Old Rules on Admission to Candidacy, MATH and STAT Ph.D. Programs
(now obsolete)
(Applicable to students who have passed the Ph.D. written
examination)
1. A student who wishes to pursue thesis research in algebra/number theory will be required to complete Math 600, 601, and either 606 or 620.
A student who arrives with advanced training may be exempted from one or
more of these course requirements. 2. In addition, the
student must take at least one course chosen from
among Math 607,608, and 621. 3. The student must present an
oral report on a research paper or advanced
monograph chosen in consultation with the student's advisor. The report
will typically take the form of two lectures lasting approximately one
hour. The examining committee for this oral examination will consist of
the student's advisor and two other faculty members chosen by the
advisor.
4. A student will not be permitted to take the oral examination more than twice.
In order
to be eligible for admission to thesis research in PDE, a student
must have passed the Ph.D examination in the analysis segment and a one
year sequence on differential equations, this sequence being taken from
MATH 673/674, 685/686, 670/671, or 680/681. The student must satisfy the
following requirements for admission to thesis research: 1. Pass MATH
685/686
and one of the other year sequences offered in differential equations:
MATH 673/674, 670/671 or 680/681. 2. Participate for at least two
semesters in the continuing PDE seminar,which will be offered for credit.
This will involve the presentation of papers from the Literature, suitably chosen for the student's level. 3. Pass an oral examination by a
subcommittee of the PDE field committee,or other appropriate faculty
members, consisting of at least three members.The examination will cover
material based upon, but not limited to, the two year courses required in
part 1 above. In the event of failure of the oral examination, reexamination
will be permitted. In no case will a student be permitted to take the
examination more than twice.
1. A student will be required to take at least 15 credit hours of
coursework in topology or geometry. These 15 hours shall include not less
than3 of the courses 730, 734, 740, 742 and at least one special topics
course.
2. The student will be expected to have chosen an "area" in
topology or geometry in which to specialize and, preferably, to have chosen
a thesis advisor.
3. The candidate will report on one or more research articles chosen
by the advisor. The student should be prepared to answer questions on the
report as well as basic questions on the courses in paragraph 1 above,
not necessarily related to the report. The examining board for this oral
examination will consist of three faculty members (usually but not necessarily
from the Geometry/Topology Field Committee) chosen by the student's advisor
in consultation with the chairman of the field committee.
4. A student who fails the examination on his first attempt will generally
be permitted to retake the examination put the field committee reserves
the right to inform a student whose performance has been unusually poor
that he will not be allowed to retake the examination and will not be admitted
to thesis research in geometry/ topology. 5. A student will not be
allowed to take the examination more than twice.
In order to be eligible for admission to thesis research
a MATH student in numerical analysis must: 0) Fulfill the departmental
requirements for admission to candidacy. 1) Pass the Ph.D. written
examination in numerical analysis. 2) Pass two of the following MAPL
courses: 600, 604, 607, 610, 612, 614, with a grade of B or better. 3)
Pass an oral examination before a committee of at least three UMCP
faculty members. The chairman of the examining committee must be a member
of the Numerical analysis field committee and must approve the makeup of
the committee. The subject matter will normally include, but not be limited
to, the contents of two of the courses listed in requirement 3 above. A
written prospectus for the exam must be prepared and approved by all members
of the committee in advance of the exam. In the case of failure, a second
attempt, but in no case More than two attempts, will be permitted.
1. A student who wishes to pursue thesis research in
real/functional analysis will be required to have completed Math 630, 631,
and 660, or
the equivalent.
2. The student must have completed two of the following courses:
Math 632, Math 634, Math 636. 3. The student must pass an oral
examination of moderate length (usually
one hour but in no case longer than 2 hours). The material for
this examination may come from 2 above and/or the student may report on
a paper chosen by examiner. There will be two examiners, appointed by the
chairman of the field committee, with student input invited. 4. A
student will not be permitted to take the examination more than
twice
As a condition for
the Ph.D. candidacy, the student must make an oral
presentation in an area of current research. The level of the presentation
should demonstrate depth of knowledge, familiarity with research literature,
and ability to write a doctoral dissertation on a topic related to the
subject of the presentation. The subject matter will be determined by the
student with the help of his prospective thesis advisor. An examining
committee of three statistics faculty members is appointed by the Program
Committee.
At the conclusion of the presentation, the committee judges the presentation
as acceptable or unacceptable. The committee may question the student on
other material, if they deem such questioning necessary to reach a
judgment.
The requirement consists of two parts: seminar talks and a preliminary
oral examination. The student will be expected to give talks in the Logic
Seminar on two separate topics. Each of the two talks may extend over one
or more seminar sessions. An unusually long or deep presentation on one
topic may suffice instead of two separate topics. Upon completion of his
seminar talks, the student may consult with the chairman of the Logic Field
Committee for the purpose of arranging a preliminary oral examination.
The chairman will appoint an examining committee and arrange a date for
the examination. Ordinarily, the committee will consist of all faculty
who regularly teach graduate logic courses. The content of the examination
will ordinarily be covered in Math 446, 447, 710, 712, 713, 716. If the
student passes the examination and if his seminar talks are judged favorably
then he will be considered eligible to proceed towards thesis research
in Logic. Otherwise, the field committee will have full discretion in
deciding what requirements remain to be satisfied. In any case, a student
will not be allowed to take the preliminary examination more than twice.
1. A student who wishes to pursue thesis research in ODE/Dynamical
systems is required to have completed Math 630, 631 and 670 or the
equivalent. 2. The student must also have completed two of the
following: Math 671,633, 642, 643, 730 or appropriate courses by
arrangement with the chairman of the field committee.
3. The student must pass an oral examination of moderate length
(one to 2 hours). The material for this examination may come from item
2 above and/or the student may report on a paper chosen by the examiner.
There will be two examiners, appointed by the chairman of the field
committee, with student input invited. The date, topic and format of
this examination must be set at least four weeks prior to its
administration. 4. A student will not be permitted to take the
examination more than twice.
Students wishing to specialize in complex analysis must fulfill
the following requirements before being accepted formally for thesis
research. 1. Course requirements. Math 660, 661, 680, 681 plus
two additional special topics courses in complex analysis (generally
660 and/or 634, though some other courses may be equally acceptable).
2. Seminar participation. Students planning to specialize in complex
analysis are expected to participate in the complex analysis seminar.
3. Written exam. Before a student can be considered for thesis research
he must have passed the departmental written exam at the Ph.D level.
4. Oral exam. The student will be examined on his knowledge of complex
analysis and related areas by the field committee. This examination will
concentrate on the content of Math 660 and 661 and the advanced courses
offered by the student. The exam will be oral and will in general last
from 1 to 2 hours. Time and place will be arranged, on the initiative
of the student, in consultation with the field committee members. All regular
faculty members of the complex analysis field committee will be eligible
to participate in this examination, and in no case will there be fewer
than three examiners. A majority vote of the examiners will be required
for passing. Ordinarily, this exam will be taken only after the student
has fulfilled the requirements of items 1) through 3) above; in special
cases, however, it may be scheduled somewhat earlier.
Remarks. 1. The field committee feels it important that
the student have as strong a background as possible in areas of
mathematics that impinge on complex analysis (e.g.; functional
analysis, PDE, ODE, probability, differential geometry, etc.)
Students are urged to take this into account in preparing their
schedules and selecting courses. However, courses in these areas are
neither required nor will they be accepted in lieu of the requirements
of item 1). 2. The requirements of items 1) and 2) may (in very
exceptional circumstances) be waived at the discretion of the committee.
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