Requirements for a PhD Degree
- Preliminary Written Examinations: The student is expected to demonstrate proficiency in basic areas of mathematics by passing these exams
- Declare Track: Mathematics or Applied Mathematics - After passing the Preliminary Written Examination requirement, students must declare one of the following tracks they will pursue: Mathematics OR Applied Mathematics
- Coursework Requirement
- Declare Minor
- Graduate Degree Plan (GDP)
The student is expected to pass all:
- Prelim Oral Exam
- Master's Final Oral Exam - is done at the same time as Prelim Oral Exam
- Thesis and Thesis Credits
- Advanced Doctoral Status
- Foreign Language requirements
- Pass final oral/dissertation examination
Students are expected to demonstrate proficiency in basic areas of mathematics by passing the Preliminare Written Exams. This requirement should be completed before 10 May of the student's second academic year of studies.
Students must pass two written examinations as follows:
- Either: Real Analysis OR Complex Analysis
- Either: Algebra OR Manifolds/Topology
No penalty is attached to unsuccessful attempts to pass these examinations.
Any schedule of part-time study (which would reduce the rate at which written preliminary examination requirements would be met) must be approved in advance by the Director of Graduate Studies (DGS). Part-time study schedules change when written preliminary examination requirements must be met and need to be approved in advance by the Director of Graduate Studies (DGS).
Upon successful completion of the Written Preliminary Examination requirement listed above, the DGS Assistant electronically records and submits the results to the Graduate School.
The Ph.D. Preliminary Written Examinations are given twice each year, once before the start of fall semester, and again in the late spring. Each individual examination lasts four hours.
Find out more about upcoming Written Prelim Exam dates.
Mathematics or Applied Mathematics - After passing the Preliminary Written Examination requirement, students must declare one of the following tracks they will pursue:
Mathematics OR Applied Mathematics
MATH 8001 - Preparation for College Teaching should be completed during the first semester of the first year.
Before the end of the fourth year, students pass coursework as follows:
Math 8201/02 (Algebra)
Math 8301/02 (Manifolds/Topology)
Math 8601/02 (Real Analysis)
Math 8701/02 (Complex Analysis)
Note:Students must complete core courses with a grade of "B"or better in each course. Any of the four core courses can be passed by examination.
Coursework meeting the requirements of a minor in another department,
12 credits of graduate level classes meeting the requirements of an internal supporting program. (The same as Other on the Graduate Degree Plan form.)
Math 8401/02 (Math Modeling)
Math 8441/42 (Numerical Analysis)
Note: Students must complete core courses with a grade of "B"or better in each course.
A full year graduate course in an outside department,
Coursework meeting the requirements of a minor in another department,
12 credits of graduate level classes comprising the requirements for an internal supporting program.
After selecting the major area in Mathematics where the Ph.D. thesis will likely be written, students should declare one of the following Minor tracks:
Outside Minor Course(s)
The Director of Graduate Studies (DGS) in the field should be consulted, and a written plan should be submitted to the DGS in Mathematics.
This plan must include:
- the list of outside courses,
- a description of the content of each and how it fits into the proposed thesis work of the student,
- as well as the place of this material in the outside department's offerings.
The plan must satisfy the minor requirements of the outside department.
Supporting Program Course(s)
Two 8-xxx year-long course sequences in mathematics, outside the major area must be selected. These may not include any of the Regular Mathematics or Applied Mathematics courses (Math 8201/8202, 8301/8302, 8601/8602, 8701/02 or Applied Math 840102, 844/42).
Approval from the DGS and adviser is needed. The oral examination only covers one of these supporting sequences.
The supporting program must total at least 12 graduate credits and student must complete each of the above courses, with an average grade of "B" or better. (The same as Other on the Graduate Degree Plan form.)
Partial Internal Supporting Program:
One 8-xxx sequence as in i) above, and a sequence with graduate credit outside Mathematics should be chosen. Prior approval from the DGS in Mathematics should be obtained by the written proposal process described in Outside Minor.
