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The Mathematics Department
of the
University of Southern California
Francis Bonahon, Professor and Acting Chair
Asher Shamam, Graduate Student
USC Math at a glance
Faculty:
32 tenure track and emeriti
6 joint appointments with teaching
12 postdocs (9 teaching)
6 lecturers
9 joint appointments without teaching
7 research faculty
USC Math at a glance
53 PhD students
All fully supported by TAships,
RAships, Fellowships
29 master’s students (including math
finance)
The two PhD Programs
The PhD in (pure) Mathematics
The PhD in Applied Mathematics
First year: Introduction to discipline and
department
PhD in Mathematics
Screening exam at the end of first year:
Algebra OR Analysis
Typically 3 courses/semester
Graduate seminar: Introduction to dept
faculty and problem solving
First year: Introduction to discipline and
department
PhD in Applied Mathematics
Screening exam at the end of first year:
Real analysis, numerical analysis,
probability, statistics
Typically 3 courses/semester
Graduate seminar: Introduction to dept
faculty and problem solving
Introduction to the research
enterprise
After passing screening exam, student
is expected to select a thesis advisor
Usually, begins to read some research
articles
Significant Transition
PhD in Mathematics
Qualifying Exam before the end of the second
year:
Two written exams: algebra, analysis,
topology/geometry, differential equations,
or proba/stats.
One oral exam: the student is expected to
show that he/she can understand research
level mathematics
Significant Transition
PhD in Applied Mathematics
Qualifying exam after significant body of
research (third or fourth year)
Oral exam: the student presents the
research already accomplished, and
indicates plans for further research
leading to the completion of the PhD
Breadth requirements
Student expected to take a certain number
of courses, covering a wide spectrum
of mathematics
PhD in Mathematics: 3 required
courses, plus 5 out of a list of 8
PhD in Applied Mathematics: 6 courses
out of a list of 19
Dissertation: choosing the
topic
Usually, major input from the advisor.
Several models:
Advisor suggests specific problem
Advisor suggests general area, until
student/advisor converge on something
“doable”
Team work on the topic of a grant/contract
(applied math)
Dissertation: When to defend?
General rule: When the advisor says so
Often, little input from rest of dissertation
committee
Limit of 5+ years of financial support implies
strong incentive to finish on time (pressure
on both student and advisor)
Trend in the USC Math Dept
Push student to begin research as early
as possible
There had been problems in the past
Innovation
Revised PhD in Applied Mathematics:
Get graduate exams out of the way
sooner
Qualifying exam after significant body
of research
Novel Idea
PhD in Mathematics, with a minor
outside of mathematics
Possible minors: Biology, Computer
Science, Computer Engineering,
Electrical Engineering, ...
PhD with a minor
Rationale:
Some students were already doing it,
getting an master’s degree in
engineering over their summers
Increase breadth, in particular in
Applied Mathematics
Better employability?
PhD with minor
Investigating two tracks:
PhD in Math with full fledged master’s
in other department (negotiations to
make it easier)
Internal route: MS in Math with
specialization, requiring taking 15 units
outside of math department