Applied Math Requirements

Field Requirements in Applied Mathematics at Cornell University

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., MA 413-414 and MA 433-434). 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 600 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.

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 400 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

(a) Computational Methods

(b) Mathematical Analysis

(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 Examples of suitable courses in these areas can be found on the Center for Applied Mathematics web site (www.cam.cornell.edu). In addition, Field requirements in mathematics and its applications can be satisfied by courses, offered by any department, that contain substantial mathematical content in the specified Focal Area.

Examples of Recommended Courses in the Focal Areas

In addition to the courses listed below, the field requirements for eight courses can be satisfied in part by courses, offered by any department, that contain substantial mathematical content in the areas specified below.

(a) Computational Methods, e.g.,
CS 621, 622, 624;
MAE 736;
Math 425

(b) Mathematical Analysis, e.g.,
Math 611, 612, 621, 622 (not both 611 and 621);

(c) Differential Equations and Dynamical Systems, e.g.,
Chem. Eng. 753;
Math 617, 618, 619, 620, 628, Math/T& AM 717/776;
T& AM 612, 613, 671, 675.

(d) Stochastic Methods (Probability, Stochastic Processes, Statistics, Machine Learning, Signal and Image Processing, etc.) e.g.,
Math 671, 672, 674, 774,
BTRY/STBTRY/BSCB 682, 717 (note: most 600-level courses not suitable)
ILRST 613, 614, 615, 712, 713, 714, 715, 717;
ORIE 650, 651, 662, 670, 671, 677;
ECE 548, 562, 565, 577.

(e) Discrete Mathematics and Optimization, e.g.,
Math 441, 442;
ORIE 625, 630, 631, 632, 634, 635, 636;

(f) Algorithms and Complexity, e.g.,
CS 681, 682, 683, 684.

(g) Algebra and Logic, e.g.,
CS 686;
Math 631, 632, 634, 649, 681, 788

Updated February 21, 2003.