Welcome to the Thunderdome: The GRE

I know that many of the readers of this blog are physicists, former physicists and proto-physicists, which means that at some point in your worldline, you’ve taken or will take the Physics GRE. I remember taking it near the end of my undergraduate career thinking (quite literally at the time) that this really represented a close approximation to the sum total of human physics knowledge. In short, I was an idiot.

This year, I’m running a boot camp for Drexel seniors thinking about grad school (where they call me “coach” in what is an almost painfully misguided attempt to make this seem like a training montage). Historically, our seniors haven’t done as well on the exam as they really should, considering their grades, research, and the rigor of our courses, so we decided to take it up a notch. I’ve written a little about this before, but here, for free, let me share with you some of the lessons learned so far, both in this course and throughout my time at Drexel:

  • The GRE subject exam matters. A lot.

    The very top grad programs in the country have average subject scores of about 90 %-ile, and very good ones usually have minimum scores of at least 50 %-ile. This may not seem like a high bar to clear, but remember that everyone taking the exam is/was a physics major thinking about grad school. You’re in pretty elite company. Also, while most top grad programs will claim that they don’t perform a triage using a strict cut on GRE scores (and while you’ll hear of the occasional case of a student being admitted to a top program on the basis of grades and research with a poor to mediocre GRE score) this is the exception, not the rule.

  • It’s a marathon, not a sprint.

    The subject test consists of 100 questions which you have to answer in 170 minutes. That’s a minute and 42 seconds per question, which means that there’s not a lot of time for monkeying around with abstractions. For each problem, just do your business and move on, and if you get it wrong, them’s the breaks. You probably won’t have a lot of time to come back. That’s the bad news.

    The good news is what it takes to succeed. Like many multiple choice tests, you get 1 point for each correct answer, 0 for leaving it blank, and -0.25 for an incorrect answer. Strategically, of course, this means that it’s a good idea to guess on questions where you can eliminate a couple of answers on dimensional or symmetry grounds.

    But more to the point, you’d be amazed at how few you need to get correct to do well. Take a look at the sample test that ETS posts on their website. Out of a maximum of 100 points:

    • 50th %-ile (which along with very good grades, letters and research will likely land you in a good grad program) requires only 44 points.
    • 90th %-ile (typical averages at the very top programs), only 76 points.

    These numbers vary from year to year (and getting the various scores is obviously no guarantee to admission at the top programs), but the picture is clear: you don’t objectively need to do that well in order to get a high school. There’s a hell of a curve.

  • For the most part, it’s not terribly advanced.

    The actual physics tested on the exam really isn’t that sophisticated. You’ve likely seen (and forgotten) half of it from your freshman sequence. The quantum mechanics part really only tests a few key concepts (expectation values, the relationship between wavefunction and probability, eigen-energies, and simple 1-d solutions to the Schroedinger equation), most of which will be taught near the beginning of your first term of quantum. It’s not that there aren’t any complicated problems on the exam. There are.

    It’s just that, for the most part, the ones that I advise my students to skip are ones that come from a lack of breadth of knowledge, not a lack of depth. For that matter, there are a few problems on every exam which, even if you know exactly how to solve them, you’re not going to finish in under 10 minutes. Yes, you’re very smart, but you’re even smarter if you’re smart enough to skip these. 10 minutes on one problem means 5 other problems get short shrift.

  • The best prep is practice.

    Besides the one on the GRE webpage, there are lots of old exams flying around the web. Download them. Do them for time. If you don’t want to do the full exam at a sitting, do 20 problems and give yourself 34 minutes. Go over every problem afterward and try to classify them into different categories:

    1. Concept problems. Here’s a classic that I’ve seen on at least two previous exams: How would Maxwell’s equations change if there was a magnetic monopole. (A: nabla cdot vec{B}=mu_0 rho_B and nabla times vec{E}=-dot{vec{B}}+vec{J}_B). There’s nothing you can do to “solve” these problems in the sense of chugging through math. It’s just a matter of having seen them (or similar ones) before. The great thing is that these problems are about 10-15% of the exam and will allow you to make up some time.

