# Degree Requirements

## Requirements for the MA Degree

For the Statistics Track, go to the Statistics Program website.

### Coursework

Ordinarily, eight semester courses in mathematics are required for the MA degree. At most, two courses may be transferred from another institution; in this case, the courses should correspond to Boston University courses.

Only courses at the 500 level or above count for the MA degree. Courses numbered 500–599 are aimed at both advanced undergraduate and beginning graduate students, while courses numbered above 700 are designed primarily for graduate students. While there is no formal requirement concerning the number of 700-level courses a graduate student must take, the qualifying examination requirement (see below) necessitates a certain amount of advanced coursework.

### Examinations

The examination requirements differ for students in Pure & Applied Mathematics and for students in Probability & Statistics. Students must fulfill the requirements for the program they are admitted to, although students in Probability may elect either system. A detailed description of the examinations is available here.

For students in Pure & Applied Mathematics, a preliminary exam is given in the spring of each year.

Some previous sample exams are available:

- 2003 (analysis)
- 2003 (algebra)
- 2004 (analysis)
- 2004 (algebra)
- 2005 (analysis)
- 2005 (algebra)
- 2006 (analysis)
- 2006 (algebra)
- 2007 (algebra)
- 2007 (analysis)
- 2008 (algebra)
- 2008 (analysis)
- 2009 (algebra)
- 2009 (analysis)
- 2010 (algebra)
- 2010 (analysis)
- 2011 (algebra)
- 2011 (analysis)
- 2012 (algebra)
- 2012 (analysis)
- 2013 (algebra)
- 2013 (analysis)
- 2014 (algebra)
- 2014 (analysis)
- 2015 (algebra)
- 2015 (analysis)
- 2016 (algebra)
- 2016 (algebra solutions)

- 2016 (analysis)
- 2016 (analysis solutions)

- 2017 (algebra)
- 2017 (algebra solutions)

- 2017 (analysis)
- 2017 (analysis solutions)

- 2018 (algebra)
- 2018 (algebra solutions)

- 2018 (analysis)
- 2018 (analysis solutions)

- 2019 (algebra)
- 2019 (algebra solutions)

- 2019 (analysis)
- 2019 (analysis solutions)

The exam tests the student’s knowledge of core material in undergraduate mathematics, and it is expected that every student will take the exam during the first year. The exam consists of two 3-hour sections, one covering advanced calculus, differential equations, and analysis, and the other covering linear algebra and abstract algebra. Students must demonstrate a thorough understanding of these topics to pass this exam at the MA level.

## Requirements for the PhD Degree

For the Statistics Track, go to the Statistics Program website.

### Coursework

A PhD student must complete 16 courses, with a grade of “B-” or higher, for the PhD. At most, four of the courses may be transferred from other institutions. If the PhD student is admitted to the post-MA PhD program, then eight courses are usually required.

### Foreign Languages

PhD students must give evidence of sufficient mastery of at least one foreign language (usually French or German) to enable them to use that language effectively in their areas of special study. Consult with the Director of Graduate Studies for dates and times at which the language examination is offered.

### Preliminary Examination

PhD students in Pure & Applied Mathematics must also take the MA Preliminary Exam and pass it at the PhD level.

### Qualifying Examinations

The Qualifying Examination system differs for students in Pure & Applied Mathematics and for students in Probability & Statistics. In any case, each student must pass a Qualifying Examination to certify that he/she is ready to begin work on a dissertation.

For students in Pure & Applied Mathematics, the oral examination is three hours long and covers two areas of graduate study as well as a specialized topic within one of these areas. The examination in each of the two main areas is based on at least a full year of 700-level coursework. Currently, the department offers examinations in the following areas: algebra, algebraic geometry, applied mathematics, analysis, differential equations, differential geometry, differential and algebraic topology, dynamical systems, functional analysis, number theory, probability, logic, partial differential equations, and numerical analysis. To organize a Qualifying Examination, the student is assigned a committee of three faculty members who work in the two chosen areas to be on his/her examination committee; the student and the committee then decide on a specialized topic. The Qualifying Examination must be completed within the first three years of the student’s graduate-level studies.

A detailed handout on the Qualifying Examination is given to entering graduate students.

### Dissertation

The dissertation is the major requirement for a PhD student. After the student has completed all coursework, the Director of Graduate Studies, in consultation with the student, selects a three-member dissertation committee. One member of this committee is designated by the Director of Graduate Studies as the Major Advisor for the student. Once completed, the dissertation must be defended in an oral examination conducted by at least five members of the department.

### Satisfactory Progress Toward the Degree

Upon entering the Graduate Program, each student should consult the Director of Graduate Studies. An advisor will be assigned to each student depending on his/her initial interests; this choice can be changed later. The graduate advisor, who will be able to guide the student through the course selection and possible directed study, should be consulted often. Indeed, the department considers it important that each student progress in a timely manner toward the degree. Each MA student must have completed the examination by the end of his/her second year in the program, while a PhD student must have completed the qualifying examination by the third year. Students entering the PhD program with an MA degree must have completed the qualifying examination by October of the second year. Failure to meet these deadlines may jeopardize financial aid. Some flexibility in the deadlines is possible upon petition to the graduate committee in cases of inadequate preparation.

### Residency

Students must complete all of the requirements for a PhD within seven years of enrolling in the department. This total time limit is set by the Graduate School. Students needing extra time must petition the Graduate School. Also, financial aid is not guaranteed after the student’s fifth year in the program.