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Graduate PhD Program

Program of Study

The Department of Mathematics offers a program leading to the degree of Doctor of Philosophy.

The PhD program is an intensive course of study designed for the full-time student planning a career in research and teaching at the university level or in quantitative research and development in industry or government. Admission is limited and highly selective. Successful applicants have typically pursued an undergraduate major in mathematics.

In the first year of PhD studies, students must pass written examinations in the areas of the basic first-year courses. In the second year an oral examination on two selected topics must be passed. Students must also acquire a reading knowledge of one language, either French, German, or Russian. Subsequent years are devoted to seminars, research, and the preparation of a dissertation. Students are required to serve as teaching assistants or instructors for four years beginning with the second year of study. Those contemplating academic careers are strongly encouraged to serve as instructors for at least two semesters. En route to the Ph.D., students will earn three degrees: a Master of Arts (after year one), a Master of Philosophy (after year four), and the Doctorate of Philosophy (after a successful thesis defense).

There are also allied doctoral programs in statistics, computer science, and applied mathematics.

Research Facilities

The Mathematics Department is housed in a comfortable building containing an excellent mathematics library, computing and printing facilities, faculty and graduate student offices, a lounge for tea and conversation, and numerous seminar and lecture rooms.

Financial Aid

The department has a broad fellowship program designed to help qualified students achieve the PhD degree in the shortest practicable time. Each student admitted to the PhD program is appointed a fellow in the Department of Mathematics for a period of five years, contingent on good progress. A fellow receives a stipend for the nine-month academic year and is exempt from payment of tuition.

A fellow in the Department of Mathematics may hold a fellowship from a source outside Columbia University. When not prohibited by the terms of the outside fellowship, the University supplements the outside stipend to bring it up to the level of the University fellowship. Candidates for admission are urged to apply for fellowships for which they are eligible (e.g., National Science Foundation, Ford and Hertz Foundations).

Cost of Study

All students admitted to the PhD program become fellows in the Department and are exempt from tuition. Students may be responsible for certain fees: a student activity fee and transcript fee.

Living and Housing Costs

Students in the PhD program are entitled to affordable University housing near the Department in Morningside Heights. This makes it possible to live comfortably in the University neighborhood on the fellowship stipend.

Student Group

The PhD program in mathematics has an enrollment of approximately 60 students. Typically, 10-12 students enter each year. While students come from all over the world, they form an intellectually cohesive and socially supportive group.


New York City is America’s major center of culture. Columbia University’s remarkably pleasant and sheltered campus, near the Hudson River and Riverside Park, is situated within 20-30 minutes of Lincoln Center, Broadway theaters, Greenwich Village, and major museums. Most department members live within a short walk of the University.

The University

Since receiving its charter from King George II in 1754, Columbia University has played an eminent role in American education. In addition to its various faculties and professional schools (such as Engineering, Law, and Medicine), the University has close ties with nearby museums, schools of music and theology, the United Nations, and the city government.


The application deadline is December 15th for admission the following September.  Applicants must submit their undergraduate transcripts, three letters of recommendation, a curriculum vitae and statement of purpose, and scores from the GRE General Test and Mathematics Subject Test. Students whose undergraduate degree was not from an English-speaking country must also submit scores from the TOEFL or IELTS.  Applications must be filed online.

Correspondence and Information

Information for Prospective Doctoral Students

For information on the application process:

Graduate School of Arts and Sciences
Columbia University
Office of Student Affairs
107 Low Library, MC 4304
New York, NY 10027

For information on the department and program:

Mikhail Khovanov
Director of Graduate Studies
Department of Mathematics
Columbia University
2990 Broadway
509 Mathematics, MC 4406
New York, NY 10027

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