### Coursework Requirements

#### I. Credit requirements

- The Graduate School requires Ph.D students to complete a minimum of 60 credits beyond the baccalaureate degree.
- A minimum of 12 of these credits must come from Math 899, Dissertation preparation.
- Students must take 12 credits beyond the courses covering their qualifying exams and comprehensive exams for breadth.

#### II. Typical coursework

Most but not all students will take the following courses as a Ph.D student.

- Four courses on material covered by the qualifying exam: 2 year-long sequences (12 crs.).
- Six courses on material covered by comprehensive exam: 3 year-long sequences (18 crs.).
- Four courses for breadth (12 crs.).
- At most two further elective courses (0 - 6 crs.).
- 12 - 18 credits of Math 899.
- Math 791 (Pedagogy I) and Math 792 (Pedagogy II), 1 credit each. It is necessary for students to pass these courses in order to qualify to be the instructor of record for lower division courses (e.g., Math 111, 115, 122, 170) in the Department.

### Examination Requirements

#### 1. Qualifying Exam

##### A. Structure

The Ph.D. qualifying exam consists of two four-hour written exams. The Department offers these exams two times per year, once in August, and once in January.

##### B. Coverage

Students take exams on two year-long course sequences:

- Analysis: Math 703 and 704.
- either of

a. Algebra: Math 701 and 702.

b. Applied and Computational Math: Math 708 and 709.

##### C. Rules

- Number of attempts. A student gets at most two attempts per exam on two exams. (A student does not get two attempts on each of the three exams.)
- Standard exam schedule.
- A student’s first attempt on both exams should take place on or before August of the start of the second year.
- A student’s second attempt at one or both exams, if necessary, must take place on or before January of the second year.
- A student with exceptional preparation may make a first attempt on one or both exams on entrance (August of the first year) or in January of the first year.
- A student may attempt the qualifying exam without having taken corresponding

preparatory coursework.

- A student must pass both exams within two years of admission to the Ph.D program. Hence, the last opportunity to take exams is January of the second year.
- The exams are uncoupled. If a student chooses to attempt only one exam in a given exam period, the student does not forfeit an attempt on the exam that they did not take.

#### 2. Comprehensive Exam

A student’s comprehensive exam consists of written and oral parts. The student’s Comprehensive Exam Committee oversees all aspects of the student’s exam.

**A. Structure**

- The written part consists of 3 four-hour exams. The exams are offered two times per year, once in August, and once in January.
- The oral part is scheduled for two hours.

**B. Coverage**

- Each of the 3 four-hour written exams is based on a two-course sequence. Therefore, the written part covers material from six courses or three two-course sequences.
- The oral part may cover topics from the written part and from the student's research area not covered by the written part.

**C. Rules**

- Committee: The Comprehensive Exam Committee must have at least four faculty, exactly one of which must be from an external unit.
- Number of attempts. A student gets at most two attempts to pass the comprehensive exam.
- Standard exam schedule.
- A student's first attempt must take place no later than January of the third year. Typically, the first attempt takes place in August after the second year.
- A student's second attempt must occur within one year of the first attempt.

### Dissertation requirement

The doctoral dissertation is the ultimate requirement for a student to earn the Ph.D degree. The dissertation should be original work which contributes significantly to the body of current research and which has the potential for publication in a reputable journal. The Dissertation Committee has the same requirements as the Comprehensive Exam Committee. While these committees do not have to be the same, they frequently are. The final requirement is the student's defense of the dissertation in an examination before the Dissertation Committee.