Sunday, May 23, 2010

Thoughts on the Qualifying Exam

I am pleased to announce that I have passed my qualifying exam, which means UNC will allow me to continue on and get my PhD (assuming I actually do some research). So now that I have successfully passed my qual I will now express my thoughts on the matter.

Here at UNC-CH the department is a combined physics and astronomy department which means the astro students are mixed in with the rest of the physics students for the basic classes (E&M with Jackson, Classical Mechanics with Goldstein, and Quantum Mechanics with Sakuri, Statistical Mechanics with some book that I never heard of, nor wish to hear of again), but after that the astro students separate off into a different set of classes (Stellar Structure, Galaxies, "High Energy" (compact stellar objects, the class is called High Energy for historical reasons, and the university is being very picky at the moment and won't let the department change the name, so the professor teaching the class changed the material, room location etc. and didn't bother to tell the university. It's a little easier to do when you only have seven students in the class.)). Then when the students are done with those basic classes they then take the qualifier that consists of six written tests roughly corresponding to the classes that we have taken. In my case that meant E&M, Classical Mechanics, Quantum, Stat Mech, Stellar Structure and "High Energy".

Each test consists of five questions, of which we only have to answer three (or if we answer more, then they will only take the three highest scores into consideration). We are given two tests at a time and we have three hours to complete the two tests (for completeness, the groupings were: E&M and Classical, Quantum and Stat Mech, Stellar Structure and "High Energy"). Each question is graded out of 10 points and to pass each test a minimum of 10 points is needed out of 30 possible. If a student fails any one test then they fail the entire qualifying exam (there are some exceptions made for students who do sufficiently well on the other tests, or do exceptionally well in the corresponding class that that failure is waived). Then assuming the student passes each individual test, then the committee looks at the overall score. The overall score must be above a certain level in order for the student to pass (last year the cut off was set at 50%, I don't know yet what the cut off was for this year, but apparently I was above it). This means that a student must get an average of 15 out of 30 points on each test (assuming a cut off of 50%).

The pass/fail rate changes year to year, I have heard of years where everyone passed, whereas last year the failure rate was 20%. Anyone who fails is given another chance to pass it. If they do not succeed on the second try then they are typically awarded a masters and not allowed to get a PhD.

Now the actual tests:

Typically the professor who taught the corresponding class will submit and write at least two of the five questions for the test. The other questions come from any other professor who chooses to submit them to the qualifying committee (typically the professors who submit the questions also sit on the committee). So they try to have at least a few questions coming from the person who actually taught the class, so that if the professor emphasized a particular topic then the students will have a better chance at answering the questions submitted by that professor. But this also means that the majority of the questions came from a professor who the students never had a class from, and thus are not familiar with the type of questions they ask on exams.

Some of the test problems are actually written by the professors, while others come from various sources (i.e. the University of Chicago qual book, sometimes this can be painfully obvious as one year on a previous exam the question was copied straight out of the Chicago book word for word, including typos). Other sources include previous midterms and finals given by professors who have taught the classes in previous years. Thus in response to this, the grad students at UNC have built up a standard battery of study materials, including old qualifying exams (we have access to them, and some questions repeat on a ~5 year cycle (+/- 2 years), sounds predictable but it really isn't because it only happens on a very select set of problems, and this has only held true over the last 11 years), question and solution books for qualifying tests (including the already mentioned Chicago book and the Lim books), and of course old midterms and finals (with solutions! which we really aren't supposed to have but some how someone got a copy that has been passed around...).

So in reality for some of the subjects it doesn't turn into a test of our ability to work problems in physics, but it turns into a test of our ability to work out, memorize and regurgitate problems from the standard set of problems. Granted, for some of these subjects there is only so much that you can test on so that necessarily limits the total number of problems that can possibly be used. But some of the subject tests are actually well written and really do test our understanding of physics (or astronomy as the case may be).

For my particular studying I stuck with old qual problems, and the Chicago book, old midterms and finals, and a general review of important subjects. Specifically in the Chicago book I stuck with the stat mech portion (more explanation about that here, it was a really interesting experience). This turned out to be very advantageous because two problems on the stat mech portion of the qual came straight from the Chicago book.

Overall the tests were hard (but only two of them I felt were actually good measures of my knowledge and understanding of physics and astronomy), but from one perspective I can see why having the tests is necessary. As my adviser put it, the qualifying exam is a very imperfect method of separating PhD candidates from everyone else, but until they come up with a better method, we will have to stick to this.


  1. Quantumleap42,

    This is such good news! Congratulations.

    I also found your write up interesting as there are some similar elements to here at UC Irvine.

    "So in reality for some of the subjects it doesn't turn into a test of our ability to work problems in physics, but it turns into a test of our ability to work out, memorize and regurgitate problems from the standard set of problems. "

    I noticed the same thing. Sure professors gave problems I had technically never solve before, but after you've worked through like 100 past qual problems, you seemed to have covered the general idea for just about all the types of questions to see on the qual.

    I've said this before, but just for comparison for those interested how these exams go from school to school: we had three 3 hour tests on Quantum, E&M and the third test on Classical and Statistical Mechanics. The pass rate is ~50% and you get up to three attempts with the test being administered every 6 months. (After the 3 attempts the pass rate is about 85-90%.)