      Other common categories include things like spectroscopic and electronic notation of atoms, basic results in particle physics (including the left-handedness of the weak force), classic quantum experiments (especially the Stern-Gerlach) and the like.

    2. One liners. About half of the exam can be solved with a line or two of algebra.
    3. Specific knowledge. Most of the questions on the exam should be able to be solved by any student in any program across the country or around the world. Something like 80% of the problems are simply classical mechanics, thermo, E&M, quantum, and very elementary special relativity (make sure you know how to compute a gamma factor and know time dilation, length contraction, and relativistic momentum and energy relations).

      Beyond that, there are often questions that you simply won’t know unless you’ve taken a specialized course (or just studied the topics for the exam). There are a fair number of questions on optics, for instance, and a lot of questions on experimental methods. Most aren’t difficult, but they will require memorizing a half dozen or so equations.

    4. Long problems. I’ve been a physicist for over 10 years, and have run courses on the GRE, on preparing for our graduate qualifying exam, and have taught classes all across the spectrum. I’m pretty good at solving problems, and very good at solving them fast. That said, on any given exam, there are maybe a half dozen problems for which there is no shortcut or which would have required you to memorize an insanely abstract and infrequently used equation. These problems take me 10 minutes, and are likely to take you even longer.

      Learn to identify these problems and then skip them and return if you have time. One hint is that on the solution key to every exam there’s a number indicating the fraction of students who answered correctly. If that number is under 20% then you should probably skip it.

  • Finally, make sure you hit the basics.

    There are some very straightforward equations/areas for which you should make sure you have a pretty good mastery. This is not a complete list:

    • The Euler-Lagrange Equation
    • 1-d elastic collisions
    • Circular orbits.
    • The Biot-Savart Law
    • Ampere’s Law
    • Gauss’s Law
    • Lens’s Law and Faraday’s Law of Inductance
    • Circuit elements (and the energy stored in each, and the voltage across each), along with solving the differential equation describing an RLC Circuit. (Hint: It’s an exponential solution).
    • The motion of a particle in a uniform magnetic (or electric) field. Note that it is almost always the case that the angle between the particle’s motion and the magnetic field is 90 degrees, so your right-hand-rules will serve you well.
    • The method of images.
    • The properties of EM waves incident on conductors.
    • The properties of an ideal gas. (Also, the specific heat of molecules at very temperatures. Hint: 3/2, 5/2, 7/2).
    • The Fundamental Thermodynamic Identity and how to apply it.
    • Ordinary wave relations (including the relationships between propagation speeds, wavelength, frequency, etc).
    • Solutions to the 1-d Schroedinger equation, especially plane-wave solutions and solutions for which E < V. (Hint: [latex]e^{pm ikx}[/latex] and [latex]e^{pm kappa x}[/latex], respectively).
    • Probabilities and the amplitudes of various eigenstates of the wavefunction.
    • Expectation values.
    • Interference and the double slit experiment. (Also, Bragg’s law).
    • Spectral and electronic notation.
    • The energy of hydrogenic atoms (including positronium).
    • The energy, momentum, frequency, and wavelength of a photon, including the relativistic Doppler shift.
    • Calculation of the gamma factor in SR, and calculations of the relativistic momentum and energy.
    • The properties of thin lenses (especially the relationship between focal length, image, and source position).

Best of luck to all of you who are taking the exam in a couple of weeks. And, for those of you studying for the exam or who’ve taken it recently and want to give other pieces of advice or suggest other basic or common areas to hit, feel free to comment.

-Dave

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One Response to Welcome to the Thunderdome: The GRE

  1. So now do we have to write GRE or only GRE subject test (Math) or both if we want to join a grad college or they are all just moot now ?

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