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

1. Qualifying exams
2. Coursework requirement

The department has introduced a new system of qualifying exams beginning in August 2008.  Former qualifying exam papers and materials are still available for information, but do not directly relate to the new system.

QUALIFYING EXAMS

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: linear algebra (vector spaces, linear transformations)

Part B: abstract algebra (theory of groups, rings)

Part C: applied algebra (numerical linear algebra)

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:

Part A: real analysis (Lebesgue measure theory)

Part B: complex analysis

Part C: applied analysis (functional analysis with applications to linear differential equations)

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.

Past Qualifying Exams

COURSEWORK REQUIREMENT

In addition to passing qualifying examinations, a student must take and pass at least 18 credits of 500-level mathematics courses in order to be admitted to candidacy.  No more than 12 credits towards this requirement may come from the six courses Math 501, 502, 503, 524, 535, 536 listed above.

INDIVIDUAL PLAN OF STUDY

In consultation with the Director of Graduate Studies or the Assistant Director of Graduate Studies, you should develop and file an Individual Plan of Study (IPS) form early in your first semester, which describes your personal plan for meeting these requirements.  We want every student entering our PhD program to be successful, and setting clear personal objectives and regularly reviewing them with your mentor will allow us to help you achieve this.