Ph.D Degree
In Mathematics
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For the first year or two, the student prepares for the
preliminary examination. This consists of a written
examination in each of three subject areas chosen by the
student. The three subjects are chosen from the following
list, each subject being represented by a two semester
sequence of graduate courses.
- MA580,
MA780:
Numerical Analysis
- MA534,
MA734:
Partial Differential Equations
- MA523,
MA723:
Matrix Analysis
- MA515,
MA715:
Functional Analysis
- MA520,
MA720:
Linear Algebra and Lie Algebras
- MA532,
MA732:
Ordinary Differential Equations
- MA778,
MA779:
Probability
- MA521,
MA721:
Abstract Algebra
- MA555,
MA755:
Differential Topology
- MA551,
MA751, or
MA753:
Topology
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Each student is required to take the analysis course
MA515
and the algebra course
MA521
as well as selecting additional courses from a list of
course offerings
designed to ensure a broad background in mathematics. Generally,
the latter requirement is satisfied by the courses taken for the
preliminary exam.
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The student must produce a thesis of new and original research in
an area of mathematics. The thesis is defended at a final oral
examination.
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Students opting for the Ph.D with the Computational Math
concentration take numerical analysis
(MA580 and
MA780)
as one of the three subject areas for the preliminary examination.
The additional course requirements include both numerical analysis and
computer science
courses.
In Other Areas
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Most NA Ph.D degrees are given in the
Mathematics department, but Ph.D degrees with NA components
can also be obtained through joint programs with
Computer
Science and
Operations Research.
The requirements vary depending
on the program chosen.