Before scheduling the Preliminary Oral Examination AND no later then your third year of Graduate School, Graduate Degree Plans must be approved and submitted to the Graduate School at least one semester prior to your preliminary oral exam.
Note: The Graduate Degree Plan milestone must be on the student's record before they can access the committee workflows. This means the GDP must be approved by the college and/or program, in addition to central data entry completed by the Graduate Student Services & Progress (GSSP) and the Office of the Registrar (OTR).
A student is allowed only one committee request per degree objective (i.e., master's or PhD) in the workflow at the same time.
If a student requests a committee before their GDP is approved and processed or while they have a committee in queue, they will receive a message that their new request cannot be processed.
Advice on completing Graduate Degree Plans
For the M.S. Graduate Degree Plan, you should not list any foreign language or any courses for which you have not already registered.
For the Ph.D. Graduate Degree Plan, you must list your foreign language.
M.S. Graduate Degree Plan is similar to the Ph.D. Graduate Degree Plan, and preparing them at the same time will save time and effort.
A minimum of 12 graduate course credits for a declared minor or supporting program are required.
Do not include any ineligible coursework (audited courses, withdraws, undergraduate level coursework, and courses with a grade below C-).
Master’s Graduation Packet
In the M.S. Graduation Packet you will find:
(1) The "Examination Report Master's Degree and Certificate of Specialist in Education" forms. The M.S. "Examination Report" form should be brought to the Preliminary Oral Examination, to obtain the required signatures from committee members.
(2) The "UNIVERSITY OF MINNESOTA/GRADUATE SCHOOL APPLICATION FOR DEGREE" which must be filled out and submitted per instructions. The "APPLICATION FOR DEGREE" is a form that the student can fill out; it does not require signatures from the Preliminary Oral Examination committee or Director of Graduate Studies signatures. The Master's Degree should be granted by 31 July following the fourth year.
The purpose of the preliminary oral examination is to demonstrate proficiency in a major area and a minor area. The minor area is either a supporting program in the School of Mathematics, or a minor in another field.
The Preliminary Oral examination, along with the required coursework, completes the requirements for a Plan B Master's degree.
This requirement must be completed before 10 May of the student's fourth academic year of studies.
The preliminary oral examination concentrates on the major area and the supporting program (or minor). The examination committee of four faculty members consists of the major area advisor and three additional faculty members.
The student should choose a major area advisor as soon as possible, certainly before starting the fourth year of study. The advisor will recommend coursework in the basic material, as well as expository and research papers for individual study.
This study, including the recommended research papers, will be summarized in an expository paper (approx. 10 pages), with a substantial bibliography. This will demonstrate a knowledge of the definitions and results in the area, and indicate open problems which may form the basis for the Ph.D. thesis.
At least three months before the Oral Examination, the student must select the remaining three members of the examination committee (and obtain their consent, the consent of the major advisor, and approval of the DGS). The examination committee will normally have at least two members in the major area (including the major advisor) and at least one in the minor/supporting program. The student must obtain the signatures of the members on an Oral Examination Form, documenting the committee's composition and the members' assent.
The student, by this time, should be writing the expository paper and soliciting advice from the major area committee members.
One month before the examination, final copies of the expository paper should be submitted to the major area advisor and committee members. The student must obtain the signatures of the major area committee members, attesting to the general acceptability of the expository paper, on another Oral Examination Form. (This form is available from, and is to be returned to, the Graduate Program secretary in Vincent Hall 127).
Scheduling the Exam
The examination is scheduled at the convenience of the student and the examiners. The School of Mathematics Application for Preliminary Oral Exam Form should be completed at least two weeks prior to the examination.
You are also required to complete the Graduate School's Preliminary Oral Examination Scheduling requirement. Note: If you try to schedule your online Preliminary Oral Examination before you complete and submit the Degree Program Transmittal and Foreign Language Proficiency forms to the Graduate School, they will deny your request until they receive these forms. Once you have completed the online Graduate School's Preliminary Oral Examination Scheduling requirement, the Examiner’s Report Form for the Ph.D. Oral Examination will be sent directly to the advisor a few days prior to the examination.
