# PhD in Mathematics

**TRACKS**

- Pure Mathematics
- Discrete Mathematics
- Probability/Statistics

**QUALIFYING EXAMS**

Qualifying exam sessions are given once in spring and once in fall. Students will be required to pass four qualifying exams: algebra 1, analysis 1, and 2 other exams. A qualifying exam may be taken twice by any student. Additional attempts may be allowed at the discretion of the graduate committee with permission from the graduate dean in the College of Science. Two qualifying exams should be passed no later than the end of the second year and all four by the end of the third year.

**TEACHING REQUIREMENT**

Some teaching experience is required while in the program. Students must attend university-led TA training at the start of the program; attend a one semester TA training course conducted by faculty from the Department of Mathematics teaching committee; spend one semester shadowing faculty in the undergraduate classroom; perform recitations and grading for the undergraduate course they are shadowing; and become a teacher of record for the undergraduate course they have been shadowing.

**RESIDENCE REQUIREMENT**

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

**COURSE REQUIREMENTS**

**Review the Curriculum and Graduation Requirements here**

Students entering with a bachelor’s degree are required to take 64 credits of course work divided between foundational and advanced offerings. Students entering the program will be allowed to place out of some (possibly all) of the eight basic-level courses; the graduate coordinator together with the first-year graduate advisor will determine the allowable course substitutions and will advise the student which foundational courses to take. Students may satisfy requirements for MATH 5111 Algebra 1 and MATH 5101 Analysis 1 by taking qualifying exams in algebra 1 and in analysis 1 at the start of the program. Students may satisfy foundational course requirements if they demonstrate proficiency by passing an assessment exam in the course at the beginning of the semester or by demonstrating that they have taken a similar course and have adequate knowledge of the course material (syllabus and transcript are required; a brief oral examination is also required in that case). Academic advising will happen just before the start of each term and during the add/drop period in order to plan a student’s course registration for the term. A complete listing of foundational and advanced courses is available from the Department of Mathematics and the graduate dean’s office. Students are not permitted to register for more than two “readings” courses and three “topics” courses for credit toward the degree without explicit permission from the graduate dean. A minimum GPA of 3.000 is required for degree conferral.

**DOCTORAL CANDIDACY**

PhD candidacy is reached when all of the following conditions are met:

- Completion of eight advanced courses
- Identification of an unsolved research problem
- Successful passing of four qualifying exams
- Assignment of PhD supervisor and creation of a one-page initial plan
- Completion of a three-page plan of research
- Completion of a ten-page progress report and a one-hour defense of proposal, presented to supervisor and three faculty members of graduate committee

**DISSERTATION REQUIREMENT**

Each candidate 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 dissertation supervisor within two years after joining the PhD program. The department views 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 dissertation 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 dissertation 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 advisor, who should be familiar with the student’s progress in finding a dissertation supervisor. The dissertation 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. Students must enroll in Dissertation or Dissertation Continuation while fulfilling the dissertation requirements. - Stage 2 (Dissertation Defense):

The final oral examination on the dissertation is held in accordance with university regulations and given by a dissertation committee of four faculty members (three from the university, including the supervisor, and one from outside Northeastern University). The dissertation supervisor should propose this dissertation committee to the graduate committee for its approval at least one month before the PhD dissertation defense.