# Information about the MA and PhD Programs

Here we provide information about admissions, financial aid, and degree requirements both in Pure and Applied Mathematics and in Probability and Statistics at Boston University. Please browse the Department’s home page for the list of faculty and their research interests, the list of select faculty publications, the list of recent books by faculty members, and the lists of graduate courses in mathematics and in statistics.

Prospective students should have the equivalent of an undergraduate degree in Pure or Applied Mathematics and prospective Statistics students should have a substantial undergraduate background in statistics; certain intermediate-level courses may be taken at Boston University before the student enrolls in graduate courses. The Graduate School requires at least three letters of recommendation from faculty members familiar with the student’s ability in mathematics, transcripts, as well as scores from both the aptitude and advanced mathematics Graduate Record Exams. A complete application is described a the Graduate School website.

## Financial Aid

The main source of financial aid for graduate students in the Department is the Teaching Fellowship. These awards carry a stipend as well as tuition remission for six courses per year. Teaching Fellows are required to assist a faculty member who is teaching a large lecture section of an introductory mathematics course. Generally, the Teaching Fellow is responsible for conducting a number of discussion sections consisting of approximately twenty-five students each, as well as for holding office hours and assisting with grading. The Teaching Fellowship usually entails about twenty hours of work per week. For that reason, Teaching Fellows enroll in at most three courses per semester. A Teaching Fellow Seminar is conducted to help new Teaching Fellows develop as instructors and to promote the continuing development of experienced Teaching Fellows.

Other sources of financial aid include University Fellowships and Research Assistantships. The University Fellowships are one-year awards for outstanding students and are service-free. They carry stipends plus full tuition remission. Students do not apply for these fellowships.

Regular reviews of the performance of Teaching Fellows and Research Assistants in their duties as well as their course work are conducted by members of the Graduate Committee.

## Requirements for the M.A. Degree

### For Statistics Track go to

**Course Work.**

Ordinarily, eight semester courses in mathematics are required for the M.A. 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 M.A. 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 course work.

**Examinations. **

The examination requirements differ for students in Pure and Applied Mathematics and for students in Probability and 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 and 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)

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 three-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 M.A. level.

## ** **Requirements for the Ph.D. Degree

### For Statistics Track go to

**Course Work.**

A Ph.D. student must complete sixteen courses for the Ph.D. At most four of the courses may be transferred from other institutions. If the Ph.D. student is admitted to the post MA PhD program, then eight courses are usually required.

**Foreign Languages.**

Ph.D. 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.**

Ph.D. students in Pure and Applied Mathematics must also take the M.A. Preliminary Exam and pass it at the Ph.D level.

**Qualifying Examinations.**

The Qualifying Examination system differs for students in Pure and Applied Mathematics and for students in Probability and 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 and 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 course work. 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 Ph.D. student. After the student has completed all course work, 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 M.A. student must have completed the examination by the end of his/her second year in the program, while a Ph.D. student must have completed the qualifying examination by the third year. Students entering the Ph.D. program with an M.A. 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 Ph.D. 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 students fifth year in the program.