Remember, you must also bring the MS "Examination Report" form to the preliminary oral exam to get the required signatures from committee members.
On the day of the examination, the student must bring four more copies of the expository paper (typed, doubled-spaced, and in final form), for the examiners. After the examination, the Examiners Report Form should be returned to the Graduate Program secretary in Vincent Hall 127.
The examination itself consists of:
- Presentation of the expository paper (about 30 minutes), combined with questions in the major area. (Approx. 60 minutes total)
- Examination in the minor area, or in one of the year long sequences, constituting the supporting program. (Approx. 30 minutes)
Forms and Paperwork
In conjunction with passing the PhD Preliminary Oral examination (which also counts as the MS final oral exam), the student is expected to complete, and to submit to the Graduate School, all paperwork needed to receive a Plan B MS in Mathematics. Before the Ph.D. Preliminary Oral exam, please complete the Plan B MS Degree Program form, as well as the PhD Degree Program form.
After approval of both Degree Program forms, you should assign your Master's Final Oral Examination Committee which is done at the same time your assign your Preliminary Oral Examination Committee. After the committee has been approved, you will need to download your Master's Graduation Packet. In the MS Graduation Packet you will find the "Examination Report Master's Degree and Certificate of Specialist in Education"form. The MS "Examination Report" form should be brought to the preliminary oral exam, to get the required signatures from committee members.
Also in the Graduation Packet, is the "UNIVERSITY OF MINNESOTA/GRADUATE SCHOOL APPLICATION FOR DEGREE" which must be submitted. The "APPLICATION FOR DEGREE" is a form that the student can fill out; it does not require committee signatures. The MS should be granted by 31 July following the fourth year.
Advice for paperwork at the PhD Preliminary Oral exam:
Bring the M.S. Final Examination Report form to your Preliminary Oral Examination. The Ph.D. Preliminary Oral Examination Report form is sent to your advisor from the Graduate School prior to your exam. Avoid the need to seek out the examiners later to obtain signatures.
NOTE: It is very important that you bring you signed forms to the Assistant to the Director of Graduate Studies (DGS) BEFORE you deliver your forms to the Graduate School for submission.
The Preliminary Oral Examination serves as both the M.S. Final Oral Examinationand Ph.D. Preliminary Oral Examination. All Ph.D. students have the option to obtain an M.S. Degree on the way to their Ph.D.
Students should bring the Examination Report Master's Degree and Certificate of Specialist in Education form supplied in their M.S. Graduation Packet to the preliminary oral exam. The Preliminary Oral Examination Report Doctoral Degreeform is sent to the chair of the Preliminary Oral Examination Committee from the Graduate School. Both the Examination Report Master's Degree and Certificate of Specialist in Education and the Preliminary Oral Examination Report Doctoral Degree require the same signatures.
It is recommended that a brief meeting among committee members (without the student present) precede the student’s presentation; this allows the committee to go over the order of events, collect suggestions, and seek answers to any questions. Such a meeting is particularly recommended when an examiner from outside the department is present.
At the beginning or at some time prior to the exam, the student should be told how much time is available for their presentation.
After the student's public presentation, all those not examining the student should be asked to leave. The examination phase should not begin until everyone else has left and the door is shut.
The examination period may be run as the chair wishes, but it is advised to clarify procedures during the five-minute meeting preceding the student's presentation.
Immediately after the examination, the candidate is excused from the room, and a written secret ballot is taken before discussing the examination. Following the discussion, a second and final vote is taken, and the participants sign in the appropriate places on the two report forms.
Review the Graduate School examination policies: See University Catalogs,Doctor of Philosophy Degree information. Scroll down to the red lettering readingPreliminary Written and Oral Examinations.
Students: In contacting a potential committee member, please remember that many faculty are very busy. Do not suggest, by your tone, that the faculty member is required to be on your committee. We recommend that you offer to meet in person in advance to discuss your work.