  2. Congratulations! It's nice when the academic establishment allows you to torture yourself and live like a peasant for several more years. =:) When I took Physics 122 (E&M) at BYU I spent 7 hours in the testing center on one advanced exam. 3 questions, open book, 7 hours. I got like a 45% and I was happy with that. It was a cool class but I never want to see a big glob of resistors or a charged wire of infinite length ever again! =:)

  3. Congratulations! I know I breathed a huge sigh of relief when I passed mine, so take a minute to breath deeply and slowly - then remember you still have to come up with a thesis and get a job somehow. :)

    I am amazed that for both Quantum and Joe the problems were predictable. For our comprehensive exam the problems are generated fresh each year by a committee of faculty members and post-comps grad students. This is a lot of work but it means that students can't just memorize problems. Of course it also means that sometimes the problems aren't as well-studied (and thus prone to issues like misinterpretation, poor-wording, being too easy or hard, etc.). However, I think that essentially faculty have these things so that they have a somewhat quantifiable way to separate the grad students who are progressing towards a PhD-level of mastery and those who aren't. As long as faculty can put a number on people, everyone feels better about it.

  4. Nick,

    I'm actually surprised yours were not very predictable. First, you did Astro, so things may be a little different.

    But think about it, lets take classical mechanics. After you've solved ~50 classical problems where you take some Lagrangian, work out the equations of motion and apply necessary constraints you pretty much have seen everything. Soon, though the qual problems are technically different, it is the same bag of tricks needed to solve the problem.

    Or take Quantum Mechanics. Once you've solved a few dozen problems involving some wired potential you quickly realize pretty much everything solvable no matter how weird boils down to something simple like a hydrogen atom where the potential is perturbed and then you just use the same perturbation techniques you used on every other type of problem.

    So for a basic physics qual, after you do enough problems I actually find it hard to think that problems you encounter would be completely foreign to what you have solved already.

  5. Congratulations! I will take my quals next spring. Here at U of Michigan (in Aerospace Engineering) our quals recently had an overhaul! Now the exam is entirely oral consisting of 5 30 min oral exams with 5 different professors covering material from 5 different courses (3 required, 2 elected). I must confess I am very anxious/nervous for it!

  6. Joe,

    "So for a basic physics qual, after you do enough problems I actually find it hard to think that problems you encounter would be completely foreign to what you have solved already."

    I suppose some of the change in predictability from your comps to mine could be the difference between astro and pure physics, but I think it also has more to do with the way astronomers solve problems. Often in astronomy we have to approximate to a degree that many physicists find hard to digest because it simply is not possible to rigorously solve the full problem. So it becomes more a game of physical reasoning than simply a math problem.

    The second thing that makes our questions harder to predict is that they are "interdisciplinary", meaning that a single question may incorporate material from several classes. For example, we could be asked to solve for the spectra of some element in some ionization state and then create a statistical test to see if one of our predicted lines is present in a data set at a statistically significant level. This means that the number of permutations of questions increases extremely rapidly, making it very hard to predict.

  7. jmb275,

    I like the idea of oral exams. I think when you talk to someone it becomes quite clear very quickly if they know what they are talking about or if they are simply making things up. Good luck!

  8. Nick,

    Good points, I'm sure the more interdisciplinary nature helps as well as the types of problems Astro people solve.

    Nick and jmb275,

    Yes, I agree that orals can really be more helpful in many respects than written. I have a professor here who said while at Berkeley their finals (Not Quals) were oral and in his experienece the exams were much better at sifting through who knows what and how well.

  9. We had both written and oral quals (in neuropsychology). I picked the 3 broad topics to study, created my own reading list (with suggestions from my committee), and went from there. I found that a few good review articles in each area really contained the bulk of information my committee would probably ask me about. My committee submitted questions that were then put together. I had to answer 6 of 9 questions (2 of 3 in each of my 3 topics). We had 9 hours in a room to write out our answers (there is only one of us doing this at a time) using nothing but our memory and a list of the references of our reading list. In those 9 hours, I ended up typing about 22 pages (double-spaced). Then, about 10 days later I had my oral exam where I defended my written answers. My oral exam was little more than a discussion though because I had done well on my written portion so my committee wasn't grilling me as much as just asking me what I thought about certain things.

    I preferred this method of quals because I got to pick topics I liked (mostly) and then just spend time studying them. Granted, I didn't have any equations to solve or things like that but I at least could study thing relevant to me and not "waste" time studying things I probably would never use again.

  10. btw, I served my mission in the N.C. Charlotte mission. Go UNC-CH! I hope you get some time out of the lab to visit those beautiful mountains.

  11. Jared,

    Very interesting. Thanks for sharing qual from a non-physics perspective.


    You're right about NC's beauty (Lived there myself for a time) but the humidity is what killed me.

  12. I'm quantumleap42's brother by the way, just in case anyone was wondering...

  13. Jared,

    Good to know. I enjoyed doing physics with Ryan at BYU a lot so you must have good genes.


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