This is 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). The Preliminary Oral examination, along with the usual course work, 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 Ph.D. Written Preliminary 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 by 10 May of the end 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 written preliminary examination requirements would be met) must be approved in advance by the Director of Graduate Studies (DGS).
Students must pass two written examinations as follows:
1. EITHER Real Analysis OR Complex Analysis AND
2. EITHER Algebra OR Manifolds/Topology
Upon successful completion of the Written Preliminary Examination requirement listed above, the DGS Assistant will fill out the Preliminary Written Examination Report Form, obtain required signatures, and submit the form to the Graduate School on your behalf.
After passing the Written Preliminary Examination, students must declare one of the following tracks they will pursue:
OR
Before the end of the fourth year, students pass coursework as follows:
Mathematics Track
Core requirements
Math 8201/02 (Algebra)
Math 8301/02 (Manifolds/Topology)
Math 8601/02 (Real Analysis)
Math 8701/02 (Complex Analysis)
Note: Any of the four core courses can be passed by examination.
Additional requirements
coursework meeting the requirements of a minor in another department,
OR
12 credits of graduate level classes meeting the requirements of an internal supporting program.
Applied Mathematics Track
Core requirements
Math 8401/02 (Math Modeling)
Math 8441/42 (Numerical Analysis)
Additional requirements
a full year graduate course in an outside department,
coursework meeting the requirements of a minor in another department,
OR
12 credits of graduate level classes comprising the requirements for an internal supporting program.
After having selected the major area in Mathematics where the Ph.D. thesis will likely be written, students should also 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 advisor 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 the each of the above courses, with an average grade of "B" or better.
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.
Students are required to fill out both an M.S. and Ph.D. Degree Program Transmittal Form. Before scheduling the Preliminary Oral Examination AND no later then you third year of Graduate School, Degree Program Forms must be approved and on file at the Graduate School.
Advice on completing Degree Program forms:
For the M.S. Degree Program form, you should not list any foreign language or any courses for which you have not already registered. For the Ph.D. Degree Program form, you must list your foreign language. Except for these two points, and a few other obvious differences, the M.S. degree program form can be very similar to the Ph.D. Degree Program form, and will save time in preparing the two degree program forms at the same time.
After approval of both the M.S. and Ph.D. Degree Program Transmittals forms, you should request your M.S. Graduation Packet from The Graduate School by going to the following website:
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.
Also in the Graduation Packet, is 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 M.S. should be granted by 31 July following the fourth year.
Before the end of the fourth year, 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. 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.
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. Though not required, you may want to do this at the same time as the Degree Program Transmittal form since it requires some of the same signatures.
Before the end of the fourth year, students pass the Preliminary Oral examination by:
| 1. | Prepare an expository paper on a specialized area of mathematics, |
| AND |
| 2. | Pass an eximation consisting of: |
a. An expository lecture covering the material in the paper, b. A defense of the major area of study, c. A defense of the minor area or the supporting program
(click here for additional information on the Preliminary Oral Examination)
The Preliminary Oral 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 and returned to the Assistant to the Director of Graduate Studies in 127 Vincent Hall.
You are also required to complete the online Graduate School Preliminary Oral Examination Scheduling. NOTE: If you try to schedule your online Preliminary Oral Examination with the Graduate School before you complete and submit the Degree Program Transmittal and Foreign Language Proficiency forms, the Graduate School 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 M.S. "Examination Report" form to the preliminary oral examination, to obtain the required signatures from committee members.
Please note: In conjunction with passing the Ph.D. Preliminary Oral Examination (which also counts as the M.S. final oral exam), the student is expected to complete, and submit to the Graduate School, all paperwork needed to receive a Plan B M.S. in Mathematics. REMEMBER: The M.S. "Examination Report" form should be brought to the Preliminary Oral Examination, to obtain the required signatures from committee members.
See information on further regulations and comments regarding your Preliminary Oral Examination.
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.
Before the end of the sixth year, students pass the 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.
Forms Required to be submitted to obtain the Ph.D. Degrees