Doctor of Philosophy

Total: 32 semester hours

The Doctor of Philosophy degree is awarded to candidates who show evidence of high scholastic attainment and research ability in their major field.

Areas of Specialization

  • Algebra, Geometry/Topology, Geometric Analysis/PDE, Probability/Statistics, Combinatorics.

Course Requirements

  • A total of eight 4-semester-hour courses beyond MS degree and two PhD dissertation courses leading to a dissertation topic are required. Two of the eight courses must be in a minor specialty, which is different from the thesis area. Any master’s level course which has not previously been taken must be completed by the end of the first year in the program. The 2 PhD thesis courses must be completed by the third year in the program. Candidates must also satisfy any additional course requirements specified by their thesis adviser. A minimum GPA of 3.000, equivalent to a grade of B, is required for degree qualification. 

Qualifying Exams

  • Qualifying exams are given several times each year—including late January, late April and late September. They cover algebra, analysis, and the student’s specialized field. Students will be given an opportunity to practice on a sample test. Students must pass these exams by May of their second year in the PhD program in order to continue in the program.

Minor Specialty

  • Each doctoral candidate selects some specific mathematical subject of an advanced nature, which must be reasonably unrelated to the topic of the student’s dissertation. The student should render work in this area equivalent to eight semester hours of coursework.

Language Requirement

  • Ability to read and translate mathematical texts and journals in one foreign language must be established by the candidate. The language may be chosen from French, German, and Russian; any other choice requires special approval. Students should notify the chair of the departmental Graduate Committee when they are prepared to be examined on a language. The examination is conducted by a member of the faculty of the Mathematics department.

Teaching Requirement

  • Some teaching experience is required while in the program. This requirement may be satisfied by teaching an undergraduate course or presenting at least two talks in conferences or departmental seminars.

Residence Requirement

  • The residence requirement is satisfied by one year of full-time graduate work or two-year continuous registration for part-time work. 

Doctoral Candidacy

  • Doctoral students must complete a minimum of 32 semester hours (8 Math courses) beyond the Master of Science degree and pass the Qualifying Exams. It is expected that students will pass the Qualifying Exams within one academic year of coursework completion.

Dissertation Requirement

  • Each doctoral student must complete a dissertation that embodies the results of extended research and makes an original contribution to the field. This work should give evidence of the candidate’s ability to carry out independent investigation and interpret in a logical manner the results of the research. There are two stages to this process.

Stage 1: Students in the PhD program must have a thesis supervisor within two years after joining the PhD program. The department would view the failure of a student to find a supervisor within two years of joining the PhD program with concern and considers this sufficient cause to review the student’s status in the PhD program. The process of obtaining a thesis supervisor always involves two choices—the student chooses the supervisor, and the supervisor chooses the student. For this reason, the department does not guarantee a thesis supervisor for every student, but the department recognizes its responsibility to help the student find a satisfactory match. This aid is usually provided by the student’s graduate adviser, who should be familiar with the student’s progress in finding a thesis supervisor. The thesis supervisor guides the student’s further education as well as directs the student’s dissertation. The dissertation itself must represent an original solution of a problem in the chosen area of mathematics that makes a significant contribution to the mathematical knowledge in that area.

Stage 2: The final oral examination on the dissertation is held in accordance with the Graduate School regulations and given by a thesis committee of four faculty members (three from the university, including the supervisor, and one from outside Northeastern University). The thesis supervisor should propose this thesis committee to the Executive Committee for its approval. By the end of the third year in the PhD program, if the student has not succeeded in presenting the PhD thesis, he or she will be required to present the progress made to date and a plan of the remaining work to a committee of three faculty members. The committee evaluates the student’s progress up to that point, and its report is placed in the student’s file.