The Physics GRE: a guide for undergrads

13Sep06

Autumn for physics students: finishing up summer research reports, asking for letters of recommendation for grad school, signing up for general education requirements, and … taking the Physics GRE. I had meant to post this over the summer for anyone who might be preparing for the November exam, but this is around the time when I started studying last year anyway. Hopefully this will be helpful for a few people. It’s based on a talk I gave to the Stanford Society of Physics Students in my senior year.

(from PhD Comics, click for full size comic)

The huh-what GREs? I just wanna go to grad school!

‘GRE’ aren’t just the first three letters of Tony the Tiger’s opinion of Frosted Flakes. Like the SATs, the GREs are standardized exams for entrance to graduate programs in the US. There is a computer-based general exam, which will score you on verbal, math, and essay skills (though it will be revised in 2007); and also subject based exams, including Physics and Mathematics. Here’s an analogy (do they still do these in the SAT?):

SAT : SAT II subject :: general GRE :: subject GRE

Most graduate programs in physics don’t look too closely at one’s general GRE score, especially if one is a US native. Just make sure your math score is up there, as the math sections on the general exam should be really basic for a physics major.

The Physics GRE is prerequisite for most, if not all, graduate physics programs. I have heard urban legends of students who refused to take the test and applied to graduate schools anyway, but I have no idea if this is true and certainly didn’t want to test the idea myself.

About the Exam: The ‘ETS’entials

Official information on both the general and subject GREs is available at the ETS website (physics details). Here’s the gist of the Physics exam:

1. The test is multiple choice and paper based. That means to pull out those #2 pencils you used in high school. (Did anyone else save their “exam-slaying” pencils?)
2. There are 100 questions in three hours spanning a ‘standard’ undergraduate physics curriculum.
3. There are no calculators or outside references. There will be a list of physical constants and maybe moments of intertia.
4. It costs money, $130 last I checked.
5. It is only given in November, December, and April. For seniors, November is your last chance to take the exam and meet deadlines.

Interpretation

From (1) and (2) one can deduce that speed is an issue. You’ve got just over a minute and a half per question. Factor in bubble-filling, erasing, scratchwork, and that’s not much. However, there’s some consolation: every problem can be solved in that time. You just need to attack it from the right angle.

From (2) and (3) one can deduce that ‘quick and dirty’ is better than getting things right to five decimal places. Also you need to know formulas in some delicate balance between memorization and quick derivation.

From (4) and (5) one can deduce that it’s important to take the exam seriously. You don’t get many attempts and those that you do get are expensive. (1 physics GRE = a month’s worth of hot dogs.) Luckily, there are practice exams (see below).

A ‘Standard’ Undergrad Physics Curriculum

As I’ll note below, you shouldn’t spend too much time ‘studying’ for the GRE in the conventional sense of opening up books and reading. However, it does help to have a map of what you’ll be responsible for. (Depending on one’s background, one might be ready to take the exam much earlier in their undergraduate career.) Your best bet is to look at the general breakdown of questions, available in the practice booklet and on ETS’s informational webpage. I encourage you to actually read the detailed breakdown of each topic and make sure you are familiar with them. Below are my rough interpretations of the level at which the Physics GRE exam will require facility in each general topic. As a convenient scale I’ll use popular textbooks (these were roughly the reference books I used).

