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University of Wisconsin–Madison

The Qualifying Examination -- Frequently Asked Questions

(1)What is the Qualifying Exam? The Qualifying Exam (or QE) is a written examination whose purpose is to help the AOS faculty assess which students should be encouraged to pursue a Ph.D. in this department. It is required for all students entering the Ph.D. track.

(2)When is it given? It is given once per year on a weekend early in the Fall semester. Scheduling is subject to change.

(3)How do I sign up? QE Candidates should identify themselves to the Graduate Program Coordinator (Dee VanRuyven) as soon as they know they will take the exam. The Coordinator is responsible for distributing pre-exam memos from the QE Committee, as well as information about the pre-exam meeting with the QE Committee, so he/she needs to know who is intending to take the exam.

(4)What is the format? Two sets of questions are prepared and administered over a Saturday and Sunday, typically from 9am to 4pm. Students are expected to submit solutions to exactly eight questions, four from each day. Each question will have two faculty graders.

In recent years, the QE Committee has arranged the Saturday questions under four broad headings: Dynamics, Radiation/Physics, Oceans and Climate. Each candidate is asked to answer one of two questions under each heading. The questions for Sunday also fall under the four headings but there may be only one or more than one question pertaining to each heading. Students may choose which four questions to answer from those provided.This arrangement may be changed in future years, and such changes will be communicated to the candidates prior to the exam.

Students are expected to have a calculator, but no notes or other materials are permitted.

Students write out their solutions longhand on ruled paper that is provided. Solutions for different problems are written up on separate sheets so that solutions may be distributed separately for grading.

There is a lunch break from noon to 1pm during which no work may be done on the exam, but current policy is that students remain in the room during the break.

The examination is proctored by one of the faculty. However, the function of the proctor is solely to oversee the conduct of the exam. They will not provide significant hints or help with questions on the exam. If you perceive an ambiguity in the wording of a question, you should draw attention to it in your written solution so that the graders can consider your concerns when evaluating your response.

(5)What kinds of questions are on it? Some may be essay-type questions, others require derivations and/or quantitative problem solving; many employ a combination of both. The best way to get a feel for the types of questions that you might encounter is to review past exams.

(6)Which topics are fair game? We expect students to have background equivalent to our six first-year graduate "core" courses -- AOS 610, 611, 630, 640, 650, and 660. This does not mean that questions cannot be asked on other areas in the atmospheric, oceanic, planetary or other physical sciences, as long as excessively specialized knowledge is not required. Generally speaking, students with excellent analytical skills and physical insight should be able to give credible answers to any QE problem using a combination of common sense, reasonable simplifications, and the fundamental physical relationships and knowledge of the earth and atmosphere acquired through the core courses.

(7)How is the QE prepared? Faculty are asked to provide candidate questions within broad areas relevant to their expertise. The QE Committee quality-controls the questions submitted and selects and edits the set of questions to be utilized in the exam. The Committee tries to achieve balance in the representation of questions from various subject areas (see 4, above). Once a draft of the QE has been prepared, the entire faculty are asked to review the questions. For example, individual faculty members attempt to solve the selected questions and work with the question authors to improve wording and provide feedback to the QE committee. A final draft of the QE is presented for approval at a regular faculty meeting.

(8)How do I study for it? You must have mastered the fundamental relationships governing fluid motions, mass and energy balance, and the physics of the atmosphere and ocean, as well as the observed structure and behavior of both. However, the exam is less about detailed knowledge than it is about your ability to apply physical insight and logical analysis to problems you most likely have never seen before. After reviewing the subject matter from the core courses, you may wish to practice working questions from past exams (see the Graduate Coordinator) to develop confidence in your problem-solving skills and your ability to clearly communicate your findings. If you have questions about the solutions to any of the old problems, see your advisor first.

(9)Do I need to memorize a lot of equations or physical constants? The values of relevant physical constants are provided. Equations that you should have memorized include the Navier-Stokes equations, the hydrostatic law, the thermodynamic laws, conservation laws, other well-known physical laws and relationships, and of course a variety of fundamental definitions and concepts relevant to radiative transfer, fluid motion, etc. However, the overall emphasis in the QE is not on memorization of a large body of obscure facts but rather on the physical insight, analytical aptitude, and written communication skills essential for PhD-level research.

