Requirements for the Ph.D. Degree in Mathematics
Major Steps Leading to the Ph.D. Degree
- Before the end of the second year, the student is expected to demonstrate proficiency in basic areas of mathematics by passing the Preliminary Written Examinations. This requirement must be completed before 10 May of the student's second academic year of studies.
- Before the end of the fourth year, a student is expected, pass all the coursework, foreign language requirements, and the Preliminary Oral examination.
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.
- Before the end of the sixth year, a student is expected to pass the final oral/dissertation examination.
All these points are addressed in detail below.
Additional, helpful, information can be found on The Graduate Schools, Information for Doctoral Students.
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 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:
|| Real Analysis
|| Complex Analysis
Upon successful completion of the Written Preliminary Examination requirement listed above, the DGS Assistant will fill out the Preliminary Written Examination Report, obtain required signatures, and submit the form to the Graduate School on your behalf.
After passing the Preliminary Written Examination requirement, students must declare one of the following tracks they will pursue:
- 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: 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.
Applied Mathematics Track
Math 8401/02 (Math Modeling)
Math 8441/42 (Numerical Analysis)
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 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 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 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. Graduate Degree Plan. 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.
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. Except for these two points, and a few other obvious differences, the M.S. Graduate Degree Plan can be very similar to the Ph.D. Graduate Degree Plan, and will save time in preparing the two Graduate Degree Plans at the same time.
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.
Before the end of the fourth year, students should find a thesis adviser (major area adviser) and pass the Preliminary Oral Examination by:
||Preparing an expository paper on a specialized area of mathematics,
||Pass an eximation consisting of:
||An expository lecture covering the material in the paper,
||A defense of the major area of study,
||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. The School of Mathematics Application for Preliminary Oral Exam Form, must be completed at least two weeks before the examination and submitted to the Assistant to the Director of Graduate Studies in 127 Vincent Hall. Once the signed form has been received, the Assistant to the Director of Graduate Studies (DGS) will schedule a room for your examination and will notify you. Only the Assistant to the DGS is authorized to schedule rooms for preliminary oral examinations.
At least one month prior to your Preliminary Oral Examination, you are required to assign members to the Preliminary Oral Examining Committee by going to the Graduate School's, Forms for Doctoral Students website and linking to Assign/Update Preliminary Oral Examining Committee.
At the same time, you must also assign members to the M.S. Final Examining Committee by going to the Graduate School's, Forms for Master's Students website and linking to Assign/Update Examination Committee.
Once your committee's have been approved, you are 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 Graduate Degree Plans, 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 Committee Chair. You should check with your committee chair at least two days prior to your Prelim Oral Examination and make sure that the Committee Chair has the proper form.
At the same time that you schedule your Preliminary Oral Examination, you must also request your Master's Graudation Packet which can be found by going to the Graduate School's, Forms for Master's Students website. You will find two forms in the M.S. Graduation Packet. The M.S. "Examination Report" form which must be signed by the preliminary oral examination committee members. The second form will be filled out by the Graduate Student and submitted to One Stop Student Services.>
See information on further regulations and comments regarding your Preliminary Oral Examination.
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 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.
A thesis adviser (major area adviser) should be found 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. Prelminary
Oral Examination is passed.
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 Full-time 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 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 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 informationon regarding Examination Committees, see the Graduate School's Examination Committees website.
At least one month prior to your Final Oral Examination, you are required to assign the Final Oral Examining Committee by going to the Graduate School's, Forms for Doctoral Students website and linking to Assign/Update Final Oral Examining Committee.
Preparing the Doctoral Dissertation.
Scheduling the Doctoral Final Oral Exam.