Course Program
The most common way for students to gain the knowledge and skills to succeed in the Ph.D. program is through coursework. The relevant courses for the Ph.D. are of three types
- basic graduate-level courses;
- additional specialized courses appropriate to the student's field of research; and
- an elective one-year course selected to broaden the student in applied mathematics.
Basic Courses: All students are encouraged to master basic material in:
- probability (550.620), statistics (550.630), or stochastic processes (550.426)
- optimization (550.661, 550.662)
- numerical and matrix analysis (550.681, 550.692), and
- discrete mathematics (550.671, 550.672).
Normally, a student will have completed at least eight basic courses by the end of the fourth semester of residence.
Specialized Courses: Each student takes advanced courses appropriate to the proposed area of dissertation research. Sample programs in the areas of probability/statistics, operations research/optimization, discrete mathematics, and numerical mathematics are given below, but a student with different goals is free to propose an appropriate program meeting the approval of the research advisor.
Elective Courses: A one‑year graduate course (or the equivalent) in a field distinct from the student's specialized area is required. This is a minimal requirement. Students are encouraged to take more than two semesters of elective coursework, either covering one area in depth or covering two areas. Typical courses or areas in other departments are econometrics, mathematical economics, mathematical ecology, computational geometry, systems theory, health systems, mathematics, facility location, psychometrics, and physics. These courses may complement or supplement the student's previous experience, but if a student has no previous experience in an area some elementary coursework may be necessary as a prerequisite to acceptable graduate level courses. Although students are strongly encouraged to take the elective courses outside the department, with the approval of the advisor they may be chosen within the department, provided they are 600 or 700‑level courses in a field clearly distinct from the student's specialized area.
To promote a well-rounded education and record, all full-time graduate students are expected to enroll in an appropriate number of courses for their stage in the program. Students are required to enroll in and attend 550.600, the Applied Mathematics and Statistics Department Seminar, every semester.
Prior to passing the Introductory Exam, students should take the normal course load of at least nine lecture hours, not counting the department seminar.
After passing the Introductory Exam, students in the first three years of the program should take the normal course load of at least nine lecture hours, not counting the department seminar. However, with the approval of a student’s dissertation advisor, 550.800 Dissertation Research may be substituted for up to three lecture hours.
In a student’s fourth and any subsequent years, the student will take at least three hours of ordinary lecture courses per semester, except that the student may choose to take no lecture courses when both the student and the advisor certify the expectation that the upcoming semester is to be the semester in which the student defends the dissertation. Any student working on a dissertation should sign up each semester for dissertation research, (and should register for and attend the weekly department seminar each semester.)
Grades of B- or better (or equivalent level of performance in “pass-fail” courses) are expected of all department graduate students in their coursework.
In a consultation with his or her advisor, each student will develop a program of proposed coursework. This program should not be thought of as a firm contract but as a basis for planning; typically it will need to be updated from time to time.