# PhD Requirements

Mathematics PhD candidates must show satisfactory work in Algebra (110.601-602), Real Variables (110.605), Complex Variables (110.607), and one additional mathematics graduate course in their first year. The seminars and qualifying exam preparation course cannot be used to fulfill this requirement. This first-year algebra and analysis requirement can be satisfied by passing the corresponding written qualifying exam in September of the first year; these students must complete at least two courses each semester. In addition, the candidates must take Algebraic Topology (110.615) and Riemannian Geometry (110.645) by their second year. Students having sufficient background can substitute an advanced topology course for 110.615, or an advanced geometry course for 110.645 with the permission of the instructor.

Candidates must pass written qualifying exams by the beginning of their second year in Analysis (Real & Complex) and in Algebra. Exams are scheduled for September and May of each academic year, and the dates are announced well in advance.

Candidates must show satisfactory work in at least two mathematics graduate courses each semester of their second year, and if they have not passed their oral qualifying exam, in the first semester of their third year.

Candidates must pass an oral qualifying examination in the student’s chosen area of research by April 10 of the third year. The topics of the exam are chosen in consultation with the faculty member who has agreed (provisionally) to be the student’s thesis adviser, who will also be involved in administering the exam.

There is no longer a math department foreign language requirement. With the vast majority of articles written nowadays in English, the importance of having the capability of reading another language has diminished. However, important earlier literature in certain areas of mathematics may be written in French, German, or Russian; moreover, some articles are still being written in French. It is now at the discretion of the student’s thesis adviser whether the student needs to learn to read mathematics in another language.

Candidates must produce a written dissertation based upon independent and original research.

Candidates will have teaching experience in mathematics as a teaching assistant for undergraduate courses. The student will be under the supervision of both the faculty member teaching the course and the director of undergraduate studies. First-year students are given a reduced TA workload in the spring semester, in preparation for the qualifying exams.

After completion of the thesis research, the student will defend the dissertation by means of the Graduate Board Oral exam. **The exam must be held at least three weeks before the ****Graduate Board**** deadline the candidate wishes to meet**.

#### The MA Degree

Although the Department of Mathematics does not admit students seeking a terminal MA degree, students in the PhD program may earn an MA degree.

MA candidates must complete:

- Four graduate courses given by the Hopkins Department of Mathematics
- Two additional courses at the graduate or 400 level, other than 110.401, 110.405 and 110.415, given by the Hopkins Department of Mathematics, or with the permission of the graduate program director, graduate mathematics courses given by other departments or universities.

All courses used to satisfy the requirements must be completed with a grade of B- or better. (Advanced graduate courses completed with a grade of P can also be used to satisfy the requirements.)