Theoretical Physics and Graduate School

[phreak]

I'm a second year undergraduate at UChicago, and I plan on doing graduate work in theoretical physics. So when the time comes, to which graduate program should I apply: mathematics, applied mathematics, or physics?

From my research, it seems that the answer differs by institution. For example, it would be no problem to apply to the Applied Mathematics program at Chicago and do research in theoretical physics, but Princeton, for instance, does not consider theoretical physics as applied mathematics.

Let me clarify. I'm currently at math major. Last year, as a first year, I took Honors Analysis and Complex Analysis, receiving As in both class. By the end of my second year, I will have taken Topology, Functional Analysis, Algebraic Topology, Differentiable Manifolds, and three quarters of Honors Algebra. (However, I did research in manifold theory last summer, so that I already know quite a bit of differential geometry and algebraic topology.) I have not taken any physics courses here (although I've done quite a bit of independent study), but I'll probably take graduate quantum physics and advanced mechanics by the end of my 4th year. I will have completed graduate analysis and graduate geometry/topology by the end of my 3rd year. Clearly, I'm more of a mathematician than I am a physicist.

The main areas of math and physics that interest me are differentiable geometry and its connections with relativity/cosmology and functional analysis and its connections with quantum physics. So, at least according to Wikipedia's definition, I'm interested in mathematical physics. Unfortunately, this interest doesn't seem pure enough to qualify as pure math, and most institutions apparently don't consider mathematical physics as applied mathematics. This leaves physics, but to be honest, I'm really not interested in any other branches of physics than what I already stated, and I would be required to take graduate classes in many different areas of physics, most of which are completely unrelated to my research area, and in which I have no experience. In addition, it would be difficult to get into the top physics programs in the country considering the fact that by the time I apply to grad school (early in my 4th year), I would only have 3 physics courses max on my transcript. Can anyone give me any advice?

 

[andrewm]

I won't be able to give you very good advice, but I do know one thing: most graduate schools require undergraduates with a background in, at least, classical mechanics, electromagnetism, thermal and statistical physics, and some quantum mechanics. From the sounds of it, you will not be able to enroll as a grad student in those schools.

EDIT: I mean: as a grad student in physics in those schools.

 

[WarPhalange]

Right. How much physics do you know? That will be very important.

Secondly, decide on a per school basis. I want to go into physics, but some schools have more interesting applied physics research projects, so I am applying there instead.

In the end it matters what you do, not what department you did it in.

 

[phreak]

Thanks for the responses.

I won't be able to give you very good advice, but I do know one thing: most graduate schools require undergraduates with a background in, at least, classical mechanics, electromagnetism, thermal and statistical physics, and some quantum mechanics. From the sounds of it, you will not be able to enroll as a grad student in those schools.

I checked a number of schools' admissions pages, and most of them say that there are no specific requirements other than a solid background in physics and mathematics. You would certainly know better than I would, though. If I took Intermediate and Graduate Mechanics, 2 quarters of Undergraduate Electricity and Magnetism, and 2 quarters of Undergraduate Quantum Mechanics, do you think that this would give me a fair shot given my math background?

Right. How much physics do you know? That will be very important.

I took AP Physics C in high school, and got 5s on both examinations and As in both semesters. Not that that counts for anything, as the tests were a joke, but I do think I have a very strong grasp on the fundamentals of vector-calculus-based physics. I also know a good portion of the material in what most schools call modern physics.

Secondly, decide on a per school basis. I want to go into physics, but some schools have more interesting applied physics research projects, so I am applying there instead.

In the end it matters what you do, not what department you did it in.

This is undoubtedly correct, but I first have to discover which departments I should apply to and which that I shouldn't. I also don't want to get into a particular department and then find out that I should've gone into another department if I wanted to study under a particular faculty member.

 

[WarPhalange]

I checked a number of schools' admissions pages, and most of them say that there are no specific requirements other than a solid background in physics and mathematics. You would certainly know better than I would, though. If I took Intermediate and Graduate Mechanics, 2 quarters of Undergraduate Electricity and Magnetism, and 2 quarters of Undergraduate Quantum Mechanics, do you think that this would give me a fair shot given my math background?

Yeah that sounds good. Don't forget thermodynamics. This is kind of the bare minimum, though.

I don't know if they'd also require some sort of lab class, but at least I think that this is enough to get accepted, even if you have to take extra courses once you're there to make up for it.

This is undoubtedly correct, but I first have to discover which departments I should apply to and which that I shouldn't. I also don't want to get into a particular department and then find out that I should've gone into another department if I wanted to study under a particular faculty member.

That's my point. Check out all of their departments and see which one you like better. If in School X it's Applied Math, apply there in School X, if School Y has it in Physics, apply there in School Y.

 

[t!m]

To add on to what everyone else is saying - you should also consider the option to take an advisor in a different department. Most schools will let your thesis advisor be in a related department - so if math is definitely your academic interest, but you want to do research in theoretical physics, you could get a PhD in math while working with a physics professor.

 

[Troponin]

I'm currently a Physics major, general Math minor but have thought about switching to Applied Mathematics major with Physics minor.
The Applied Math major has a few courses I am interested in that aren't required in the Physics major/math minor program, such as Differential Geometry of curves and surfaces, Vector Calculus and Complex Variables, and advanced Differential equations.