1. Classical Mechanics: Most questions are at the level of a freshman physics for engineers, such as Halliday and Resnick. There will also be basic questions on Lagrangian and Hamiltonian mechanics at the level of Marion & Thornton. Some questions on central potentials may also be at the Marion & Thornton level.
2. E&M: You are responsible for most of Griffiths’ Introduction to Electrodynamics in various levels of detail. Most calculations are at the Halliday and Resnik level, but you are expected to know qualitative relations for advanced topics (e.g. how does the total power radiated by a point source depend on charge?). There will be DC/AC circuit questions that one should be familiar with at the level of an introductory circuit lab: mostly RLC, but once in a while something like a diode may show up. Horowitz and Hill’s Art of Electronics is definite overkill… but then again, isn’t it always?
3. Optics and Wave Phenomena: Most topics here can be found in Halliday and Resnick or even a “physics for premeds” level text such as Giancoli.
4. Thermodynamics and Statistical Mechanics: You do not need to have taken a complete course in statistical physics. Most questions are at the Halliday and Resnik level with a few conceptual questions about the partition function and basic stat mech. Reif is overkill.
5. Quantum Mechanics: Griffiths Introduction to Quantum Mechanics covers all of your bases and then some. In fact, if you’ve had a class at this level or above, then you’ll probably be insulted at how easy the quantum questions are. Most of the questions are at the level of a modern physics text such as Beiser.
6. Atomic Physics: What, you’ve never taken an atomic physics course? Don’t worry, your modern physics course probably covered everything you need. Beiser is actually pretty good for this topic.
7. Special Relativity: Doing calculations at the modern physics level as well as a good conceptual understanding is sufficient. I think Taylor’s Spacetime Physics is about the right level, but I’ve never really gone through it in detail. No four-vectors, chapter 12 of Griffiths’ E&M book is already overkill.
8. Laboratory Methods: I don’t know of any good textbooks, but a lab course or two should cover all the basics (oscilloscopes, lasers, statistics).
9. Specialized Topics: There isn’t much you can do here–you’re either familiar with these topics from extra coursework, research, or personal interest. I’ve found that a modern physics text like Beiser as well as the modern physics sections of books like Halliday and Resnick cover all sorts of gems. Griffiths Elementary Particles text (to complete the triumvirate) helps a little for one or two particle questions. (Anecdote: a friend at Harvard said that there will always be a positronium-related question.)

Strategies and Tips

Okay, so here are suggestions based on my personal experience with the Physics GRE:

• Important: Do as many practice problems as you can. This is the only way you’ll get a feel for the exam, which is probably going to be very different from any exam you’ve had as a physics major. The 2001 exam (“GR0177”) is available free online and a paper version is mailed to you when you register for the test. Additionally, there are three other exams that have been released in the following book published by the ETS:
  However, this book has long been out of print. Fortunately, copies of the exams (GR8677, GR9277, GR9677) are available online if you look around hard enough. (A website at Brandeis had them posted for a while, but they have since restricted access.)
• It’s really important so I’ll repeat it: the practice exams should be the centerpiece of your studying. Do not waste any time on any other GRE Physics test prep material, and certainly not the error-ridden REA book that’s not quite like the exam anyway.
• How to use the practice exams: the ’86, ’92, and ’96 exams go from easy to hard and span the extremes of the kinds of questions ETS will ask. The ’01 test is a good representative of what current tests are like. I suggest starting with the ’96 exam, as it’s likely to provide some motivation to study.
• Study in a group! This is also really important. If you don’t have a group of physics buddies you feel comfortable studying with, then you’ve been approaching college all wrong for these past three years. Set up a study group schedule and stick to it. Make studying for the GRE Physics a priority. Consider meeting once a week for a few hours at a time. Decide if you want to spend your time together reviewing questions, exchanging problem strategies, or doing sections of an exam together; but use each other as resources for alternate points of view. I cannot stress enough how much the structure and added motivation of a study group helps in your preparation. It might actually be a little fun. Your study group can also double as a grad school support group.
• How to use those reference books: I suggest not using reference books until you’ve done a set of practice problems and have identified (from the problems) some specific topics you need to brush up on. By ‘specific’ I mean notation for atomic electrons, particular formulae and how to use them, etc. I do not mean “all of thermodynamics.”
• Find time to study. You can do a couple of practice problems in the five minutes before class starts, or on the bus, or while you’re walking to your apartment. These aren’t replacements for sitting down for 3 hours and taking a whole practice exam in test conditions, but it helps to study little bits where you can fit them in. (It also helps memorization and identification of problem spots.) Keep a print out of the latest page of questions in your back pocket if you need to.
• Review all questions: There are 400 practice questions available. You should review every question you ever get wrong at least once, and ideally a few times over the course of your GRE prep. I firmly believe that someone who can solve all 400 practice questions, even if it’s because he/she reviewed every missed question several times, will be able to ace the exam. (Again, the point is that these questions should be the focus of your studying, not the outline of topics.)
• Solve questions the right way: quickly. There might be multiple correct ways to solve a given question, but the right way is the one that takes the least amount of time. This “least amount of time” is around one minute. There are plenty of short cuts:
  • process of elimination (working backwards)
  • dimensional analysis
  • order-of-magnitude estimation (clever us of the physical constants provided)
  • ‘numerology’ (is there any sensible way the provided numbers can equal a given answer choice?)
  • don’t bother being neat for your scratch work
• Easy questions first. Don’t miss easy points at the end of the exam because you didn’t get to them. Skip hard questions and get back to them. Also, mark questions that you answer but want to check. I circled questions that I wanted to get back to when I finished my test.
• Memorize questions sparingly, but as necessary. The better you understand the physics of a subject, the fewer equations you’ll have to memorize and the easier it will be to memorize meaningful equations. For the most part you won’t be quizzed on factors of 1/2 (unless it’s a well known result, such as the vacuum energy of the quantum harmonic oscillator), so it’s more important to know how one quantity depends on another.
• Guess intelligently. You’re penalized a quarter of a point for every wrong answer, so you can maximize your total scores by playing the intelligent-guessing game (that you once used on the SATs, and more recently used to solve ODEs).
• Use what you’ve got. You are given a table of information including formulae for common moments of intertia and fundamental constants. Learn to use these in clever ways to make order of magnitude estimations.
• For some reason, positronium is important. Positronium tends to show up in one form or another at least once in each exam. If you miss the positronium question on your practice exams, brush up on positronium and why it’s important pedagogically (i.e. reduced mass, how its energy spectrum differs from hydrogen, etc.).
• Don’t lose time peeing: it’s also worth noting that depending on your test center, you may not be able to leave the room for bathroom breaks in the last 30 minutes of the test. The lesson? It’s a long exam. Get used to test-taking conditions while you’re studying. You don’t want to exhaust yourself on the real deal just because you didn’t practice with an entire 3-hour exam. You don’t want to lose time and concentration because you didn’t learn not to drink too much from taking such a 3-hour practice exam. That being said, it does help to have a bottle of water and some non-crunchy snack nearby. Your test center may not allow you to drink\eat them during the exam, but you’ll be hungry when you get out.
• Celebrate: go out for lunch with your study group after the exam. That’s the last standardized test you’ll ever take in your academic career. Unless you quit physics and become a lawyer, that is.

