涩里番下载

The requirements for the Ph.D. are summarized below. For more details and the complete requirements, see聽Official Requirements and Guidelines for the Ph.D. in Mathematics.

Residency

A student must be in residence in the Mathematics department at 涩里番下载 for at least two consecutive semesters of one academic year with full-time registration. Full-time is two courses per semester.

Coursework

Students must complete at least 50 credit hours at the graduate level, including the first-year courses in Algebra, Geometry/Topology, Real and Complex Analysis, and second-year courses such as Number Theory, Representation Theory, Geometry, or Topology. Very well-prepared students may be allowed to skip some or all of the first-year graduate courses and proceed directly to advanced study.

Examinations

There are three types of exams:

• Qualifying, Language, and Doctoral Comprehensive Qualifying exams:

After the first year, students take two of the three qualifying exams in Real and Complex Analysis, Algebra, and Topology. Well-prepared students may take these exams earlier, upon consultation with the Assistant Chair, Graduate Programs.

• Language Exam:

This exam consists of translating mathematics from French or German into English.

• Doctoral Comprehensive Exam

During the third year, the student requests that a faculty member serve as their research advisor. Upon agreement of the faculty member, the student forms a comprehensive examination committee, consisting of the research advisor and at least two other members. The doctoral comprehensive exam consists of a research topic and one secondary topic, chosen by the student in consultation with the comprehensive examination committee. Typically these are based on topics courses of independent study completed by the student in the second and third years.

Teaching

In addition to their responsibilities as teaching assistants and teaching fellows, students participate in the Teaching Seminar during their first two years.

Dissertation

Upon satisfactory performance in exams, the student is admitted to candidacy for the Ph.D. and begins research for the doctoral dissertation. The dissertation must consist of original scholarly work. The doctoral committee will read and evaluate the completed dissertation and conduct an oral examination, at which the dissertation is defended in a public meeting.