# Degree requirements

## Degree plans (Thesis vs. Non-Thesis)

Students may complete the program of “Master of Science in Mathematics” by choosing one of two possible degree plans:

- The Master’s Thesis Degree Plan (Thesis Plan), or
- The Comprehensive Exam Plan (Non-Thesis Plan).

To complete their master’s degree via the Thesis Plan, students must

- Complete at least 30 credits of acceptable graduate courses.
- Complete at least 6 thesis credits (by enrolling in the thesis course MATH 797).
- Complete at least 12 non-thesis credits of 700-level courses.
- Complete at least 21 credits through on-campus courses at the University. For transfer credits, please consult the Graduate Director.

To complete their master’s degree via the Non-Thesis Plan, students must

- Complete at least 30 credits of acceptable graduate courses.
- Complete at least 18 non-thesis credits of 700-level courses.
- Complete at least 23 credits through on-campus courses at the University. For transfer credits, please consult the Graduate Director.
- Pass the Comprehensive Exam.

## Degree Options (Pure Mathematics vs. Applied Mathematics)

Within the program of "Master of Science in Mathematics," each student chooses either *Pure Mathematics* or *Applied Mathematics* as their *Degree Option*. This choice determines the list of courses the student needs to complete for successful graduation.

### Pure Mathematics

The Pure Mathematics option provides a solid foundation in the theoretical aspects of mathematics. To graduate, students must successfully complete the following two courses:

- MATH 713 (Abstract and Real Analysis I, offered every fall semester), and
- MATH 731 (Modern Algebra I, offered in fall semesters of odd-numbered calendar years).

Additionally, students must complete at least one of the following three courses:

- MATH 714 (Abstract and Real Analysis II, offered in spring semesters of odd numbered calendar years),
- MATH 732 (Modern Algebra II, offered in spring semesters of even-numbered calendar years), or
- MATH 741 (Algebraic Topology I, offered in fall semesters of even-numbered calendar years).

### Applied Mathematics

The Applied Mathematics option provides a broad technical background for solving real-world problems. Students are required to complete

- MATH 713 (Abstract and Real Analysis I, offered every fall semester)

Additionally, student must complete one of the following sequences of courses:

- MATH 701-702 (Numerical Analysis and Approximation I and II),
- MATH 721-722 (Nonlinear Dynamics and Chaos I and II),
- MATH 751-752 (Operations Research I and II),
- MATH/STAT 753 - Stat 754 (Stochastic Models and Simulation and Mathematical Statistics), or
- MATH 761-762 (Methods in Applied Math I and II).

An internship may be included in the plan of study, subject to the availability and approval of the Graduate Advisor.

## Electives

Electives must be approved by the student’s Graduate Committee (Section 4). Appropriate courses outside the Department of Mathematics and Statistics may be approved, depending on the student’s research interests.

## The Master’s Thesis

Students who choose the Thesis Plan must write a Master’s thesis to complete the program. This process starts with the student choosing a Thesis Advisor (Advisor), a choice typically made during the student’s first year in the program. The Advisor is a graduate faculty member of the Department of Mathematics and Statistics who works in a research area of interest to the student. To initiate the Student-Advisor collaboration, the student should approach the faculty member and ask her/him if she/he is willing to serve as the student’s Advisor. The student and Advisor jointly choose members of the student’s Graduate Committee.

Once an Advisor has been identified, she/he will guide the student through the thesis writing process. This may involve preparatory work such as reading books and/or research papers, computer programming, intense calculations, etc. While working on the thesis, the student needs to be enrolled 6 in the thesis course MATH 797, completing a total of 6 credits. These are typically broken up as 3 credits during the student’s third semester and 3 during the student’s fourth semester (though the student could choose to take all 6 credits in the fourth semester, for example).

The Advisor will instruct the student about the content and format of the thesis. A Master’s thesis, unlike a Ph.D. thesis, is not required to contain original content but should demonstrate the student’s mastery of a particular area of pure or applied mathematics. Upon completion, the student will defend her/his thesis by giving a public presentation, followed by a period of questions by the student’s Graduate Committee.

## The Comprehensive Exam

Students who choose the Non-Thesis Plan must complete the Comprehensive Exam. This exam is offered once per semester, on a Saturday during the last three weeks of the semester. The exact date for the exam is announced by the Graduate Director in a timely fashion.

The Comprehensive Exam is based on four courses that the student has taken in prior semesters. One of these courses is MATH 713 (Abstract and Real Analysis I), while the remaining three courses are chosen by the student in concert with the Graduate Director or Graduate Advisor.

The Comprehensive Exam is 6 hours long and is broken up into a 3-hour morning session (9 a.m.-noon), and a 3-hour afternoon session (1 p.m.-4 p.m.). During each of the sessions, the student must complete exams in two courses. The student is given the choice of which two courses to test in each of the sessions. If a student completes the exams from the morning session early, she/he may not start the exams of the afternoon session prior to the start of the said session at 1 p.m.

Students will be allowed a maximum of two attempts at passing the Comprehensive Exam.

## 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 graduate GPA.

### Probation

If the student’s cumulative graduate credit GPA drops to 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 credit GPA drops to 2.30 or lower, or if the graduate GPA remains below 3.0 for two consecutive semesters, the student is dismissed from graduate standing. Dismissed students are no longer in a graduate program but may take graduate-level 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 re-apply to a graduate program. Any courses taken to raise their GPA will be included in the graduate special/transfer credit limitation (9 credits for M.S. degrees).

All M.S. coursework must be completed within six years preceding the awarding of the degree.

Please note: this represents the program handbook for the 2021-2022 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.