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.
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 examination (qual) results remain valid for a minimum of three years from the date the examination is taken, regardless of the student’s status at the time (e.g., undergraduate, graduate, etc.). If more than three years have passed, the QEAC or the Council should review and determine whether the results remain valid.
Qualifying Exam Requirements
These requirements apply to PhD students in Mathematics. For students enrolled in the specializations in Statistics or Computational Science, the requirements can be found here: Statistics Computational Science
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.
| Area 1 | 220ABC Complex Analysis |
240ABC Real Analysis |
|
| Area 2 | 200ABC Algebra |
202ABC Applied Algebra |
290ABC Topology |
| Area 3 | 270ABC Numerical Analysis |
281ABC Statistics |
Requirements for students entering our program in Fall 2024 or later
For students who enter our PhD program in Fall 2024 or later, the following are the requirements to complete the qualifying exams.
- Each exam is assigned one of four grades: PhD Area Pass, PhD General 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.
- 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.
- Masters Pass is only relevant for Masters students. A Masters Pass does not count toward completion of qualifying exams for PhD students.
- Students must pass at least 3 qualifying exams.
- 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.
Other Aspects of Qualifying Exams
- 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. Advisors should meet again with their advisees before the beginnings of Winter and Spring quarters, and possibly make adjustments at those times.
The previous scoring system, which applies to students who entered the program prior to Fall 2024, may be found here.
Spring 2026 Qualifying Exam Schedule
| Exam | Date | Content |
|---|---|---|
| Algebra | Thursday, May 14, 2026 | content |
| Applied Algebra | Monday, May 11, 2026 | content |
| Complex Analysis | Wednesday, May 20, 2026 | content |
| Numerical Analysis | Tuesday, May 12, 2026 | content |
| Real Analysis | Monday, May 18, 2026 | content |
| Statistics | Friday, May 15, 2026 | content |
| Topology | Wednesday, May 13, 2026 | content |
Guidelines for qualifying exams can be found here.
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, SP25, FA25, SP26
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, FA25, SP26
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, SP25, FA25, SP26
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, SP25, FA25, SP26
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, SP25, FA25, SP26
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, SP25, FA25, SP26
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, SP25, FA25, SP26