Directory of Useful Links

• The Official ETS GRE Page: online registration, test information, etc.
• www.physicsgre.com: an online forum with some additional advice and discussion of official practice test questions.
• GRE Physics.Net: A collection of solutions for the official practice exams. I can’t vouch for the quality of the answers, however, and have been somewhat disappointed with some of the ones I perused.
• PhD Comics: Nothing to do with the exam, but if you’re taking the exam you’ll probably like it.

By the way, if anybody wants to become really popular with younger generations of physicists, I suggest starting a Physics GRE Official Practice Exam Solutions wiki. If you set it up with LaTeX support it could be an amazing resource for Physics GRE takers. I strongly suggest that someone consider starting up such a project. It might actually be a nice study tool with a group of study buddies.

Appendix: Critical Acclaim for the Physics GREs

A snippit from an IM conversation:

Me: So I’m writing about the physics GRE, any thoughts?
Anon: booooooo

And that’s from someone who did extremely well!

At the end of the day, the Physics GRE is not always pleasant, but it’s something you have to do. It’s also material that one should reasonably be responsible for and are likely to be tested on (more rigorously) at your grad school’s qualifying exam. Think of it this way: if you do really well on the GREs, then you’ll have more leverage to get into grad programs and choose one that doesn’t have quals.

Don’t worry too much about your score. Different grad programs weight the Physics GRE in differently. Theory programs may tend to be a little stricter with GRE scores because a good theorist should (apparently) be able to think outside the box and draw on all sorts of ‘clever’ tricks to do well. The bottom line, however, is that nobody expects a 3-hour multiple choice exam to really identify one’s potential as a researcher in graduate school. A really good score, on the other hand, definitely doesn’t hurt!

Good luck to everyone taking the Physics GRE!

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