(10)What strategies should I keep in mind when taking the QE?

  • Make sure you understand what the question is asking. If you're not completely sure what is being asked, be sure to state in your writeup what you think (or will assume) is being asked. That way the grader can assess your response in light of your interpretation of what was being asked.
  • Be prepared to make assumptions. You will not necessarily be given every piece of information needed to reach a definitive result. Common sense and/or knowledge of "typical" conditions can help you nail down unknown parameters. Be sure to clearly state whatever new assumptions you make. It is as important that you clearly describe your approach to solving the problem as it is that you solve the problem. You should also make reference to how your solution might depend on the assumptions you have made.
  • Be clear and organized in writing up your solution. You might want to work out a first draft on a separate sheet of paper and then transcribe it to the sheet you turn in. It doesn't matter how elegant your method is if your grader can't easily follow what you're doing. Figures and sketches, where appropriate, can be very useful, both to help you clarify your own thinking as well as to help communicate your reasoning to the graders.
  • Don't try to snow the grader with lots of irrelevant information, especially if there's a risk that some of that information may be wrong. If there are ten relevant facts and you omit one of them, it will not make nearly as bad an impression on the grader as it will if you confidently assert something of questionable validity. It's okay to make assumptions or guesses that may or may not be correct, but be sure to label them as such and, if possible, clearly explain your basis for making them.
  • Remember that when analyzing a physical problem, the conservation laws -- momentum, angular momentum, energy, and mass --- are powerful constraints that can often yield insights not so easily obtained through blind application of the detailed governing equations.
  • Dimensional consistency is essential. If an equation you derive is not dimenensionally consistent, either internally or with respect to the property you are trying to derive, it is wrong, period.

(11)How it is graded? All solutions turned in for a particular question are photocopied and distributed to two faculty graders. Graders do not know whose work they are grading. Graders do not consult with each other during grading. Graders assign one of six categories to a solution. The categories are "Low Fail" (0.0), "Fail" (0.6), "Marginal Fail" (1.2), "Marginal Pass" (1.8), "Pass" (2.4), "High Pass" (3.0), where the numerical values are used for computing an overall average for the exam. The category assigned is NOT based on points or on percent correct but rather on the grader's subjective assessment of the student's overall preparedness for PhD level study, taking into account all facets of the student's response. A solution that is 90% correct may receive a mark of "Fail" if the remaining 10% reveals unacceptable shortcomings in the student's knowledge or logic.

(12)What are the graders' criteria? Every grader is free to apply his/her own criteria. Basically, they are forming a judgment as to whether the student's solution to a problem is consistent with the intellectual qualities and academic achievement expected of a successful PhD student. No two graders will have the same expectations. Graders are guided by a standard checklist that references mathematical correctness, logical development, critical thinking, physical insight, and clarity of presentation, among others. However, graders are not required, or even expected, to give equal weight to all of these criteria.

(13)How do I know how much weight is given to each subpart of a problem? There is generally no fixed weight applied to any particular subpart. As noted above, grading is not based on points or percent correct. Rather, the grader is making a subjective judgment, based on the entire solution submitted, as to the preparedness of the student for PhD level research. Each grader may give greater or lesser weight to any particular aspect of the solution, depending on that grader's sense of its relative importance.

(14)The two graders assigned very different marks to my solution on one problem. What's up with that? Because different graders may have differing subjective criteria for assessing a student's apparent preparedness for PhD level study, it is not expected that different graders will always reach the same conclusion. For example, one grader may downgrade sharply for reaching an incorrect final solution; another may find merit in the student's insight and logic, even if the final solution isn't correct. The point of having multiple questions and multiple graders is that variations in graders' individual criteria will average out to yield an assessment that is reasonably representative of the standards of the department as a whole. This is why the two grades are not averaged for a given problem -- all 16 grades (8 problems times 2 graders each) are considered completely independent pieces of information to be considered as a statistical sampling of the faculty's judgment.

