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 before
10 May 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 before 10 May 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 10
May 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 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 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 21 May
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. Oral Preliminary 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.
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.
(i) 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.
(ii) 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.
(iii) 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 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. This form can be
obtained from the Graduate Program secretary in Vincent Hall 127, to whom
the completed form should be returned.
(iv) The student, by this time, should be writing the expository paper,
and ought to be soliciting advice from the major area committee members.
(v) 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).
(vi) 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. The Examiners Report Form for the Ph.D. Oral Examination will be sent directly to the advisor a few days prior to the examination.
(vii) 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.
(viii) The examination itself consists of:
a) Presentation of the expository paper (about 30 minutes),
combined with questions in the major area.
(Approx. 60 minutes total)
b) Examination in the minor area, or in one of the year long sequences, constituting the supporting program.
(Approx. 30 minutes)
(ix) 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. Please have
both approved, and also pick up the MS Graduation Packet, which
can be reqested
by clicking here.
In the MS Graduation Packet is the "Examination Report Master's Degree
and Certificate of Specialist in Education". This MS "Examination Report"
form should be brought to the prelim oral exam, to get the required
signatures from committee members. (NOTE: The Prelim Oral "Examiners
Report Form" mentioned in Items (vi) and (vii) above must also be
brought and signed.) 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.
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 oral preliminary
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.
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 form since it requires some of the same signatures.
Advice for paperwork at the PhD Preliminary Oral exam: Bring both
the MS final oral Examiner's Report form and the PhD prelim oral
Examiner's Report form to the 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.
last updated October 2009
Director of Graduate Studies in Mathematics
(612) 625-1306
gradprog@math.umn.edu
127 Vincent Hall
206 Church St. S.E.
Minneapolis, MN 55455 USA
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www@math.umn.edu
URL http://www.math.umn.edu/grad/phdprogrequire.html
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