I spoke to the graduate advisor of a school I'm interested in for Theoretical Physics about making the change and he had no problems with it.
He said that I would probably need to take a senior level Physics course or two while in the graduate program, but that isn't uncommon for them.

He pretty much said that the most common problem with their Physics students is their shortcomings in math, which seemed like he was insinuating that "catching up" on the physics was easier than "catching up" on the mathematics...which I would agree with. I'm not a grad student, and far from a theoretical physicist, but when looking at the work being done at that level, I feel much more lost on the mathematics than on the application of physics concepts.

 

[billardkarr]

I am in a situation very similar to yours, except I have not taken as much mathematics courses as you have, yet. I am double majoring in math and physics. I would like to get a master's degree in mathematics before I go into a Ph.D. program in physics in order to get more experience with topology, analysis, and differential geometry.

I have read a lot into it and have a great mentor at my university. Most good schools for theoretical physics (like Princeton, MIT, Cal Tech, or Berkley) will be looking for students with undergraduate degrees in physics. However, a large part of the decision is the scores in the GRE subject test for physics. My advice would be to pick up Physics GRE study books and learn the material it covers. My mentor (who did his undergraduate and master's degree at the Indian Institute of Technology and Ph.D. at Indiana University with post-doc work at Los Alamos) told me that if I want to go somewhere really good for theoretical physics, to do the following:

1) Get in the top 5% of scores in the nation on the physics GRE subject test.
2) Have a good amount of research as an undergrad, and do a research project at a good university (U of Chicago is definitely among these universities) Note: he told me it doesn't matter if the research is in mathematics or physics.
3) Meet people from the university you're wanting to go to. Visit it. Go to conferences. Get recommendations from people who know people there. Etc.

Also, keep in mind that most universities which have great math departments have a great number of professors in the math department doing research in theoretical physics. So, if you settle into a specific branch of math like functional analysis, differential geometry, or algebraic topology, you will be a strong candidate for joining a professor who is doing research in mathematical physics. In short, you won't go wrong with doing a Ph.D. in mathematics or physics as long as you're talking to people who are doing research in that field in which you're interested.

 

[creepypasta13]

I too am deciding between theoretical physics and applied math. I like the research done by theoretical physicists, in that they're trying to discover new physics, whereas mathematical physicists seem to work on the mathematical theory behind physics problems that are already solved. But I like math courses more, such as analysis, linear algebra, etc and proving theorems more, than taking the physics classes in E&M , mechanics, thermo, etc

so if math is definitely your academic interest, but you want to do research in theoretical physics, you could get a PhD in math while working with a physics professor.

But would the research be math or physics-oriented? That is, if a math student works for a physics prof, will the math student just do stuff like prove the upper-bound of an equation and see how accurate the solution is? If not, how could he help with coming up with physical theories if he doesn't have as strong of a physics background as a physics phD student, who has taken more physics courses?

Also, keep in mind that most universities which have great math departments have a great number of professors in the math department doing research in theoretical physics. So, if you settle into a specific branch of math like functional analysis, differential geometry, or algebraic topology, you will be a strong candidate for joining a professor who is doing research in mathematical physics. In short, you won't go wrong with doing a Ph.D. in mathematics or physics as long as you're talking to people who are doing research in that field in which you're interested.

From what I've seen, it seems like differential geometry and algebraic topology are done more by pure math than applied math departments. It also seems like the physics involved are problems that are already solved, such as the Schrodinger equation, statistical mechanics, etc, not current research done by theoretical physics.

I certainly would like to be able to work on current theoretical physics, such as string theory, as an applied mathematician, but it seems a lot of applied math programs (that is, ones that have separate depts from pure math) do research and require students to take classes in stuff like numerical analysis, numerical PDEs, etc, which I don't want to do

 

[twofish-quant]

I certainly would like to be able to work on current theoretical physics, such as string theory, as an applied mathematician, but it seems a lot of applied math programs (that is, ones that have separate depts from pure math) do research and require students to take classes in stuff like numerical analysis, numerical PDEs, etc, which I don't want to do

Any particular reason why you don't want to do numerical analysis and numerical PDE's. If you don't like/don't want to do these sorts of things, it's going to greatly limit your options in theoretical physics. Even in areas like HEP and relativity, the very active areas of research are heavily numerical and computational.

 

[creepypasta13]

Any particular reason why you don't want to do numerical analysis and numerical PDE's. If you don't like/don't want to do these sorts of things, it's going to greatly limit your options in theoretical physics. Even in areas like HEP and relativity, the very active areas of research are heavily numerical and computational.

I'm ok with doing them, its just that I don't want to focus my research on developing those techniques. I'm willing to USE them if I did research in theoretical physics or something else

 

[twofish-quant]

I'm ok with doing them, its just that I don't want to focus my research on developing those techniques. I'm willing to USE them if I did research in theoretical physics or something else

There isn't a very sharp line between using techniques and developing them. What happens in numerics is that you are usually running the machine at its limits, so you'll find that you have to come up with new and original numerical techniques to solve any non-trivial problem.

One thing that makes numerical research very different from analytic techniques is that there isn't any external driver that fundamentally changes the playing field. Whereas in the numerical world, people are constantly getting hit by new technologies. The cost of CPU and the computer architectures are changing very rapidly, and every time something new comes down the pipe, there is a lot of work to do with trying to figure out how to use those CPU (or GPU cycles) in physics.