All I got out of that was a lot of debt (all of my current debt, in fact).

The math and physics PhD programs near me are very difficult to get into and/or don't have the curriculum that I'm looking for. Unfortunately there's no way of knowing how one will like a program until one has spent some time in it.

 

[artfullounger]

Haha, your experiences sound a lot like mine xD I'm currently rolling on 5th year of undegrad due to changing universities, programmes and having a breakdown forcing me to take 3 quarters of a year out xP

Anyhue, your stats sound pretty solid tbh. They'll definitely want to hear about your thesis thought (you should make sure you're comfortable talking about it and the subject matter generally for interviews if you do apply), and getting Bs in "advanced" maths courses probably won't hurt your chances too much (well, maybe for part III maths or QFFF, but part III physics or any of the other physics courses at imperial you should be fine, and for phd's they'll just make sure you know the stuff you need to and don't really care beyond on that).

With regards to the hating memorization, you'll probably feel at home in a UK programme, as they definitely emphasise a more conceptual approach to rote memorization (at least for undegrad). One of my friends actually managed to get full marks for a question on his advanced math methods final by basically saying "I'm not going to compute this horrible integral, because it'll take 10 pages to do so, and all the relevant physics is outside the integral and by inspection the integral is some value between 0 and 1. So essentially the answer is *blah* with a damping coefficient in front, which physically means *blah*." Although the marker for that paper was possibly more generous than some :P

Plus the approach for PhD stuff is basically "you can look in whatever books you want for equations and compute all the integrals in MATLAB you want as long as you understand the physics" from what I hear. Although apparently the Russian supervisors are a little more...intense (also the one Indian Prof we have is apparently completely insane according to my flatmate). The UK undergrad physics pedagogy is very much focused on developing physical intuition, and then developing the relevant mathematical tools as necessary (compared with the french/russian way of teaching them 2 years of pure maths and then showing the physics from that). And you can't really memorize intuition :P [Also the IOP requires all physics undegrad programmes have a synoptic paper/general problems exam which can ask questions from any area of the undergrad physics and are generally designed to require more creative problem solving and original thought to solve (you can't just write down the relevant equations and substitute all the numbers in), so there's that.]*

Anyway, I digress. From the sounds of it, applying wouldn't hurt and you have a resonable chance of at least getting interviewed.
*not 100% sure if this is an actual requirement or just a common occurrence, I haven't read the IOP specifications, but at the very least Southampton, Exeter and Cambridge have this.

 

[Arsenic&Lace]

while a program that is 100% physics oriented will have too much of the usual hand-waviness

Describe this "hand-waviness" and why it bothers you.

 

[QuantumCurt]

The advantage of a official degree program in mathematical physics is the recognition by the advisors that one's research straddles both fields. On the other hand, a program that is 100% pure math oriented will emphasize proofs, while a program that is 100% physics oriented will have too much of the usual hand-waviness. Also, time will be allowed for coursework in both math and physics, rather than a curriculum in entirely one field and independent study in the other.

These are some rather big assumptions. A future employer is likely to be less worried about the official title of your degree and more worried about the content of it. There are many students doing a mathematical physics topic for their PhD, and yet they are 'just' in a physics PhD program. Similarly, the majority of astrophysicists in the world -do not- have a degree in astrophysics. They have a degree in physics, because so few schools offer a degree specifically in astrophysics. This distinction is not important.

A graduate program is what you make it into...not just what is assigned to you. You can do a mathematical physics topic at just about any physics grad school. The advantage you're envisioning simply isn't really there. Most graduate programs are likely to allow you to take both the math and the physics that you need, provided that you can explain why it is relevant to your graduate studies. You seem to have some slightly misguided ideas of how this all works.

 

[Ryan007]

In the process of looking up the UK schools that you suggested, I realized the differences between UK/US systems. I had to look up the terms "taught/untaught programme", "1st class", "mathematical tripos", etc.

Realistically, it would be very difficult to have debt and live off a student salary in another country. European schools don't always guarantee funding.

 

[Ryan007]

@ Arsenic&Lace:
Ah yes, the hand-waviness. This comes in many forms. Physics by its nature isn't 100% accurate, and that's not what I'm aiming for. But some take this to mean that they don't have to be mathematically rigorous. In the course of my research, I came across blatant but not obvious errors in papers. The thing is, papers are so complicated that referees and members of the community aren't going to read them in detail. When authors see errors (most likely typos) in their own papers they would submit corrections, but most others won't bother. Anyway, I devoted 2 long appendices in my thesis to corrections to a couple of papers that I based my research on. One of the authors for a paper was still alive so I contacted him. We went back and forth and I tried to explain 10 different ways why his conclusion was right but his method was wrong. He was persistent. Both appendices involved heavy mathematical breakdowns. I had to use things like the "derangement" concept...

