### Ph.D. in Mathematics - 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 mathematics must include:

- Three of the year sequences chosen from

MATH 6215-6216 (Real Analysis),

MATH 6417-6418 (Functional Analysis),

MATH 6330-6331 (Differential Equations),

MATH 6351-6352 (Complex Analysis),

MATH 6585-6586 (Topology). - (a) Two other 6000 level courses,

(b) an algebra course requiring MATH 5105 as prerequisite, and

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

Courses used to fulfill requirements 2 (b) and (c) can also be used to satisfy requirements 1 and 2 (a).

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 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**. A reading knowledge of one modern foreign language (usually French, German, or Russian) is required for the Ph.D. degree. Please see the **Graduate Catalog** for more details.

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

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

- Three of the year sequences chosen from:

MATH 6215-6216 (Real Analysis),

MATH 6417-6418 (Functional Analysis),

MATH 6330-6331 (Differential Equations),

MATH 6351-6352 (Complex Analysis),

MATH 6585-6586 (Topology). - (a) Two other 6000 level courses,

(b) an algebra course requiring MATH 5105 as prerequisite.

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 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**. A reading knowledge of one modern foreign language (usually French, German, or Russian) is required for the Ph.D. degree. Please see the **Graduate Catalog** for more details.

**Ph.D. Language Requirement**

**Ph.D. in Mathematics, Mathematics Emphasis**. Students should demonstrate reading knowledge of one modern foreign language, chosen from French, German, or Russian. Another language may be substituted only if approved by the student's Ph.D. advisory committee. This requirement can be satisfied by either native fluency or a translation examination consisting of successfully translating a mathematics paper, or other mathematics text, from the chosen language into English. The material to be translated shall be chosen by the student's Ph.D. advisory committee. The structure of the translation examination will be three to four hours long with a dictionary, language textbook, and glossary allowed as aids. The use of a computer as an aid will not be allowed, and the examination may not be taken home to be worked on. As stated in the Graduate Catalog, "The foreign language requirement may be met either before or after the comprehensive examination is passed."

The Mathematics & Statistics Department shall establish a "Ph.D. Language Committee" to aid the advisory committees in administering either of the above requirements. This committee shall consist of four departmental faculty members, at least one of whom shall be a statistician, who are members of the Graduate Faculty, elected by the department to two-year terms, and members may succeed themselves. The Ph.D. Language Committee shall aid the advisory committees as needed in choosing material to be translated, grading the translations, and help statistics students' advisory committees with details related to the programming competency requirement.

(Revised 8/18/15)