## UCSD Physics Department Graduate Qualifying Exam

This document describes the composition and grading practices for the physics graduate qualifying exam (hereafter the qual).

### Executive Summary

**CONTENT:** Five sections spread over two days.

**Day One:** Classical Mechanics, Electromagnetism, Math/General.

**Day Two:** Quantum Mechanics, Statistical Physics.

**NUMBER OF PROBLEMS:** Each section consists of three problems: one undergraduate-level and two graduate-level. Students are to submit any two (and only two).

**TIME ALLOTTED:** Day One (six problems) four hours; day two (four problems) two hours and forty minutes (40 minutes per problem average).

**GRADING:** Each problem scored on 0 to 10 point scale. For each subject, the Exam Committee will, based only on scores (i.e., with no knowledge of student identities), set an upper pass bar and a lower pass bar. Exceeding the upper bar is called a **clear pass**. A student between the bars has achieved what we will call a **marginal pass**.

**RULES FOR PASSING (continuing students):** To pass, a student needs to score above the lower bar on all five sections and above the upper bar on at least three sections. If a student fails to do so on their first sitting, that student may retake the exam the next time it is offered, selecting any combination of subjects for which they did not pass above the upper bar in order to bring the number of clear passes to three and achieving marginal passes on the remainder.

*Note for students matriculating Fall 2017 or later: If a student has satisfied core class criteria (B- or better in related core courses), a passing qual grade is irrespective of UG/grad composition; otherwise at least half of the points required to meet each pass line must come from grad-level problems to qualify for that category of passing.*

**RULES FOR PASSING (entering students):** Entering students scoring above the upper bar for any of the five subjects have passed that subject, if at least half of the points required to meet the upper bar come from grad-level problems. Subjects with scores less than this must be retaken, starting no later than Fall of the student’s second year, at which point the passing rule for continuing students applies.

**NUMBER OF ATTEMPTS:** Not including the "free shot" offered to entering students, each student may sit for the exam (or any of its component sections) twice. All sections must be attempted in the first "official" sitting.

### Overview

The qual tests five subject areas (Classical Mechanics, Electromagnetism, Quantum Mechanics, Statistical Mechanics, and Math/General). Each instance of the qual consists of three problems from each area: one at the undergraduate level and two at the graduate level. Graduate-level problems are to correspond to material covered in the previous year’s core courses (200A, 200B,201, 203A, 203B, 210A, 212A, 212B, 212C), generally contributed by the instructors of said courses. The qual may be offered just prior to Fall orSpring quarters, but note that the Qual Committee may choose to cancel the Spring qual some years, depending on demand.

Testing will transpire over two days, organized by subject. Day 1 will be four hours and cover Classical Mechanics, Electricity & Magnetism, and Math/General. Day 2 will cover Quantum Mechanics and Statistical Mechanics in two hours and forty minutes.

Students are to turn in up to two problems for each subject, equally weighted. Failure to submit problems for any subject constitutes an official omission.

Each subject is passed separately/individually, so that only those sections for which performance is unsatisfactory need to be re-taken by the student. The entire exam period is available in all cases, even if a student is only re-taking a sub-set of subjects.

Grading employs a two-bar system, the bars being set separately for each subject to allow variations in difficulty among subjects and from one exam to the next. The upper bar establishes an unconditional pass line, and the lower bar separates decent from inadequate performance (marginal pass). The qual committee has freedom to adjust the levels each time. A student exceeding the upper bar in a subject has completed the pass requirements for that subject and need not face this subject again in any future qualifying exam. Please note that for graduate students matriculating Fall 2017 or later, if a student has satisfied core class criteria (B- or better in related core courses), a passing qual grade is irrespective of UG/grad composition; otherwise at least half of the points required to meet each pass line must come from grad-level problems to qualify for that category of passing. The entire exam is passed if a student achieves at least three clear passes (in any three subjects) and at least marginal passes in the remaining subjects. For example, three clear passes and two marginal passes constitutes satisfactory completion of the qualifying exam, while a student achieving four clear passes only (and below the lower bar on the remaining subject) has not passed the exam and will need to re-take the failed subject.

