Doctor of Philososphy [Ph.D] [Applied and Computational Math] From Princeton University

• Students must choose three areas in which to be examined out of a list of six possibilities specified below. The student should choose their specific topics by the end of October. The director of graduate studies, in consultation with the student, appoints a set of advisers from among the faculty and associated faculty. The adviser in each topic meets regularly with the student, monitors progress and assigns additional reading material. Advisers are traditionally members of the Princeton University faculty within the department, but members of the faculty from other departments may serve as advisers with approval. They can be any member of the University faculty, but are normally either program or associated faculty. In consultation with the topic advisers, the first-year student should choose three topics from among the following six applied mathematics 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); and Stochastic modeling, probability, statistics and information theory. Additional topics may be considered with prior approval by the director of graduate studies.
• Typically, students take regular or reading courses with their advisers in the three topic areas of their choice, completing the regular exams and course work for these courses.  

Pre-Generals Requirement(s):

• At the end of the first year, students will also take a preliminary exam, consisting of a joint interview by their three first-year topic advisers. Each student should decide with their first-year advisers which courses are relevant for their examination areas.
• Students should assess their level of preparation for the preliminary examination by reviewing homework and examinations from the previous year’s work.  Students who fail the preliminary examination, may, with the support of the first-year advisers, take the examination a second time.