Education

Harvard University: Arts & Sciences: Mathematics

Category Art and Social Sciences, Doctoral, Harvard University, Mathematical Sciences, Postgraduate, USA
Tags Arts, Harvard University, Mathematics, Sciences

The graduate mathematics program at Harvard is designed for students who hope to become research mathematicians and show definite promise in this direction. Once the student has demonstrated a command of basic mathematical concepts by passing the qualifying examination, the emphasis is on getting to the frontiers of some field by independent reading, advanced courses, and seminars. The Cambridge area is one of the most active centers of mathematics in the world. Harvard, Brandeis, MIT, and Northeastern have an especially close association in mathematics, sharing several seminars and a weekly colloquium.

The PhD Program

The degree of doctor of philosophy is awarded to students who have demonstrated their mastery of the basic techniques of mathematics and their ability to do independent research. The former is tested in the qualifying examination; the latter in the dissertation. The dissertation, however, is the more important of the two.

The qualifying examination is given twice annually, and students are encouraged to take it as soon as possible so that they may begin work towards their theses. Most students pass the exam during their first year. For those who do not pass it on their first attempt, it may be retaken any number of times.

The PhD dissertation is an original treatment of a suitable subject leading to new results, usually written under the guidance of a faculty member. The final manuscript must conform to the requirements described in The Form of the PhD Dissertation, a booklet available from the Registrar’s Office.

Many of the more advanced courses and seminars are designed to lead the student to areas of current research.

The University requires a minimum of two years’ academic residence (16 half-courses). (See The Graduate School of Arts and Sciences Handbook for financial residence requirements.) On the other hand, the PhD usually takes four to five years.

A reading knowledge of two modern languages, French, Italian (if deemed related to the student’s field of study), German, or Russian, is required of PhD candidates. One language requirement must be passed by the end of the second year of graduate study and the other by the end of the third year. Each candidate must also write a “minor dissertation.” This is an original presentation of a standard subject about which the student is ignorant but wishes to learn. It is intended to give the student experience in assimilating and presenting unfamiliar material. The research and writing must be done during a three-week period, soon after the qualifying examination is passed. Each candidate must also participate in the Teaching Apprentice Program and have two semesters of classroom experience of teaching, usually as a teaching fellow.

Applications for transfer from other programs granting PhDs in mathematics are not ruled out, but are discouraged.

AB-AM Degree

Candidates for the AB-AM degree in mathematics must meet both the academic and course requirements for the AB degree in mathematics and for the AM degree in mathematics. A given course can be counted for only one of the two degrees, i.e., one course cannot meet the requirement for the AB degree and then be counted again for the AM degree. See below for the AM requirements. Any undergraduate who wishes to apply for this degree must file an application form for the graduate program in mathematics just as any other student files for graduate work at Harvard. Only students with advanced standing are eligible to apply for this four-year program. Undergraduates taking graduate courses in their third year may bracket those which they wish to apply on their graduate degree.

Requirements for the AM Degree

The master of arts degree is not a prerequisite for the PhD, but is often obtained by students on their way to a doctorate. However, applicants are not accepted for the terminal master of arts in mathematics. The formal requirements are a minimum academic residence of one year, eight half-courses in mathematics at 100 or 200 level, with at least four at the 200 level; a reading knowledge of one of three languages—French, German, or Russian—is also required. (See The Graduate School of Arts and Sciences Handbook for financial residence requirements.)

Financial Aid

All students in the Department of receive substantial financial support during their graduate training. This support may be in the form of grants or teaching fellowships from Harvard, or fellowships and research assistantships from outside organizations such as the National Science Foundation. Students are strongly encouraged to apply for outside awards.

Sources from outside the University support a great many graduate fellowships. In particular, students who are US citizens should investigate the predoctoral fellowship opportunities provided by the Fannie and John Hertz Foundation (Box 5032, Livermore, CA 94551-5032), the National Defense Science and Engineering Graduate Fellowship Program (200 Park Drive, Suite 211, P.O. Box 13444, Research Triangle Park, NC 27709-3444), the National Physical Science Consortium for Minorities and Women (c/o New Mexico State University, O’Loughlin House, University Boulevard, Box 30001, Department 3 NPS Las Cruces, NM 88003-8001), and the National Science Foundation (Washington, DC 20550).

Students without outside support are required to teach as part of their financial aid package. Usually they do not teach in their first year, are a teaching fellow for one half-course (i.e., for a one-semester course) in their second through fourth years, and are a teaching fellow for two half-courses if they stay for a fifth year. Teaching fellows ordinarily teach their own sections of undergraduate calculus, but have a course assistant to help with grading and to teach a problem section. There are a few upper-class tutorials taught by experienced teaching fellows. All students must participate in the Teaching Apprentice Program run in conjunction with the Derek Bok Center for Teaching and Learning before they may teach.

Applications for admission and for scholarships or nonteaching fellowships, together with information regarding admissions procedures, may be obtained by writing directly to the Admissions Office, Harvard Graduate School of Arts and Sciences, Holyoke Center, 3rd floor, 1350 Massachusetts Avenue, Cambridge, MA 02138. We encourage online submission of the application. See https://apply.embark.com/grad/Harvard/GSAS