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Degree Requirements

In addition to the general University requirements stated earlier in this catalog, the student must meet the following requirements:

Course of Study

Each student must follow a plan of study, approved by a faculty adviser, which usually includes three years of course and seminar work. A minimum of 81 graduate credits of course work are required for the degree, at least 60 of which must be in mathematics and the rest may be in closely related fields. Course offered by other programs which are listed under Math as “See Also” may be taken for credit toward the Math degree. A determination regarding other courses not so designated will be made on a case-by-case basis. At least 36 of the 60 credits in mathematics must be in non-introductory courses or seminars.

First Examination

Students should pass their first-year examinations within the first two years of graduate study. When this is not done, notices will be sent informing them that they must complete their first-year examinations by the end of the next academic year in order to maintain their matriculated status. In extraordinary cases, which must be presented in writing to the Executive Officer, additional time may be granted at the discretion of the Executive Officer.

The Mathematics Qualifying (or Preliminary) Examinations are given in six areas. The exams are scheduled twice a year, in September and May. Students must pass three exams (of their choosing) to be considered to have passed the Qualifying exams (also called the "First Examination;" it is listed this way on the transcript.) Students may retake a failed exam once. Exams are graded Pass/Fail. Students must sign up at least three days in advance of any exams that they wish to take so that the proctor will know how many students to expect. Each exam is scheduled for three hours.

Foreign Languages

The candidate must demonstrate ability to read the literature of mathematics in two of the following languages: French, German, and Russian. Substitution of other foreign languages may be permitted in special cases. Students must demonstrate the required proficiency in one of these languages before they complete their second year of study and in the second language before graduation.

Second Examination

After passing the First Examination, the student specializes in some area of advanced mathematics. A faculty committee will be appointed to help the student arrange a program of study in an area of special interest. When this program of study is completed, the student takes an oral examination given by the faculty to determine readiness to pursue dissertation research.


Each student must complete a dissertation embodying the results of original research in mathematics. The thesis is usually written in a field of specialization recommended by the candidate's thesis advisor and approved by the thesis committee. The completed dissertation must be approved by the thesis committee and must be defended at an oral examination.

Timeline to the degree

We expect all students to complete all three parts of the First Examination by the middle of September of their second year. The students should be able to complete 45 credits and reach Level II by the end of the second year.

During the third year students select a mentor who will be willing to chair the Second Examination Committee and assign the topic for the Second Examination. The Second Examination should take place no later than the fourth year. By the end of the fourth year students are expected to complete the coursework and all other requirements for Advancement to Candidacy. In most cases, the Chair of the Second Examination Committee will become the dissertation adviser.

Thesis research is conducted during the fourth, fifth and sixth year and culminates in the defense sometime during this period.