Procedures and Requirements for the Ph.D. Degree

Major Steps leading to the Ph.D. Degree

• A. Within the first two years, the student is expected to demonstrate proficiency in certain basic areas of mathematics by passing written examinations and doing course work. This requirement must be completed by the end of Spring Semester of the student's second academic year of studies.
• B. Next, a student is expected, via the Ph.D. preliminary oral examination, to demonstrate proficiency in a major area as well as a minor area (which is either a supporting program in the School of Mathematics, or a minor in another field). This examination, along with the usual course work, completes the requirements for a Plan B Master's degree. This requirement must be completed by the end of Spring Semester of the student's fourth academic year of studies.
• C. Reading proficiency in technical literature in a foreign language (French, German, Italian, Russian - or an approved substitute) is required prior to step B above.
• D. The student is required to write a Ph.D. thesis under the direction of an advisor. This is followed by the final oral examination (which constitutes the defense of the thesis). Proficiency in a second language may be required by the thesis advisor before this examination is taken. The final oral exam should be passed by the end of Spring Semester of the student's sixth year. Please note that 7th year assistantship funding is not available, except in extreme circumstances.

All these points are addressed in detail below.

Required Written Exams and Course Work
The only course requirements involve breadth in basic areas, the minor or supporting program (12 credits) and the thesis credits (24 credits). All these are described in detail in the sections that follow. The course work planning is done in consultation with the student's Graduate Advisor and/or Director of Graduate Studies (DGS) in Mathematics.

Written Examination and Related Courses

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. A student who wishes to become a candidate for the Ph.D. degree must pass these written examinations and related course work requirements by end of Spring Semester of the second year of graduate study. No penalty is attached to unsuccessful attempts to pass these examinations. Any schedule of part-time study (which would reduce the rate at which course work and examination requirements would be met) must be approved in advance by the Director of Graduate Studies (DGS).

For the General Program there are four core areas divided into two groups:

• i.(a) Real Analysis (Mathematics 8601-8602)
• i.(b) Complex Analysis (Mathematics 8701-8702)

• ii.(a) General Algebra (Mathematics 8201-8202)
• ii.(b) Manifolds and Topology (Mathematics 8301-8302)

The student must show proficiency in all four areas. In at least two areas, of which one must be from group (i), and one from group (ii), the written examinations must be passed. For any remaining areas, the student may choose whether to pass the written examination or to pass the appropriate 8-xxx level year-long graduate course with average grade of at least B.

For the Applied and Industrial Program:

The student must pass two written examinations, one chosen from the group:

• i.(a) Real Analysis (Mathematics 8601-8602)
• i.(b) Complex Analysis (Mathematics 8701-8702)

and the second chosen from the group:

• ii.(a) General Algebra (Mathematics 8201-8202)
• ii.(b) Manifolds and Topology (Math 8301-8302)

The student must also complete the following two year-long courses, each with average grade of at least B: Numerical Analysis and Scientific Computing (Mathematics 8441-8442), and Mathematical Modeling and Methods of Applied Mathematics (Mathematics 8401-8402).

In addition, the students in the Applied and Industrial Program must complete a year-long course that carries graduate credit in another department, subject to the approval of the DGS, by the end of the fourth year of graduate study.

Language Requirements

To remain in good standing, international teaching assistants must receive an English Language Proficiency score of "1" by the end of Spring Semester of their first year.

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. See the Graduate Program Administrative Assistant to the Director of Graduate Studies (DGS) in Vincent Hall 127 for the internal procedures. The requirement must be completed before taking the Ph.D. Preliminary Oral Examination. In special cases, a thesis advisor may require a second language. Substitutions of languages may, on occasion, be granted by the advisor and DGS

Supporting Program

After having selected the major area in Mathematics where the Ph.D. thesis will likely be written, students also choose one of the following:

(i) Internal Supporting Program : Two 8-xxx year long course sequences in mathematics, outside the major area must be selected. These may not include any of the core courses (Math 8201, 8202, 8301, 8302, 8601, 8602, 8701, 8702, 8401, 8402, 8441, 8442) of the General Program. Approval from the DGS and advisor is needed. The oral examination only covers one of these supporting sequences.

(ii) Outside Minor: The 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.

(iii) Partial Internal Supporting Program: One 8-xxx sequence as in i) above, and a sequence with graduate credit outside Mathematics should be chosen. The DGS in the outside field should be consulted and prior approval from the DGS in Mathematics should be obtained by the written proposal process described in (ii).

