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.

Area 1

220ABC

Complex Analysis

240ABC

Real Analysis

 

Area 2

200ABC

Algebra

202ABC

Applied Algebra

290ABC

Topology

Area 3

270ABC

Numerical Analysis

281ABC

Statistics

 

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.
  • Students must pass at least 3 qualifying exams.
    • 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.

  • 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. This grade is equivalent to PhD Pass in the current system.
    • 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.
  • 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.

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.

 

 

Sample Qualifying Exams

Algebra (Math 200A/B/C):
SP04SP05SP06FA06SP07FA07SP08FA08SP09FA09FA10SP11, FA11SP12SP13FA13,​​​​ SP14FA14SP15SP16SP17FA17SP18, FA18SP19FA19SP20,  FA20SP21, FA21, SP22, FA22, SP23, FA23

Applied Algebra (Math 202A/B/C):
SP04FA04SP05SP06SP08FA06SP07FA07FA11SP11SP13SP15SP17 FA17SP18FA18SP19SP20FA20SP21, FA21, SP22, FA22, SP23A, SP23B, FA23A, FA23B, FA23C

Complex Analysis (Math 220A/B/C):
SP04SP05FA05SP06FA06SP07FA07SP08FA08SP09FA09FA10FA11FA15SP11SP12SP13FA13SP15FA16SP17FA17SP18SP19FA19SP20FA20SP21, FA21, SP22, FA22, SP23, FA23

Numerical Analysis (Math 270A/B/C):
SP99SP00FA00SP01FA01SP02FA02SP03FA03SP04FA04SP05FA06SP06FA07SP07SP08FA08SP09FA09FA10SP11SP13FA15SP17FA17SP18SP20FA20SP21, FA21, SP22, FA22, SP23, FA23

Real Analysis (Math 240A/B/C):
SP04FA04FA05SP06FA06SP07FA07SP08SP09FA09FA10FA11SP11SP13SP15FA16SP16SP17FA17SP18FA18SP20FA20SP21, FA21, SP22, FA22, SP23, FA23

Statistics (Math 281A/B):
SP99FA99SP00FA00SP01SP02FA02SP03FA03SP04SP05SP06SP07SP08SP09FA10SP11SP13FA15SP17FA17SP18SP18 FormulasSP19 Part ASP19 Part BCFA19 (Part A)FA19 (Part BC)SP20FA20SP21, FA21, SP22, FA22, SP23AB, SP23C, FA23AB, FA23C

Topology (Math 290A/B/C):
SP00SP01SP02FA02FA03SP04FA04SP05SP06SP07FA06FA07SP08FA08FA09SP10FA10SP11SP13FA15SP17FA17SP18FA18FA19SP20FA20SP21, FA21, SP22, FA22, SP23, FA23