### Generation of Problems

The qual committee for a given year will consist of that year's instructors of the core graduate courses (200A, 200B, 201, 203A, 203B, 210A, 212A, 212B, 212C). The instructors are asked to generate problems associated with their courses during the quarter in which said course is active, to be used in the following year's qualifying exams. This mechanism is intended to tightly couple the exam content with course content. When this becomes untenable for some reason, explicit efforts will be made to ensure that material pertaining to any substitute question was adequately covered in the preceding corresponding course, so that the student may be expected to have learned the material. Undergraduate problems may be solicited from instructors of the upper-division undergraduate courses (with the expectation that these problems are at a level suitable for exams in those courses).

The qual committee is responsible for constructing an exam based on the problems generated in the previous year (vetting, editing as needed), administering, and grading the problems.

In addition to providing a problem, the originating instructor is to provide a detailed solution AND a grading rubric, since someone else may end up grading the problem.

### Grading and Passing

Problems are worth 10 points. Each student submits two problems per subject to be graded, the earned points added for a subject total. For each subject, total scores are sorted so that upper and lower bars may be established, based in part on aggregate performance. One may imagine, for example, that the Quantum Mechanics scores in the Fall exam result in perhaps 50-60% of students above the clear-pass line and 25% between the bars. The net result should be roughly consistent with historical pass rates for the exam as a whole.

Grading is done anonymously. Bars are set without knowing student identities.

A student passes a subject if exceeding the upper bar for that subject, regardless of performance on other subjects. A student is allowed two attempts (not counting the free-shot, below) per subject.

A student passes the exam when (1) at least three subjects clear the upper bar; AND (2) no subjects are below the lower bar (thus can have two marginal-pass subjects).

If a student re-takes a marginal-pass subject and does worse (below the lower bar) on a future attempt, the highest scoring instance survives.

### Exam Sessions

The exam is split over two days. Day One is 4 hours, and consists of Classical Mechanics, Electricity and Magnetism, and Math/General. This amounts to 40 minutes per problem submitted. Day Two covers Quantum Mechanics and Statistical Mechanics, spanning 2h40m to provide the same amount of time per problem.

Regardless of how many subjects a student is taking, they must start at the beginning of the session. The entire session is available to all students, independent of how many problems/subjects are being submitted.

Each exam session counts as an attempt for any subjects not yet passed by the student, discounting the free-shot.

### Free Shot

Students arriving at UCSD may take the (Fall) qualifying exam without counting the attempt as one of the two allocated per subject. Free-shot students may elect to submit any problems they wish to have graded. Upper-bar passes will be accepted as demonstration of proficiency in the Subject if at least half of the points required to meet the upper bar come from grad-level problems, and this subject will not need to be repeated in future exams. Marginal passes will be ignored, requiring the student to re-take the qual in those subjects no later than Fall after their first year at UCSD. Students will have two attempts beyond the free-shot to pass remaining subjects, following the same criteria as continuing students in terms of number of clear and marginal pass scores.

### Strategies and Examples

A student needs to achieve clear passes in at least three subjects, the remaining subjects being at least marginal passes in order to pass the exam.

An obvious global strategy is to take all the core graduate courses, thereby building a solid foundation and preparing for content likely to appear on the qualifying exam—by virtue of the mechanism for problem creation.

A free-shot attempt scoring clear passes in all five subjects (subject to grad-level stipulation) has no further exam requirements, except that we encourage all students to take the core courses in order to strengthen their foundation in physics.

A free-shot attempt resulting in three clear passes (subject to grad-level stipulation) and two marginal passes will need to re-take the marginal pass subjects, but need not exceed their previous performance (2 marginal passes are okay).

A free-shot attempt might focus on passing a single subject above the upper bar, thus removing a constraint during the next official sitting of the exam. Because there are no penalties for omitting subjects, the free-shot may be used somewhat flexibly/strategically, if desired.

If after the first official sitting of the exam (beyond the free shot), a student has two clear passes, two marginal passes, and one failed subject, various choices present themselves for the second and final exam attempt. The student may elect to take only the failed subject again, taking steps to assure clear-pass performance. This is risky, but possible. All three marginal pass subjects could be re-taken, assuming one will result in a clear pass and that no failures will remain. Hybrid approaches may also make sense to the student.

A student failing to meet at least the 3-clear-pass plus 2-marginal-pass criterion has failed the qualifying exam and may be asked to leave the program. In cases where academic and/or research performance tell a more positive story, possibly aided by supplemental assessment in the form of an oral exam (administered by members of the qual committee, excluding the research advisor), conditional passes might be considered if clear and effective remedial action can be identified (e.g., taking or repeating a course or courses relating to the deficit subject). Continuation in the program would then be contingent on satisfying such extra requirements.