The Qualifying Exam
The qualifying exam is designed to measure the breadth of students’ knowledge in mathematics. While some students are able to pass the qualifying exam in one try, passing the exam early is mainly an indication that a student has attended an undergraduate university with a broad undergraduate program in mathematics. It is not a good predictor of the quality of the eventual PhD dissertation.
Students are required to take the qualifying examination at the beginning in the first term. The exam may prove a useful diagnostic in helping to identify areas in which a student’s knowledge is weak. There is no stigma attached to taking the exam several times, but students are expected to pass the examination by the second year in residence in order to begin more specialized study leading to research work.
The department runs tutorials and offers several introductory graduate courses (e.g. Math 212a, 213a, 230a, 231a, and 232a) to help students acquire the necessary broad basic background in mathematics to pass the exam.
The exam consists of three, three-hour papers held on consecutive afternoons. Each paper has six questions, one each on the subjects: Algebra, Algebraic Geometry, Algebraic Topology, Differential Geometry, Real Analysis and Complex Analysis. Each question carries 10 points. In order to pass each subject, students must obtain at least 20 of the 30 points in that subject. Students are considered to have passed the qualifying exam when they have passed in all six subjects (120 of 180 points) in one sitting, or they have passed at least four subjects in one sitting and obtained an A or A- grade in the basic graduate courses corresponding to the subject(s) not passed. Students are expected take the recommended course(s) at the first opportunity.
Once students have passed the qualifying exam, they no longer need to take math courses for a letter grade and may elect to receive the grade (EXC) excused. Students should inform the instructor at the beginning of the term if they elect to take (EXC) as a grade.
The first milestone in the Mathematics PhD program are the qualifying exams. Exams are offered in Fall (before the academic year begins) and in Spring. PhD students must pass at least one exam before the start of their 4th quarter. All exams must be completed before the start of the student's 7th quarter. Failure to meet these deadlines is cause for dismissal from the program. Carefully read the Guidelines for Graduate Qualifying Exams document.
Exam requirements are different depending on which program a student is in. Please refer to the UCSD catalog for specific requirements: https://www.ucsd.edu/catalog/curric/MATH-gr.html .
During any examination period the student may take as many exams as he or she chooses. The qualifying exams are written and graded by the faculty who teach the courses. The scores are brought before the Qualifying Exam Appeals Committee (QEAC) and the grades are discussed. The final decision as to whether the student has failed or passed (and at what level) is made by QEAC. This decision is based upon exam performance, and performance in exam cognate coursework, though the QEAC is free to consider additional circumstances in rendering its decision. After the QEAC meeting, the PhD staff advisor will inform students when/how they can find out their results.
Students can request to see their exams after grading in order to find out what they did well/poorly on. Students who wish to see their exam for purpose of contesting the grading should be advised that there will be a very strong burden of proof needed to sustain a grade appeal on a graduate exam because of the nature of the exam writing and grading process. Such an appeal is most likely not going change the exam result.
Qualifying Exam Requirements, Old and New
The Department of Mathematics has undertaken a reform of our Qualifying Exams. This brief note explains the old/current system, the new system, and how the changes are being phased in. These requirements apply to PhD students in Mathematics ; Statistics and CSME PhD students have separate requirements administered by the faculty.
Qualifying Exam Courses and Areas
There are 7 qualifying exams administered each Spring and Fall. Each corresponds to a three-quarter graduate course. They are organized into three Areas.
Old/Current Requirements
For PhD students who entered our program in Fall 2023 or earlier, the following are the current requirements to complete the qualifying exams.
- Each exam is assigned one of four grades: PhD Pass, Provisional PhD Pass (also known as PhD- Pass), Masters Pass, and Fail. The grade cutoffs are determined by the instructors who create/grade the exams; those cutoffs are not released to students.
- At least one exam must have a PhD Pass.
- At least one additional exam must have a Provisional PhD Pass or better.
- At least one additional exam must have a Masters Pass or better.
- Students must pass at least one exam from Area 1 , and at least one exam from Area 2 .
- Students must have two exams, each with a Provisional PhD Pass or better, from two different Areas .
