**Sample curriculum: Ph.D. in Mechanical Engineering and M.S.E. or M.A. in Mathematical Sciences**

Math. Sciences has already formalized a Joint Master's-Doctoral Program: “Graduate students who are Ph.D. candidates in other departments may pursue simultaneously a master's program in Mathematical Sciences with the approval of their doctoral department. Forms for presentation of a proposed program for approval may be obtained from the Student Coordinator in the Mathematical Sciences Departmental Office.”

“Students may elect to work toward the Master of Arts (M.A.) or the Master of Science in Engineering (M.S.E.). Both degrees ordinarily require a minimum of two consecutive semesters of registration as a full-time resident graduate student. To obtain departmental certification for the master's degree the student must: 1.Complete satisfactorily at least 8 one-semester courses of graduate work in a coherent program approved by the faculty advisor. All 600-level and 700-level courses and some 400-level courses in the department are satisfactory for this requirement. Certain courses in other departments are also acceptable. At most 3 courses outside the department may be counted toward the Master's degree requirements. 2.Meet any one of the following three options: (a) Pass one of the five written qualifying examinations. These examinations are given by the Department once annually during the January Intersession; (b) Submit an acceptable research report based on an approved project; (c) Complete satisfactorily 2 additional one-semester graduate courses, as approved by the faculty advisor. 3.Demonstrate a working knowledge of the utilization of computers in the mathematical sciences.” Option (c) could work well for CEAFM-affiliated students with the dual program. For instance:

- 550.420 Introduction to Probability
- 550.426 Introduction to Stochastic Processes
- 550.620 Probability Theory I
- 550.491 Applied Analysis for Engineers and Scientists
- 550.682 Numerical Analysis
- 550.692 Matrix Analysis and Linear Algebra
- 550.723 Markov Chains
- 530.621 Fluid Mechanics I
- 530.625 Turbulence
- 530.639 Scientific Computing

With these (or equivalent set) courses the student can petition the Mathematical Sciences Department for award of a M.S.E. or M.A. degree in Mathematical Sciences.

Completion of Ph.D. thesis in ME requires additional courses according to ME rules.