In addition, physics texts/profs/papers, etc. at higher levels don't really explain the math concepts. Math::Physics as Physics::Engineering. This becomes a problem when doing research. My research was definitely a physics problem, but I had a lot of questions/concerns about the math. I might just apply to a math PhD program...

It's just not a good idea to learn math from a physics book. Arfken/Weber is a good reference and has a lot of things that are hard to find elsewhere, but just try to learn group theory from it! I took an abstract algebra class and it's not something that can be covered in a chapter. I'm reading a book called "An Introduction to Tensors and Group Theory for Physicists" by Jeevanjee. It's truly excellent. It bridges gaps between math and physics. But if I had not taken linear algebra and abstract algebra courses, I would be lost. In the first week of my math methods class, the concept of vectors was covered. It seemed so abstract/vague and I didn't really know what I was doing. In contrast, the concept of vectors was clear and simple on the very first day of my linear algebra class.

 

[QuantumCurt]

The fact that physics is not 100% accurate is not 'hand waviness.' Not all physics is mathematically rigorous, at least not from the perspective of rigorously developing the mathematics. However, many areas of physics are very mathematically formal. One does not need to be enrolled in a PhD program titled 'mathematical physics' in order to pursue a mathematically rigorous subject for ones PhD.

If one is trying to learn pure mathematics, then no, one should not learn it from a physics book. However, if graduate level mathematics courses are an essential part of your PhD subject matter, the majority of graduate programs will allow you to take the courses that you need...even if ones program on paper is simply a "physics PhD." I'd hazard a guess that most of the major PhD granting institutions in the US have a graduate adviser in physics that is very capable of advising a student in a more mathematically oriented physics project.

 

[Intraverno]

The fact that physics is not 100% accurate is not 'hand waviness.' Not all physics is mathematically rigorous, at least not from the perspective of rigorously developing the mathematics. However, many areas of physics are very mathematically formal. One does not need to be enrolled in a PhD program titled 'mathematical physics' in order to pursue a mathematically rigorous subject for ones PhD.

If one is trying to learn pure mathematics, then no, one should not learn it from a physics book. However, if graduate level mathematics courses are an essential part of your PhD subject matter, the majority of graduate programs will allow you to take the courses that you need...even if ones program on paper is simply a "physics PhD." I'd hazard a guess that most of the major PhD granting institutions in the US have a graduate adviser in physics that is very capable of advising a student in a more mathematically oriented physics project.

Adding on to this, with some areas of theoretical physics are just about on par with mathematical physics or maybe even pure mathematics in terms of rigor. Quantum Gravity, Cosmology, a few topics in QFT, a couple in Astrophysics, Information Theory (not sure if that exactly counts as Physics), and Particle Physics all use very rigorous math because of how hard it is to make observations, ie the math in the theory is everything until the experimentalists make equipment that can observe the objects at hand (to a lesser extent with Astro and Particle since we can make better observations in those areas). A prime example is Edward Witten, who uses math to the point of being equal parts mathematician and physicist and won a Fields Medal for the math he developed in Superstring research.

 

[artfullounger]

tripos is a) a Cambridge specific pecularity (Oxford might also use the term I'm not sure) and b) translates to undegraduate studies (the exception is Part III, which can be entered as a postgrad in physics, maths and materials off the top of my head. Part III Maths has a lot of theoretical physics options and is quite well regarded in the theoretical physics sphere I hear). Taught/untaught is pretty selfexplanatory; a lot of master's courses are research oriented, untaught programmes.

Anyhue, you can apply for a scholarship to undertake a PhD e.g. Fulbright, Rhodes etc. Also they may have limited funding for international applicants otherwise (I'm not too sure).

 

[Arsenic&Lace]

Math::Physics as Physics::Engineering.

I don't think this is true. The relationship between the mathematics department and physics is much more sketchy than the relationship between the physics department and engineering.

 

[Almeisan]

'Hand-waviness' will turn out to be a very useful skill if you end up in physics/engineering/industry/therealworld.

 

[radium]

You can easily apply to a physics or math program and also have an advisor in the other department. I have a friend who does this. She does very mathematical research and spends a lot of time over in the math department