- Students must pass at least one exam with a Provisional PhD Pass or better before the start of their 4th quarter .
- Students must complete all the qualifying exams before the start of their 7th quarter
New Requirements
For students who enter our program in Fall 2024 or later, the following are the requirements to complete the qualifying exams.
- PhD Area Pass indicates readiness to begin research in that area.
- PhD General Pass indicates sufficient familiarity with the subject to begin research in a different area. This standard is lower than Provisional PhD Pass, and higher than Masters Pass .
- Masters Pass is only relevant for Masters students. A Masters Pass no longer counts towards completion of qualifying exams for PhD students.
- At least one exam must have a PhD Area Pass.
- At least two additional exams must have a PhD General Pass or better.
- Students must complete qualifying exams from at least two different Areas .
- Students must pass at least one exam before the start of their 4th quarter .
- Students must complete all the qualifying exams before the start of their 7th quarter .
Principal Differences
The new system has more flexibility: students no longer have to take quals from both Areas 1 and 2, simply from 2 distinct Areas among 1, 2, and 3. The standards for completion are simplified. Although Masters Pass is no longer a sufficient standard for PhD students, the PhD General Pass standard is lower than the old Provisional PhD Pass standard, and more consistent with the intent of the exams: to prepare students for focused research in one main area.
Phasing In Period
Any current PhD students (who entered in Fall 2023 or earlier) still progressing towards completing the qualifying exams may satisfy either the current or the new requirements . To be precise:
- Each Spring and Fall (in fact starting this past Fall 2023), qual instructors will select cutoffs corresponding to all five possible grades:
PhD Pass = PhD Area Pass > Provisional PhD Pass > PhD General Pass > Masters Pass > Fail
- At each qual session, each PhD student’s file will be evaluated using both the current and the new requirements. It will be judged complete if it satisfies the current requirements or if it satisfies the new requirements.
Caveat : students who entered in Fall 2022 or earlier already have qualifying exams graded only using the old cutoffs. Qualifying exams from Spring 2023 or earlier will not be regraded to compute PhD General Pass cutoffs.
Other Aspects of Qualifying Exam Reforms
In addition to the logistical changes described above:
- Faculty will be undertaking the creation of standardized syllabi for all seven qualifying exams, to be available to PhD students upon entry. This is a process that will take the faculty significant time and energy to complete, and is planned to be available starting in Fall 2024 .
- In the meantime, qualifying exam course instructors will give detailed syllabi in each course (as always, per Academic Senate regulations), and content cutoffs for the exams will be communicated to students by the Graduate Advisor in advance of the qualifying exams. The same content cutoffs will apply to both Spring and Fall qualifying exams, as has been standard.
- There will be closer coordination of mentoring efforts by course advisors and the Vice Chair for Graduate Affairs. All advisors for first-year PhD students will formulate plans for course enrollment for the full year, as well as plans for which qualifying exams to take in Spring 2024 . Advisors should meet again with their advisees before the beginnings of Winter and Spring quarters, and possibly make adjustments at those times.
- Preliminary full year course and qualifying exam plans should be submitted by the advisors to the Graduate Vice Chair by the end of Week 1 of the Fall quarter.
Spring 2025 exam schedule
Dates, times, and locations to be determined.
