Ph.D. in Mathematical Sciences

The goal of this program is to produce active and creative problem solvers, capable of contributing in academic and industrial environments. One distinguishing feature of this program is an optional Ph.D. project to be completed under the guidance of an external sponsor, e.g. industry or a national research center. The intention of this project is to connect theoretical knowledge with relevant applications and to improve skills in applying and communicating mathematics. 

Admission Requirements

Applicants are recommended to take the GRE Mathematics Subject Test.

Degree Requirements

The course of study leading to the doctor of philosophy in mathematical science requires the completion of at least 90 credit hours beyond the bachelor’s degree or at least 60 credit hours beyond the master’s degree, as follows:

A brief description of other Ph.D. program requirements follows below. For further details, students are advised to consult the PhD Booklet that specifies Program Requirements.  Program Requirements and Administrative Rules for the Department of Mathematical Sciences are available on the Resources Page on the Departmental website and/or can be obtained from departmental administrative assistants. 

Within a full-time student’s first semester of study (second semester for part-time students), a Plan of Study leading to the Ph.D. degree must be submitted to the departmental Graduate Program Committee for review and approval. The Plan of Study may subsequently be modified with review by the departmental Graduate Program Committee.

Extra-Departmental Studies Requirement

A student must complete at least six semester hours of courses, 500 level or higher, in WPI departments other than the Mathematical Sciences Department.

General Comprehensive Examination

A student must pass the general comprehensive examination (GCE) in order to become a Ph.D. candidate. The purpose of the GCE is to determine whether a student possesses the fundamental knowledge and skills necessary for study and research at the Ph.D. level. It is a written examination offered three times a year, once each in January, May, and August. A student must pass by January of their second year if they enter in the fall, and May of their second year if they enter in the spring.

Mathematical Sciences Ph.D. Project

A student may complete a Ph.D. project involving a problem originating with a sponsor external to the department. The purposes of the project are to broaden perspectives on the relevance and applications of mathematics and to improve skills in communicating mathematics and formulating and solving mathematical problems. Students are encouraged to work with industrial sponsors on problems involving applications of the mathematical sciences. Each Ph.D. project requires prior approval by the project advisor, the external sponsor, and the departmental Graduate Program Committee.

Ph.D. Preliminary Examination

Successful completion of the preliminary examination is required before a student can register for dissertation research credits. The purpose of the preliminary examination is to determine whether a student’s understanding of advanced areas of mathematics is adequate to conduct independent research and successfully complete a dissertation. The preliminary examination consists of both written and oral parts. A full-time student must make the first attempt by the end of his or her third year (sixth year for part-time students) in the Ph.D. program.

Ph.D. Dissertation

The Ph.D. dissertation is a significant work of original research conducted under the supervision of a dissertation advisor, who is normally a member of the departmental faculty. The dissertation advisor chairs the student’s dissertation committee, which consists of at least five members, including one recognized expert external to the department, and which must be approved by the departmental Graduate Program Committee. At least six months prior to completion of the dissertation, a student must submit a written dissertation proposal and present a public seminar on the research plan described in the proposal. The proposal must be approved by the dissertation committee. Upon completion of the dissertation and other program requirements, the student presents the dissertation to the dissertation committee and to the general community in a public oral defense. The dissertation committee determines whether the dissertation is acceptable.  

Unsatisfactory Progress

If the aforementioned milestones are not met, then the student must petition the graduate program committee to request extra time to meet the requirements or the student will be no longer be part of the Ph.D. program as of the following semester.