Stanford University

PhD Program

During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations. These two exams test the student’s breadth of knowledge in algebra and real analysis.

In addition, students must satisfactorily complete a course sequence during their first or second year. This can be fulfilled in one of the following ways:

  • Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry
  • Math 216A, B, & C: Introduction to Algebraic Geometry
  • Math 230A, B, & C: Theory of Probability
  • Another full year course sequence (Autumn, Winter, & Spring) in a single subject approved in advance by the Director of Graduate Studies

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will sit for their Area Examination, which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.