Complex Analysis
Numerical Analysis
Applied Algebra
Statistics
Real Analysis
Sample Qualifying Exams
Algebra (Math 200A/B/C): SP04 , SP05 , SP06 , FA06 , SP07 , FA07 , SP08 , FA08 , SP09 , FA09 , FA10 , SP11 , FA11 , SP12 , SP13 , FA13 , SP14 , FA14 , SP15 , SP16 , SP17 , FA17 , SP18 , FA18 , SP19 , FA19 , SP20, FA20 , SP21 , FA21 , SP22 , FA22 , SP23 , FA23 , SP24 , FA24
Applied Algebra (Math 202A/B/C): SP04 , FA04 , SP05 , SP06 , SP08 , FA06 , SP07 , FA07 , FA11 , SP11 , SP13 , SP15 , SP17 , FA17 , SP18 , FA18 , SP19 , SP20 , FA20 , SP21 , FA21 , SP22 , FA22 , SP23A , SP23B , FA23A , FA23B , FA23C , SP24 , FA24
Complex Analysis (Math 220A/B/C): SP04 , SP05 , FA05 , SP06 , FA06 , SP07 , FA07 , SP08 , FA08 , SP09 , FA09 , FA10 , FA11 , FA15 , SP11 , SP12 , SP13 , FA13 , SP15 , FA16 , SP17 , FA17 , SP18 , SP19 , FA19 , SP20 , FA20 , SP21 , FA21 , SP22 , FA22 , SP23 , FA23 , SP24 , FA24
Numerical Analysis (Math 270A/B/C): SP99 , SP00 , FA00 , SP01 , FA01 , SP02 , FA02 , SP03 , FA03 , SP04 , FA04 , SP05 , FA06 , SP06 , FA07 , SP07 , SP08 , FA08 , SP09 , FA09 , FA10 , SP11 , SP13 , FA15 , SP17 , FA17 , SP18 , SP20 , FA20 , SP21 , FA21 , SP22 , FA22 , SP23 , FA23 , SP24
Real Analysis (Math 240A/B/C): SP04 , FA04 , FA05 , SP06 , FA06 , SP07 , FA07 , SP08 , SP09 , FA09 , FA10 , FA11 , SP11 , SP13 , SP15 , FA16 , SP16 , SP17 , FA17 , SP18 , FA18 , SP20 , FA20 , SP21 , FA21 , SP22 , FA22 , SP23 , FA23 , SP24 , FA24
Statistics (Math 281A/B): SP99 , FA99 , SP00 , FA00 , SP01 , SP02 , FA02 , SP03 , FA03 , SP04 , SP05 , SP06 , SP07 , SP08 , SP09 , FA10 , SP11 , SP13 , FA15 , SP17 , FA17 , SP18 , SP18 Formulas , SP19 Part A , SP19 Part BC , FA19 (Part A) , FA19 (Part BC) , SP20 , FA20 , SP21 , FA21 , SP22 , FA22 , SP23AB , SP23C , FA23AB , FA23C , SP24
Topology (Math 290A/B/C): SP00 , SP01 , SP02 , FA02 , FA03 , SP04 , FA04 , SP05 , SP06 , SP07 , FA06 , FA07 , SP08 , FA08 , FA09 , SP10 , FA10 , SP11 , SP13 , FA15 , SP17 , FA17 , SP18 , FA18 , FA19 , SP20 , FA20 , SP21 , FA21 , SP22 , FA22 , SP23 , FA23 , SP24 , FA24
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Department of Mathematics
Qualifying exams.
The Ph.D. qualifying examination in Mathematics is a written examination in two parts. The purpose of the Ph.D. qualifying examination is to demonstrate that the student has achieved a degree of mathematical depth and maturity in the core areas of real analysis and abstract linear algebra, has additionally cultivated advanced problem solving skills in graduate level mathematics, and is poised to undertake independent mathematical research. The content and timing of the qualifying exam allows this determination to be made within the first two years of graduate study.
The two parts of the examination are as follows.
- Part 1 covers the material presented in the core course MTH 511, Real Analysis
- Part 2 covers the material in MTH 543, Abstract Linear Algebra.
The qualifying exam is given twice each year, near the beginning of Fall and Spring terms. The two parts of the exam are usually given one or more days apart. A student may take each part of the Ph.D. qualifying examination a maximum of three times, with one additional free attempt before a student's first term in the program. To advance in the Ph.D. program, a student must pass both parts, but they do not need to be passed at the same time. A student must pass both parts of the exam by the end of spring term of the student’s second year of study.
Questions about the qualifying exam can be directed to the Chair of the Qualifying Examination Committee ( [email protected] ).
Fall 2024 Qualifying exams
Real analysis.
Tuesday, September 17, 2024, from 4:00-8:00 pm.
Linear Algebra
Thursday, September 19, 2024, from 4:00-8:00 pm.
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