### Ph.D. in Mathematics - Computational and Applied Mathematics Emphasis

The Department of Mathematics and Statistics has adopted the following course requirements for the Ph.D. degree. Any of these courses may be a part of the M.S. program, since Missouri S&T courses taken for the M.S. degree may be included in the Ph.D. program of studies.

**Important Note:** There are two different sets of requirements below labeled “New Requirements” and “Previous Requirements.” The “New Requirements” must be followed by all students who enter our program on, or after, January 1, 2013. Students who entered our program before this date have the option of choosing to follow either the “New Requirements” or the “Previous Requirements.” All students must satisfy the Ph.D. Language Requirement below.

**New Requirements** (see important note above):

A Ph.D. program with emphasis in computational and applied mathematics must include:

- MATH 6601 (Numerical Analysis) and MATH 6602 (Finite Elements).
- Four of the following courses:

MATH 6108 (Applied Matrix Theory),

MATH 6215-6216 (Real Analysis),

MATH 6417-6418 (Functional Analysis),

MATH 6330-6331 (Differential Equations),

MATH 6351-6352 (Complex Analysis),

MATH 6461-6462 (Harmonic Analysis),

STAT 6841 (Stochastic Processes). - (a) Two other 6000 level courses, and

(b) one of Math 5108, Math 6108, or Math 6417.

If Math 6108 or Math 6417 is used to fulfill requirement 3 (b), then the same course can simultaneously count toward requirements 2 and 3 (a).

The complete set of eight courses is to be chosen by the Ph.D. candidate in accordance with the candidate's research interests; the courses must also be approved by the student's Ph.D. advisory committee. Ph.D. candidates are encouraged to include courses from other departments that align with their research interests.

All students who intend to pursue the Ph.D. degree must take the **Ph.D. Qualifying Examination** within the first few semesters of entering our program. At this time the student also should identify an area of emphasis. A typical program of study for a Ph.D. student in computational and applied mathematics includes at least 72 hours (90 is more common) of graduate work beyond the bachelor's degree, consisting of coursework and research. In addition, there is a **Ph.D. Comprehensive Examination **and the **Ph.D. Thesis Defense**. Demonstrated competence in a computer programming language is required for the Ph.D. degree with emphasis in computational and applied mathematics. Please see the **Graduate Catalog **for more details.

**Previous Requirements** (see important note above):

A Ph.D. program with emphasis in computational and applied mathematics must include:

- MATH 6601 (Numerical Analysis) and MATH 6602 (Finite Elements).
- Four of the following courses:

MATH 6108 (Applied Matrix Theory),

MATH 6215-6216 (Real Analysis),

MATH 6417-6418 (Functional Analysis),

MATH 6330-6331 (Differential Equations),

MATH 6351-6352 (Complex Analysis),

MATH 6461-6462 (Harmonic Analysis),

STAT 6841 (Stochastic Processes). - Two other 6000 level courses.

The complete set of eight courses is to be chosen by the Ph.D. candidate in accordance with the candidate's research interests; the courses must also be approved by the student's Ph.D. advisory committee. Ph.D. candidates are encouraged to include courses from other departments that align with their research interests.

All students who intend to pursue the Ph.D. degree should plan to take the **Ph.D. Qualifying Examination** soon after completing an M.S. program. At this time the student also should identify an area of emphasis. A typical program of study for a Ph.D. student in computational and applied mathematics includes at least 72 hours (90 is more common) of graduate work beyond the bachelor's degree, consisting of coursework and research. In addition, there is a **Ph.D. Comprehensive Examination **and the **Ph.D. Thesis Defense**. Demonstrated competence in a computer programming language is required for the Ph.D. degree with emphasis in computational and applied mathematics. Please see the **Graduate Catalog **for more details.

**Ph.D. Language Requirement**

**Ph.D. in Mathematics, Computational and Applied Mathematics Emphasis**. All students who are doctoral candidates in mathematics with computational and applied mathematics emphasis must show programming competency in one programming language, chosen from C, C++, FORTRAN, Matlab, or another programming language approved by the student's Ph.D. advisory committee, prior to his/her completion of the doctoral degree. This requirement can be satisfied by any one of the following: (1) obtaining a grade of B or better in a semester-long programming course in the programming language, taken for graduate or undergraduate credit, no earlier than six years before the awarding of the Ph.D., (2) successfully completing a programming project of sufficient complexity as determined by the student's Ph.D. advisory committee. A computing component of master's or doctoral research done by the student may satisfy this requirement if approved by the student's Ph.D. advisory committee, (3) earning a grade of B or better in a graduate-level course in computing.

(Revised 8/18/15)