## MS Mathematics Comprehensive Examination: Information

A written Comprehensive exam is required for all MS students. The exam combines three subject exams; see the detailed rules below.

**Sample subject exams in PDF format**

Core:

- algebra (Math 631)
- real analysis (Math 641) (as .tex)
- complex analysis (Math 645)
- topology (Math 651) (as .tex)

Non-core:

- mathematical physics (Math 611/612)
- numerical analysis of differential equations (Math 615) (as .tex)
- numerical linear algebra (Math 614) (as .tex)

**Procedure**

Early each spring, this form will be emailed to all current Math MS students who have not yet passed the comprehensive exam. Each such student must complete this form and return it to the graduate coordinator or the Department Chair.

**Comprehensive Exams for MS students in Mathematics**

These exams consist of three 1.5 hour written exams to be completed within one week. Dates and times will be determined in consultation with students, based on response to this form. MS students in mathematics are required to take these exams as comprehensive exams.

The subjects covered must include at least two of the four core courses (i.e. at least two of: Math 631 Algebra I, Math 641 Analysis I, Math 645 Complex Analysis, Math 651 Topology). The third subject may be chosen from some other 600-level lecture or independent-study course in mathematics. The choice of exam subjects requires the approval of the student’s committee. It is preferred that none of the exams cover courses in which the student is currently enrolled, but the committee has discretion on this. For each core subject, two faculty members will jointly prepare and grade each exam. For non-core subjects, the student’s committee must arrange the preparation and grading of the exam.

The exams will be at most as hard as the written final for the corresponding courses. Students will be given some choice of problems. Certain problems at a prerequisite level to the graduate course in question should be expected.

If the student does not pass two or three of the exams then he or she must wait at least one semester and then retake the entire comprehensive examination (i.e. three exams) again. If a student passes exactly two of the three parts, then the student has one try to retake the remaining part, preferably before the start of the following semester. If the student fails the remaining part then the entire examination must be retaken.

Only one retake of the entire examination is allowed.