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 External 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 sciences 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. 

No later than two weeks before the end of the first semester of study (two weeks before the end of the second semester for part-time students), a student is required to submit a formal Plan of Study leading to the Ph.D. degree to the Graduate Program Committee for review and approval. The Plan of Study may subsequently be modified with review by the Graduate Program Committee. International students may be subject to additional documentation of their full-time status as part of their visa requirements. Please consult WPI's International Student Handbook for up-to-date guidance. 

Extra-Departmental Studies Requirement

A student must complete at least six semester hours of courses, at the 500 level or higher, in WPI departments other than Mathematical Sciences. Cross-listed courses can be counted toward meeting the extra departmental studies requirement. The student's advisor must approve the choice of cross-listed courses. 

General Comprehensive Examination

A student must pass the general comprehensive examination (GCE) 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 consists of two three-hour exams. One exam is on real analysis, based on MA 503, and the other is on linear algebra, based on MA 502. The GCE is offered three times a year, in January, May, and August. Students must pass both exams by the end of January of their second year if they enter in the fall, or by the end of May of their second year if they enter in the spring.

Mathematical Sciences Ph.D. Project

PhD students have the option of earning up to nine Research Preparation credits by completing an external project. The purposes of the external 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 participating in an external project are required to work with a sponsor external to the department and are encouraged to find sponsors affiliated with academia, business, industry, or government. 

The policies governing the project are as follows:

• Limited to a maximum of 9 credit hours.
• Must be conducted under the supervision of a project advisor who is a member of the Mathematical Sciences faculty.
• A project proposal that outlines the nature, scope, and expected outcomes of the project must be approved prior to the start of the project by the project advisor, the external sponsor, and the Graduate Program Committee.
• The project will culminate with a report and oral presentation.

Ph.D. Preliminary Examination

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 examination is given in two parts, a written part followed by an oral part, and covers subject matter in three areas determined by the student's preliminary examination committee. The preliminary examination is intended to test a student's overall breadth in advanced mathematical topics as well as knowledge of their area of specialization, and three areas should be chosen accordingly.

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. At least two months before the proposed date for the written exam, the student must request the examination with the Mathematical Sciences department by submitting syllabi covering all three topics for the examination. All three syllabi must be sent at the same time. The student must work with different faculty member(s) for each of the three topics. A student who passes the examination is considered a dissertator and is allowed to register for dissertation credits. 

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 that must be approved by the departmental Graduate Program Committee, including at least one recognized expert external to the department. At least four months prior to the defense 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. A student's dissertation committee, with the dissertation advisor acting as chairperson, determines by a majority vote whether a 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 no longer be part of the Ph.D. program as of the following semester.