(15)What are the possible outcomes? The overall outcome of the exam is based on two variables: the average of the 16 grades received, and the number of grades in the "Pass" or "High Pass" category. The three possible outcomes are:

  • Fail -- Student's overall performance on the exam is clearly inconsistent with faculty expectations of prospective PhD students
  • Marginal -- Student's performance on the exam is inconclusive with respect to his/her preparation for PhD-level study. Additional assessment (e.g., oral questioning) will be required by prospective PhD Committee before admitting student to PhD track
  • Pass -- Student's performance on the exam is consistent with faculty expectations of prospective PhD students.

(16)I did poorly -- what are my options? You should consult with your advisor before embarking on any particular course. Not only is there no disgrace in stopping with an MS degree, it is important to understand that even if you pass the QE with flying colors, that does not necessarily mean that pursuing a PhD is the best choice for you. You and your advisor should discuss the pros and cons of continuing to seek admission to the PhD track.

That said here are your options:

  • Work toward an MS instead (if you have not already completed one).
  • Retake the QE the following year (if this was not already your second attempt). Note that intensive studying may or may not make a large difference in the outcome, depending on the nature of the deficiencies in your first attempt. Gaps in knowledge are generally correctable; difficulties with logic, clarity, and critical thinking skills may be harder to correct through study alone.
  • Attempt to make the case to your prospective PhD committee that your QE results are not representative of your ability to undertake independent PhD-level research. This option requires the concurrence and active support of your advisor. Generally speaking, compelling independent evidence of your ability will be required in order for the committee to discount the QE results.

(17)Nobody did well on this year's QE, so I think it was a bad exam. Typically, fewer than ten students take the exam in any given year. That is a statistically small sample. Moreover, the QE is by design a difficult exam, and a fairly large percentage of students are expected (on average) to earn less than a full Pass. Even if the test and grading were identical from year to year, there would still be large statistical variations such that either far fewer or far more students than average might do well in any given year.

Keep in mind also that it is not the quality of the questions that matters so much in the grading but rather the grader's perception of the quality of your answers, even those given in response to ambiguous or confusing questions. You could easily provide eight insightful responses to eight poorly worded questions and thus earn high marks from your graders. If the question is unclear to you, you have the opportunity to explain in your solution why you think it is unclear and what assumptions you actually made. Your ability to identify bona fide (and possibly even intentional!) ambiguities in a question can even count in your favor by revealing the depth of your insight into the subject area.

(18)I received a low mark for one solution, but I don't know why. Graders assign marks based on their overall perception of the quality of the answer. Some may choose to make specific comments on the solution sheets indicating which deficiencies they perceived; others do not. The objective of the QE is assessment, not learning. Nevertheless, the department is considering ways to provide more detailed feedback to students concerning the nature of perceived deficiencies.

(19)There was a question on a topic that I don't remember seeing in any course. Recall that one of the points of the QE is to assess your ability to apply familiar concepts and reasoning to unfamiliar problems. So just because you haven't had the topic in your courses doesn't necessarily mean that it's an unfair question! That said, students are given more than eight questions to choose from, so they can usually disregard at least one or two that cover unfamiliar territory. Moreover, one can completely miss at least one of the eight questions submitted and still receive an overall mark of "Pass." If you fail to earn a pass because of too many questions on unfamiliar topics, the most plausible explanation is that you need to review FAQ 6, above.

(20)I passed my QE and/or do not plan to retake it next year. When do I have to form a PhD committee? If you have already completed your MS, or if you do not plan to earn an MS prior to pursuing a PhD, then you are expected to meet with your prospective PhD committee by the end of the semester in which you took the QE. There is rarely a compelling reason to delay. Our goal is to resolve a student's status with respect to continuation in the PhD track as early as possible. We also want your committee to be actively involved as a resource early in your PhD research. It's important to note that your first meeting is with a prospective committee, regardless of how well you did on the QE. At the end of that first meeting, and based on all evidence presented (including the QE), members will decide whether to formally establish a PhD Committee.

If you take the QE while still working toward an MS, then you are expected to meet with your prospective committee within one semester of having completed your MS. Again, the goal is that your status as a continuing PhD student be resolved without delay.

(21)What else should I know? You are encouraged to discuss the QE with your advisor well in advance of the exam. If you have specific questions or concerns about the exam, you are encouraged to bring them to the QE Committee.