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Field Requirements in Applied Mathematics

Requirements for admission to candidacy

The following are required for admission to candidacy for the Ph.D., or to obtain an M.S. degree in Applied Mathematics:
  1. Prerequisite to the graduate program are familiarity with analysis and algebra at the advanced undergraduate level (e.g., MATH 4130-4140 and MATH 4330-4340). Students lacking either prerequisite (which may be determined by their special committee chair and/or the CAM Director of Graduate Studies), should take the appropriate courses within their first two years of study. No more than two of these courses can count towards meeting other CAM degree requirements.
  2. Students are required to take at least eight courses in mathematics and its applications that are approved by her/his special committee, at least 4 of which must be numbered 6000 or above. Suggested areas for these courses are given in the list below of Focal Areas for Applied Mathematics.
  3. The courses taken to satisfy item (2) must include an advanced course in computational methods (focal area (a)). In order to achieve breadth in Applied Mathematics, courses from at least three other Focal Areas should normally be included. Should a course be listed under more than one focal area, then it will count towards only one such area as chosen by the student's Special Committee.
  4. Students are required to have minors in Mathematics and in another filed relevant to their doctoral research. Note that the course requirements listed above may suffice to satisfy the requirements for a graduate minor in Mathematics.
Exceptions to these requirements can sometimes be made, if approved in advance by the student's Special Committee and the Director of Graduate Studies.

Requirements for the Graduate Minor

A student majoring in another graduate field (excluding Mathematics) can obtain a Minor in Applied Mathematics by successfully completing four courses, drawn from at least two of the Focal Areas, each of which contains substantial mathematical content. Two of the courses must be at the graduate level, the others numbered 4000 or above. The courses must be approved by a member of the Field of Applied Mathematics who is a member of the student's Special Committee. Any course used to satisfy requirements of the student's major field of doctoral study may not be used to satisfy the Minor in Applied Mathematics.

If field members or students feel that these requirements should be updated or altered, please inform the Director of Graduate Studies.

Focal Areas for Applied Mathematics

The seven major Focal Areas for the field of applied mathematics are listed below, along with examples of recommended courses for completing the requirements each focal area. In addition to the listed example courses, appropriate courses containing substantial mathematical content, offered by any department, may be taken to satisfy field requirements in mathematics and its applications, subject to approval by the student's Special Committee.

A. Computational Methods

B. Mathematical Analysis

C. Differential Equations and Dynamical Systems

D. Stochastic Methods

(Probability, Stochastic Processes, Statistics, Machine Learning, Signal and Image Processing, etc.)

E. Discrete Mathematics and Optimization

F. Algorithms and Complexity

G. Algebra and Logic