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Here we provide information about admission, financial aid, and degree requirements both in Pure & Applied Mathematics and in Probability & 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, and scores from both the aptitude and advanced mathematics Graduate Record Exams. A complete application is described on the Graduate School website.

## Ph.D. Program Milestones

The department considers it essential that each student progress in a timely manner towards

the degree. The following are the deadlines for achieving the milestones described in the Degree

Requirements, and constitute the basis for evaluating satisfactory progress towards the Ph.D.

These deadlines are not to be construed as expected times to complete the various milestones,

but rather as upper bounds. In other words, *a student in good standing expecting to complete*

*the degree within the five years of guaranteed funding will meet these milestones by the much*

*earlier target dates indicated below*. Failure to achieve these milestones in a timely manner may

affect financial aid.

- Completion of preliminary exam (post-BA only –
*not required of post-MA admits*)- Target: April of Year 1
- Deadline: April of Year 2

- Selection of dissertation advisor
- Target: Spring of Year 2
- Deadline: End of Year 3

- Completion of qualifying exam
- Target: Spring of Year 2 (post-BA) or Spring of Year 1 (post-MA)
- Deadline: End of Year 3 (post-BA) or end of Year 2 (post-MA)

- Fulfillment of course requirements
- Target: End of Year 3
- Deadline: End of Year 4

- Fulfillment of language requirement
- Target: End of Year 3
- Deadline: End of Year 5

- Completion of dissertation and dissertation defense
- Target: End of Year 5
- Deadline: End of Year 6

## Financial Aid

The main source of financial aid for department graduate students 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 25 students each, as well as for holding office hours and assisting with grading. The Teaching Fellowship usually entails about 20 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 coursework are conducted by members of the Graduate Committee.

GAANN Fellowships in Mathematics & Statistics

The Department of Mathematics & Statistics at Boston University has a grant from the U.S. Department of Education for Graduate Assistance in Areas of National Need (GAANN). This grant provides fellowships to pursue a PhD for qualified graduate students with strong academic records and demonstrated financial need. These fellowships are available to:

- citizens or nationals of the U.S.;
- permanent residents of the U.S.;
- individuals who can provide evidence from the Immigration and Naturalization Service that they are in the United States for other than a temporary purpose with the intention of becoming a permanent resident of the U.S.; or
- citizens of any one of the Freely Associated States (the Federated States of Micronesia, the Republic of the Marshall Islands, and the Republic of Palau).

Individuals with traditionally underrepresented backgrounds are especially encouraged to apply to our program.

A GAANN fellowship includes a stipend of up to $30,000 a year. (The amount of the stipend depends on the student’s financial need as determined by the financial aid officer of the Graduate School of Arts & Science.) The fellowship also includes a full tuition scholarship and a credit of 100 percent of the cost of the Student Health Insurance plan. Assuming satisfactory academic performance and progress to the degree, students will be supported in subsequent years by either another GAANN fellowship, a teaching fellowship, or a research assistantship.

To apply for a GAANN fellowship, the applicant should:

- Submit an application to our PhD program. This application should be submitted to the Office of Admission in the Graduate School of Arts & Sciences. (Please do not send materials directly to the department.)
- Mention an interest in a GAANN fellowship in the personal statement. If the applicant has a background that is traditionally underrepresented, this background should be mentioned as well.

After admission but before the final award of a fellowship, the applicant will be required to provide evidence of financial need by submitting a Free Application for Federal Student Aid (FAFSA).

GAANN fellows will be selected by the GAANN Project Director, the GAANN Steering Committee, the Director of Graduate Studies, and the Graduate Committee based on their eligibility, academic ability, research interests, and compatibility with the department.

The deadline for application is January 15, 2011. For additional information regarding our PhD program, please see the letter to prospective applicants from the Director of Graduate Studies.

## 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)

- 2021 (algebra)
- 2021 (algebra solutions)

- 2021 (analysis)
- 2021 (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

## Department Dissertation Abstracts

- William Basener
- Barry Brent
- Christina Soto-Trevino
- Robert DiSario
- Mark Evans
- Stephanie R Jones
- Kalle Karu
- Alex Kasman
- Szu I Liao
- Georgiy Medvedev
- Carlos Morales
- Gareth Roberts