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