The supporting program must total at least 12 graduate credits.

Forms Required before Scheduling Preliminary Oral Examination

1. Preliminary Written Examination Report Form
   This form will be filled out by the DGS Assistant upon successful completion of all Required Written Exam and Coursework requirements listed above, and will be submitted to the Graduate School on your behalf.




2. M.S. and Ph.D. Degree Program Transmittal Form
   These forms must be approved and on file at the Graduate School prior to scheduling your Preliminary Oral Exam.

   Advice on completing Degree Program forms:
   For the MS Degree Program form, do not list courses for which you have not already registered. For the PhD Degree Program form, you must list your foreign language; for the MS Degree Program form, you should not list any languages. Except for these two points, and a few other obvious differences, the MS degree program form can be very similar to the PhD Degree Program form, and it will save time to prepare the two degree program forms together.

   Please note: 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 pick up the MS Graduation Packet, which can be reqested by clicking here. 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 prelim 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.

   
   
3. 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 and may want do do this at the same time as the Degree Program Transmittal form since it requires some of the same signatures.
   

IMPORTANT: Before submitting any of the above forms to the Graduate School, you must see the Assistant to the Director of Graduate Studies (DGS) in 127 Vincent Hall to verify that the form is ready for submittal to the Graduate School.

Preliminary Oral Examination
This 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.

1. The student should choose a major area advisor as soon as possible, and certainly before starting the fourth year of study. The advisor will recommend course work in the basic material, as well as expository and research papers for individual study.


2. 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.


3. At least three months before the Oral Examination, the student must select the remaining three members of the examination committee (and obtain their consent, as well as that of the major advisor, and approval of the DGS). The examination committee will normally have at least three 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 Application for Preliminary Oral Exam Form, documenting the committee's composition and the members' assent.


4. The student, by this time, should be writing the expository paper, and ought to be soliciting advice from the major area committee members.


5. 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, Vincent Hall 127).


6. The examination is scheduled at the convenience of the student and the examiners. One form needed to schedule the examination is the School of Mathematics Application for Preliminary Oral Exam Form and 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 Scheduleing requirement, the Examiners 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 prelim oral exam, to get the required signatures from committee members.



7. On the day of the examination, the student must bring four more copies of the expository paper (typed, doubled-spaced, 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.


8. The examination itself consists of:
   
   1. Presentation of the expository paper (about 30 minutes), combined with questions in the major area.
      (Approx. 60 minutes total)
   
   
   2. Examination in the minor area, or in one of the year long sequences, constituting the supporting program.
      (Approx. 30 minutes)
   
   
9. Please note: 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 pick up the MS Graduation Packet, which can be reqested by clicking here. 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 prelim 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. Peliminary Oral Examination Report form is sent to your adviser from the Graduate School prior to your exam, and avoid the need to seek out the examiners later to obtain signatures.

Further regulations and comments:

For suggestions on the conduct of a preliminary oral exam, please click here.

Students: In contacting a potential committee member, please do remember that many faculty are very busy, and 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 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. We generally discourage a "pass with reservations". It is hoped that the system of the expository paper and associated 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.

Advice on completing Degree Program forms:
For the MS Degree Program form, do not list courses for which you have not already registered. For the PhD Degree Program form, you must list your foreign language; for the MS Degree Program form, you should not list any languages. Except for these two points, and a few other obvious differences, the MS degree program form can be very similar to the PhD Degree Program form, and it will save time to prepare the two degree program forms together.

Please note: 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 pick up the MS Graduation Packet, which can be reqested by clicking here. 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 prelim 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.

You are also required to fill out the Graduate School's Graduate Program Certification of Foreign Language Proficiency form and may want do do this at the same time as the Degree Program Transmittal form since it requires some of the same signatures.

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. Peliminary Oral Examination Report form is sent to your adviser from the Graduate School prior to your exam, and avoid the need to seek out the examiners later to obtain signatures.

Thesis and Thesis Credits

A thesis advisor (i.e. major area advisor) should be found before the Preliminary Oral Examination. The graduate school requires 24 thesis credits for the Ph.D. degree (Math 8888); students can only register for these credits after the Ph.D. Oral Examination is passed.

Final Oral Examination

This examination is a defense of the thesis. The regulations of the Graduate School 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 advisor, but the advisor 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).

Specific questions on the requirements for the Ph.D. programs should be e-mailed to: the Director of Graduate Studies.

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last updated October 2009