# Degree requirements

## Course work

Candidates for the degree of Doctor of Philosophy must satisfy all general requirements of the Graduate School. These include

- Completion of a minimum of 72 hours of graduate credits, including at least 48 hours of course work.
- At least 30 of the course credits must be at the 700 level, and at most 24 may be dissertation credits.
- Completion of at least six (6) graduate credits per semester for students holding 20 hr/week assistantships, or nine (9) graduate credits for students not holding 20 hr/week assistantships, during two consecutive semesters, to meet the Graduate School doctoral residency requirement.

## Required courses

The following courses or their equivalents must be satisfactorily completed for the doctoral degree in mathematics.

### Required Courses for Students in Pure Mathematics

- MATH 713, Abstract and Real Analysis I (3 units),
- MATH 715, Complex Function Theory I (3 units),
- MATH 731, Modern Algebra I (3 units),
- MATH 741, Topology I (3 units).

### Required Course for Students in Applied Mathematics

- MATH 713, Abstract and Real Analysis I (3 units),
- MATH 736, Numerical Linear Algebra (3 units),

and two courses from among

- MATH 705, Applied Functional Analysis (3 units),
- MATH 715, Complex Function Theory (3 units),
- MATH 735 – Advanced Linear Algebra (3 units),
- MATH 751 – Operations Research I (3 units).

### Dissertation credits and approved electives

- MATH 799 – Dissertation (24 credits required)
- Approved electives, based on research interests (optional, up to 21 credits)
- 12 credit maximum of independent studies (optional)

## Electives and transfer of MS coursework

Electives will be approved by the student’s Dissertation Committee. Appropriate courses outside the Department of Mathematics and Statistics may be approved, depending on the student’s research interests.

Students entering with a master’s degree may receive up to 30 credits for previous course work (excluding thesis credits), and these credits may satisfy some course requirements with the approval of the Graduate Director.

## Qualifying exams

After the 1^{st} year, and ideally by the end of their 2^{nd} year, but no later than by the end of their 3^{rd} year, every student must pass three written Qualifying Exams. The purpose of the Qualifying Exams is to verify that the student has acquired the necessary general knowledge to serve as the basis for her/his dissertation research.

Each Qualifying Exam will be based on a syllabus of topics, available by request from the Graduate Director. The syllabi are based on material covered in classes relevant to each subject; the classes for each exam are listed below. The syllabi may also include foundational material from the undergraduate curriculum. Each Qualifying Exam is a 3 hour long, written exam, and the exams will be offered at least once per semester.

Students specializing in Pure Mathematics must take and pass exams in

- Analysis (based on either MATH 713/714, or on MATH 713/715),
- Algebra (based on MATH 731/732), and
- Topology (based on MATH 741/742).

Students specializing in Applied Mathematics must take and pass the exam in

- Analysis (based on MATH 713/715, or based on MATH 705/713),

one exam from among

- Linear Algebra (based on MATH 735/736),
- Operations Research (based on MATH 687/751/752),

and one exam from among

- Numerical Analysis (based on MATH 701/702),
- Nonlinear Dynamics (based on MATH 721/722),
- Methods in Applied Mathematics (based on MATH 761/762).

Students will be allowed a maximum of two attempts at each of the exams in the first three years of the Ph.D. program. Each exam can be passed at M.S. level (low pass) or Ph.D. level (high pass). To proceed with the Ph.D. program, two of the three exams must be passed at the Ph.D. level. If all exams are passed at least at the M.S. level but fewer than two of the three at the Ph.D. level, and other requirements for the M.S. degree are satisfied, the student will end her/his program with an M.S. degree in Mathematics. A student’s failure to earn a high pass on a particular qualifying exam may affect the student’s opportunities for thesis research opportunities in related fields; students should discuss qualifying exam options with prospective thesis advisors to be aware of any such constraints.

## M.S. degree along the way to Ph.D.

Students in the Ph.D. program in Mathematics may earn an M.S. degree in Mathematics along the way to their Ph.D. by satisfying the current M.S. degree requirements. Students qualify in the semester in which all degree requirements for the master's degree have been met. Students may not receive a master’s degree along the way to the Ph.D. if the student has earned a previous master’s degree at any time and units from that degree are counted towards the Ph.D.

Besides the course requirements for the M.S. degree, the student must write a Master’s Thesis (and take the required 6 M.S. thesis credits, which will not count toward her/his Ph.D. degree), or pass the Comprehensive Exam (based on four 700-level courses, one of which must be MATH 713).

## Admittance to candidacy

To be admitted into Ph.D. candidacy, after successfully completing the first two years of coursework and passing three written Qualifying Exams, a student must pass the Oral Exam in the area of specialty. Students will be expected to complete their oral exam by the end of their 7^{th} semester. The exam is directed by the student's Dissertation Advisor and Dissertation Committee.

## Ph.D. dissertation

A student will prepare a Ph.D. dissertation supervised by the Dissertation Advisor and approved by the student's Dissertation Committee, followed by an oral public presentation. The dissertation is then submitted to the Graduate School for approval.

## Graduate school academic requirements

### Good standing

Each graduate course must be completed with a grade of "C" or better for the credit to be acceptable toward an advanced degree.

In addition, students must maintain good standing with an overall cumulative graduate credit GPA of at least 3.0 on a scale of 4.0. Students must have a minimum GPA of 3.0 in order to meet graduation eligibility. All graduate students must maintain a cumulative graduate GPA of 3.0. If their GPA drops below 3.0, they are either placed on probation or dismissed. Undergraduate courses will not count towards the graduate GPA.

### Probation

If the student’s cumulative graduate GPA drops between 2.31 and 2.99, the student is placed on probation. The student must then raise her/his cumulative graduate GPA to 3.0 by the end of the following semester or the student will be dismissed from graduate standing. Thesis, dissertation, S/U graded credits, and transfer credits have no impact on a student’s GPA.

### Dismissal

If the cumulative graduate GPA drops 2.30 or lower, the student is dismissed from graduate standing, or if the cumulative graduate GPA remains below 3.0 for two (2) consecutive semesters, the student is dismissed from graduate standing.

Dismissed students are no longer in a graduate program but may take graduate courses as a Grad Special. Students wishing to complete their degree must obtain approval to take graduate-level courses, raise their graduate GPA to at least 3.0 and then reapply to a graduate program. Any courses taken to raise their GPA will be included in the graduate special/transfer credit limitation (9 credits for master’s degrees).

Please note: this represents the program handbook for the 2022-2023 academic year only. For an archived version of a previous year's handbook, or to obtain a hard copy of this current year's program handbook, please contact the program director.