The Mathematics Department of the University of Southern California

1
The Mathematics Department of theUniversity of
Southern California

• Francis Bonahon, Professor and Acting Chair
• Asher Shamam, Graduate Student

2
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

3
USC Math at a glance

• 53 PhD students
• All fully supported by TAships, RAships,
  Fellowships
• 29 masters students (including math finance)

4
The two PhD Programs

• The PhD in (pure) Mathematics
• The PhD in Applied Mathematics

5
First year Introduction to discipline and
departmentPhD 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

6
First year Introduction to discipline and
departmentPhD 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

7
Introduction to the research enterprise

• After passing screening exam, student is expected
  to select a thesis advisor
• Usually, begins to read some research articles

8
Significant TransitionPhD 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

9
Significant TransitionPhD 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

10
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

11
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)

12
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)

13
Trend in the USC Math Dept

• Push student to begin research as early as
  possible
• There had been problems in the past

14
Innovation

• Revised PhD in Applied Mathematics
• Get graduate exams out of the way sooner
• Qualifying exam after significant body of
  research

15
Novel Idea

• PhD in Mathematics, with a minor outside of
  mathematics
• Possible minors Biology, Computer Science,
  Computer Engineering, Electrical Engineering, ...

16
PhD with a minor

• Rationale
• Some students were already doing it, getting an
  masters degree in engineering over their summers
• Increase breadth, in particular in Applied
  Mathematics
• Better employability?

17
PhD with minor

• Investigating two tracks
• PhD in Math with full fledged masters in other
  department (negotiations to make it easier)
• Internal route MS in Math with specialization,
  requiring taking 15 units outside of math
  department