The expository paper and bibliography will indicate what the student has studied. The examination may also cover foundational material and literature in the general area. The nature of the expository paper is much more than a paper surveying a year long course sequence. It is not a research paper, but may include preliminary research results and it might suggest a direction for possible future research. It should be developed in consultation with the advisor and should have the general approval of the major area examiners.
For an internal supporting program, the student will select which subject is to be covered in the examination, (from the two 8-xxx sequences, at least one of which should have been completed). For an outside minor, the rules are those of the outside department.
If a student chooses a partial internal supporting program, at least one examiner must be from the other department, in which a course sequence was taken, (if the student chooses to be examined on such a sequence).
If a student wishes to change advisors or major area, the new advisor and Director of Graduate Studies (DGS) will decide whether a new examination will be required.
The oral examination may be passed, or failed with or without the committee's consent for a retake. A "pass with reservations" is generally discouraged. It is hoped that the writing of the expository paper and associated faculty consultation will result in students being well prepared before they attempt the examination. The Preliminary Oral Examination should be passed by the end the fourth year of study. No more than two attempts are permitted by the Graduate School.
In the M.S. Graduation Packet you will find:
- The "Examination Report Master's Degree and Certificate of Specialist in Education" forms. The M.S. "Examination Report" form should be brought to the Preliminary Oral Examination, to obtain the required signatures from committee members.
- The "UNIVERSITY OF MINNESOTA/GRADUATE SCHOOL APPLICATION FOR DEGREE" which must be filled out and submitted per instructions. The "APPLICATION FOR DEGREE" is a form that the student can fill out; it does not require signatures from the Preliminary Oral Examination committee or Director of Graduate Studies signatures. The Master's Degree should be granted by 31 July following the fourth year.
Before the Final Oral Examination, students must show an ability to read mathematics written in one of the following languages:
French, German, Italian, or Russian
A student must demonstrate a reading proficiency in technical literature in one of the following languages:
French, German, Italian, or Russian.
This requirement is handled internally by the School of Mathematics and must be completed before taking the Ph.D. Final Oral Examination. In special cases, a thesis adviser may require a second language. Substitutions of languages may, on occasion, be granted by the adviser and the Director of Graduate Studies (DGS).
Certification of Foreign Language Proficiency Form
As part of your Ph.D. Degree requirement, you are also required to fill out the Graduate School's Graduate Program Certification of Foreign Language Proficiency form.
Students should find a thesis adviser (major area adviser) before the Preliminary Oral Examination.
The graduate school requires 24 thesis credits for the Ph.D. Degree(MATH 8888 - Thesis Credit Doctoral); students can only register for these credits after the Ph.D. Preliminary Oral Examination is passed.
Note: Graduate Students who have passed their Ph.D. Preliminary Oral Examination are expected to complete the 24 thesis credits during the next two semesters.
Graduate students who have completed the required 24 Doctoral Thesis Credits must register for MATH 8444, Advanced Doctoral Status.
You must complete the Application for Advanced Doctoral Status form each term to register for the full-time equivalent (FTE) benefit. Once completed and signed, submit the form to the Director of Graduate Studies (DGS) Assistant in 127 Vincent Hall.
Before the end of the sixth year, students should pass the final oral examination.
This examination is a defense of the thesis. The regulations from Graduate Student Services and Progress (GSSP) require that three of the four examiners be reviewers/readers and at least one reviewer be from outside the School of Mathematics. The chairperson must not be the thesis adviser, but the adviser may be a reviewer/reader.
The examination consists of a presentation of the results of the thesis (which may be public) followed by questions by the examiners (which are not public). For more information regarding Examination Committees, see the Graduate Student Services and Progress (GSSP) Examination Committees website.
At least one semester prior to your Final Oral Examination, you are required to Assign Members to Doctoral Final Exam Committee.
Submit Doctoral Final Exam Report no later than the last business day of anticipated month of graduation.
The Graduate School's, Doctor of Philosophy (Ph.D.) Degree Completion Steps.
Specific questions on the requirements for the Ph.D. programs should be e-mailed to: the Director of Graduate Studies.