Feeling Underprepared for Graduate School

[SuitCoatBassis]

Hello!

I'm an undergraduate physics and math major and I just finished up my third year at a small university. I plan on staying an extra year to fulfill all of my requirements, so I have over a year to figure out exactly what I want to do in the future.

I'm pretty set on going to graduate school; I do well in most of my classes and I am starting to really study for the GRE Physics subject test. My problem is this: I really like theoretical physics, but as I look into graduate school requirements and GRE scores and information needed for certain fields, I feel really overwhelmed.

Currently I'm leaning toward fields such as QFT, String Theory, Particle Physics, etc. because all of the mathematics really intrigues me. I'm stressed out because I know I won't have a huge background in a lot of fields like topology, functional analysis, differential geometry, etc. by the time I graduate, and I fear that I won't get into a good graduate program. Coming from a small university also worries me.

Does anyone have any advice on what I could do about this? What exactly can I do to effectively prepare myself for graduate studies in a mathematically rigorous field while simultaneously studying for everything else?

I'm really passionate about this and it's been on my mind constantly for months. Thanks in advance!

 

[Jolb]

To get into grad school, you don't need advanced math like topology or differential geometry. (Analysis is important though, and you may run into it on a qualifying exam; e.g. convergence of series in statistical mechanics or Fourier decomposition in quantum mechanics) You won't even need it in your required grad courses. The main topics that most grad programs treat as the prerequisites are: Newtonian mechanics, classical electricity and magnetism, statistical mechanics, and quantum mechanics. (No topology or differential geometry there.)

Remember that in most programs, the experimentalists are in the majority, and many of them are pretty rough-and-tumble with their math. Not having fancy math won't really hurt you on grad school apps--most people don't have it either. In fact, a lot of physics grad schools would rather see someone who is really focused on physics, so having too many math classes could indicate you're not as strong on your physics. However, the fancy math is important if you want your thesis research to be theoretical (vs. experimental), and especially important in high energy theory like what you're interested in.

I'm a second year physics Ph.D. student, and I also was a double major in physics and math as an undergrad. Currently it's looking like I have good chances at getting a high-energy advisor, but I've also made some good connections with a condensed matter theorist. Like you, even with a math major on my degree, I never got around to taking classes in some of the tough math that are important in some realms of physics. (Like you, I never took differential geometry or topology.) But it wasn't really a big deal. You can learn the math on your own, and most of the time if a physics textbook requires some nontrivial math, it will include a section with a distilled version of what you need to know. Moreover, physicists are often pretty loose with their math and a basic intuitive idea will get you by. [If you sat through a math class on the topic, they'd set up many intricate definitions and notations, proving everything with great rigor, and being so careful, they probably won't have enough time to make it to the results physicists use. For example, I took an entire semester math class on group theory and we didn't even make it close to Lie groups--I needed to take a non-rigorous physics course in group theory to learn the business of SO(n), U(n), etc.]

As an example, I did a reading project with a quantum Hall effect theorist (topological insulators), never having taken any topology, but I was able to get by with my basic ideas about topology (basically what I learned from skimming over wikipedia and Roger Penrose's "Road to Reality").

So don't be intimidated by the "fancy math" that physicists talk about. They often like to use mathematical vocabulary to sound more precise and sophisticated, but physicists are often not nearly as mathematical as mathematicians. Most physicists in recent times, including many of the greats, teach themselves the fancy math, so don't worry about your math courses.

BTW, the physics GRE has very little hard math. It's mostly a trivia exam.

 

[Lavabug]

I'm pretty set on going to graduate school; I do well in most of my classes and I am starting to really study for the GRE Physics subject test. My problem is this: I really like theoretical physics, but as I look into graduate school requirements and GRE scores and information needed for certain fields, I feel really overwhelmed.

Currently I'm leaning toward fields such as QFT, String Theory, Particle Physics, etc. because all of the mathematics really intrigues me. I'm stressed out because I know I won't have a huge background in a lot of fields like topology, functional analysis, differential geometry, etc. by the time I graduate, and I fear that I won't get into a good graduate program. Coming from a small university also worries me.

Does anyone have any advice on what I could do about this?

If you're dead set on going to graduate school, you should be aware that funding provisions for HEP/particle physics is very grim in the United States right now and will be for the foreseeable future. Research advisers are not getting as many research grants and graduate admissions are getting very, very competitive in this field (top MIT students with an expressed research interest in this field aren't getting into many grad schools: http://www.physicsgre.com/viewtopic.php?f=3&t=5081 )

Consider different research topics if you want any real chance of getting into graduate school.

 

[Jolb]

If you're dead set on going to graduate school, you should be aware that funding provisions for HEP/particle physics is very grim in the United States right now and will be for the foreseeable future. Research advisers are not getting as many research grants and graduate admissions are getting very, very competitive in this field (top MIT students with an expressed research interest in this field aren't getting into many grad schools: http://www.physicsgre.com/viewtopic.php?f=3&t=5081 )

Consider different research topics if you want any real chance of getting into graduate school.

Oh yes, excellent comment. I know a few people who got into grad school who lied on their applications about what they were interested into increase their odds--e.g. condensed matter instead of high energy or even experiment instead of theory. Fortunately they don't hold you to it. (It's quite common for theory hopefuls to end up in experiment.)

 

[SuitCoatBassis]

Thank you both for your informative replies. I hadn't much considered the competition and funding issues.
That's disheartening, but it's better to know where I stand now rather than later.