Students enroll in courses based on research topics that they choose in consultation with faculty.  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.  

Students must choose three areas out of a list of the following six topic areas in which to take courses and be examined:

• 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, and information theory

Additional topics may be considered with prior approval by the director of graduate studies.

The student should choose specific topics by the end of October. In consultation with the student, the director of graduate studies 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 usually program faculty or associated faculty, but faculty members from other departments may serve as advisers with approval.