Ph.D.
in
Mathematics - Program Guidelines
Described
below are the Department of Mathematical Sciences requirements for the
Ph.D. degree in Mathematics. These departmental requirements
supplement those set
out
by the Division of Graduate Education (DGE) in the Graduate Catalog for
Ph.D. Students.
There
are no foreign language requirements or qualifying exam for a Ph.D. in
Mathematics.
1. Ph.D. Committee
- The
Ph.D. committee must
include a minimum of five
members excluding the DGE-assigned Graduate
Representative.
- A committee must be formed before
the end of the student's
second semester of study.
- The Committee
Chairperson
(Advisor) must be a faculty member within the Department of
Mathematical Sciences.
- The first three committee
members
listed on a
candidate's Program of
Study read and assess the
dissertation.
2.
Course Requirements
- A minimum
of 30 credit hours are
required
(see the Graduate Catalog for
Ph.D. Students
for details).
- A minimum of 18 credit hours must
be dissertation credits
(M690)
- The Ph.D.
student's Program
of Study listing their intended coursework must be
approved by all committee members.
- The student
must take a minimum of
4 credits of the Math
500
seminar series.
Typically,
a Ph.D.
student takes 18 credits of mathematics in courses numbered 500 or higher
to prepare for their comprehensive examination. Students
are encouraged to begin some form of doctoral reading or
research (either informally or in the form of M689 credits)
with a
committee member by their second year of study.
3. Ph.D. Comprehensive Exam
The
Ph.D. Comprehensive
examination consists of both a written and an oral
comprehensive
examination. The
candidate must pass the written
comprehensive
exam before taking the oral comprehensive examination
Written Exam
component: OUTLINES Written Exam Online
library of old: EXAMS
Written
Comprehensive Exam:
How a
student may choose and re-take exam components is determined by
(a)-(f): - The
written comprehensive exam
consists of 4-hour exam
components graded as Pass or Fail.
- The
candidate must
pass three components
to pass the written comprehensive
examination though they may attempt more.
- If a
candidate fails a component it may
be attempted at
most one more time.
- The candidate must
pass the following "required"
component:
- MATH
547 ,
MATH 551
Real and Complex Analysis
- Normally
the
remaining components are from
the following list of "standard" components:
- MATH
511-512 Topology
- MATH
595-596 Dynamical Systems
- MATH
584-585 Functional Analysis
- MATH
581-582 Numerical Analysis
- MATH
544-545 Partial Differential Equations
- MATH
560-561 Applied Mathematics
- MATH
547, 586 Probability
- At most one
"nonstandard" component
not from (i)-(viii) may
be
taken. To take such a component the following petition
form must
be
completed.
Students take
components determined by the exam timeline describe in (g)-(k)
below: - Exams
components are given every
August intersession
exam period (blue) at dates determined by the department.
- Fall entry students may
take
components the
August intersession preceding their first semester enrolled.
(this
rule
can help M.S. students continuing on toward their Ph.D. for instance).
- Students must
attempt at least one component by Year 2.
- A
student who has not passed all 3
required exam components
after the Year 3 August exam period may
re-take at most one previously failed component the following
January
intersession. No new components may be attempted that January.
- Fall and Spring entry
students take exam
components
according to
the following timeline:
To
find out how written
comprehensive exam results are reported to DGE click here.
If a
second failure of the written comprehensive exams is reported to
DGE your
program of study in the Ph.D. program in Mathematics will be
terminated.
Oral
Comprehensive Exam:
After
passing the written comprehensive exam the candidate must pass an oral
comprehensive exam at a date agreed upon by the candidate's committee.
Normally the oral comprehensive exam is a thesis topic proposal where
the candidate's ability to conduct research on the proposal is
assessed. When this is not the case, the candidate will be informed of
the nature of the oral comprehensive exam by their committee. The
candidate has at most two attempts to pass the oral comprehensive
examination.
4. Disseration Requirements:
Once
the Ph.D.
candidate
has passed the comprehensive exam (both written and oral parts) the
student has at most five
years to submit a draft of their dissertation to their
committee
prior to their final defense. The first three committee members listed
on a
candidate's Program of
Study
must be given a dissertation draft at least two weeks
prior to the Final Defense. Regardless, all committee members must have
access to a dissertation draft at least one
week prior to the Final Defense. The dissertation should embody the
results of extended research by the candidate, be an original
contribution to knowledge, and include new material worthy of
publication. The dissertation must be submitted as an
electronic
dissertation, in
final form to
the Division of Graduate Education not later than 14 working days
before the end of the term in which graduate work is completed.
5.
Final Defense:
Department
policies on
the final
defense and all other administrative procedures regarding the
degree completion are exactly those as set out by Division
of Graduate
Education (DGE).
Ph.D. Comprehensive Exam Outlines
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