Requirements for Ph.D. Candidacy
Within three semesters (18 months) of arrival, each PhD student is expected to meet the requirements for PhD candidacy. These comprise
- Qualifying exams
- Coursework requirement
Qualifying examinations are offered twice a year: once in August, before the beginning of the Fall semester, and once in May, after the end of the Spring semester. Because of the 18-month rule above, students have three opportunities to pass each exam (including an opportunity to do so immediately on arrival).
These examinations are focused on two main subjects: Algebra and Analysis.
The Algebra exam contains three parts:
Part A is mandatory for all students. Parts B and C are alternatives to one another. Each part of the exam will contain four questions, and correct answers to two of these four will ensure a pass on that part.
To pass the Algebra exam, you must either pass Part A and Part B, or Part A and Part C.
Similarly, the Analysis exam contains three parts:
Each part will contain four questions, and correct answers to two of these four will ensure a pass on that part. To pass the Analysis exam, you must either pass Part A and Part B, or Part A and Part C.
The qualifying exams in Algebra and in Analysis are offered on different days, the same week. On the day of each exam, Part A is given in the morning, while parts B and C are given in the afternoon. It is possible for a student to pass Part A in one attempt, and Part B or C at a different date. For example, one may pass Algebra A in August upon arrival, then pass Algebra B and Parts A and C of Analysis in May the following year.
The subjects of the exams are given in the table below, which also shows the number of the graduate-level course that prepares for that part of the exam.
|Algebra A||Linear Algebra||Math 535||Sample Problems|
|Algebra B||Abstract Algebra||Math 536||Sample Problems|
|Algebra C||Applied Algebra||Math 524||Sample Problems|
|Analysis A||Real Analysis||Math 501||Sample Problems|
|Analysis B||Complex Analysis||Math 502||Sample Problems|
|Analysis C||Functional Analysis||Math 503||Sample Problems|
Clicking on the links in the above table will take you to a detailed syllabus for the exam and to a list of sample problems produced by the Qualifying Exam Board. These sample problems are similar to those that will appear on the new qualifying exams themselves. The following link is a list of qualifying exams for the past years.