The First Year
Coursework
After the arriving student has his or her feet on the ground, it will be the student's responsibility to choose three areas in which to be examined from a list of six possibilities specified below. The Director of Graduate Studies, Ingrid Daubechies, in consultation with the student, will then appoint a set of advisors from among the faculty and associated faculty. The advisor (any member of the University faculty, but usually affiliated with PACM) in each topic will meet regularly with the student, monitor progress, and assign additional reading material. The first-year student should choose the three focus topics by October 30th from the following six categories:
- Asymptotics, analysis, numerical analysis, and signal processing
- Discrete mathematics, combinatorics, algorithms, computational geometry and graphics
- Mechanics and field theories (including computational physics / chemistry / biology)
- Optimization (including linear and nonlinear programming and control theory)
- Partial differential equations and ordinary differential equations (including dynamical systems)
- Stochastic modeling, probability, statistics, information theory
Other topics may be possible as special exceptions, provided they are approved in advance by the Director of Graduate Studies. Typically students take regular or reading courses with their advisors in each of the three areas, completing the regular exams and course work for these courses.
Preliminary Exam
At the end of the first year, students will also take a preliminary exam, consisting of a joint interview by their three first-year advisors. Each student should discuss with their first-year advisors which of these courses are relevant for their areas. In order to assess whether they have sufficient preparation, or whether it would be good to take a particular course, it is a good idea to obtain some typical homework or a final exam from a previous year.
The Second Year
Students who have been evaluated with satisfactory performance after the first year will be readmitted for the second year of graduate study. (Students who did not achieve a Ph.D. level pass on their first-year preliminary exam are re-admitted for the fall of the second year, and normally take parts of the preliminary exam again during this semester.) Students who are admitted to the second year will continue working with at least one faculty member with the goal of achieving competence to begin Ph.D. research. This faculty member should be a potential Ph.D. advisor. A presentation by the student on research topics before a committee of three faculty members is to take place in the second semester, in late April or May. If the student passes this examination (the General Exam), he or she becomes a Ph.D. candidate.
Thesis Template
These files are provided to help graduating students prepare their thesis. Right-click on file to download.
