Mathematics Graduate Program Information

Program-Specific Degree Requirements

Master's Programs: M.A. and M.S. Plan A and Plan B

The math department maintains 4 tracks by which students may obtain a Master of Arts (M.A.) or Master of Science (M.S.) degree in mathematics.

The following requirements are common to all four tracks:

• The student must maintain a 3.0 cumulative GPA.

• The student must complete 30 hours of formal mathematics coursework at the 5000 level.

• As part of the 30 hours of formal 5000-level mathematics courses, the student must complete the following courses with a grade of B or better:

  • o MATH 5200: Real Variables I,

  • o MATH 5230: Complex Variables I,

  • o MATH 5310: Computational Methods I

  • o MATH 5400: Methods of Applied Mathematics I,

  • o MATH 5500: Advanced Linear Algebra, and

  • o MATH 5550: Abstract Algebra I.

• The student must pass the department’s Foundation Exam. This exam covers material from advanced vector calculus and linear algebra at the upper-division undergraduate level and is offered before the beginning of each semester.

• Take one hour of the seminar 4970: Professional Development in Mathematics and one hour of the seminar 4970: Professional Development in Teaching.

In addition to the common elements above, students must select and complete one of the capstone experiences described in the tracks below.

Track #1: Master's Thesis (Plan A)

Within the 30 hours of 5000-level courses, the Plan A student must complete 4 hours of MATH 5960: Thesis Research. At least 26 hours of 5000-level coursework must be math-content courses (not thesis research).

The student must prepare a master’s thesis (Plan A) and give an oral defense of the thesis. In the mathematics program, a Plan A thesis reports on the result(s) of independent and original research completed by the student under the direction of a faculty member. The thesis should describe the research and its results and be written to the standards of the appropriate area of mathematics.

Track #2: Master's Paper (Plan B)

The student must prepare a master’s paper (Plan B) and give an oral defense.

To write a Plan B paper, the student must present an expository paper on a designated mathematical subject. Students are guided by their advisor in the subject matter and in the preparation of the paper. A successful paper and defense demonstrates that the student has mastered a substantial mathematical topic that is beyond those covered in formal foundational coursework.

Track #3: Coursework/Project (Plan B)

A second M.A. or M.S. option exists for the Plan B student. In lieu of writing a paper, the student takes a sequence of three 5000-level courses that all address a common mathematical theme. The sequence must be approved by the student’s advisor and the mathematics graduate committee. Two of the courses must be mathematics-department offerings, and the third may be either a mathematics course (including reading/topics courses) or a course from another department in a related field.

• The student must complete an additional 6 hours of courses at the 5000 level. Thus, Track #3 requires the completion of 36 hours of graduate-level coursework.

• Within the 36 hours, the student must propose and complete with a grade of B or better an appropriate 3-course sequence

• The student will write a short paper illustrating how the common mathematical theme of the sequence manifests itself in the content of each course and give a presentation/defense of the paper.

In approving the student’s proposal for this option, the graduate committee and the advisor will consider how the writing and independent study spirit of the Plan B option are fulfilled within the recommended plan.

Track #4: Qualifying Exam (Plan B)

A third M.A. or M.S. option exists for the Plan B student. In lieu of writing a paper or taking additional coursework, the student must take and pass the department’s PhD Qualifying Examination in one of the three areas: Analysis, Algebra, or Applied Mathematics. These examinations focus on the material in the required courses.

• Pass one of the department’s qualifying exams in:

  • o Analysis (MATH 5200 and MATH 5230)

  • o Algebra (MATH 5500 and MATH 5550)

  • o Applied Mathematics (MATH 5310 and MATH 5400)

• The oral component of this Track will consist of a defense of the student’s written answers to qualifying exam.

These examinations are given twice a year at the beginning of the fall and spring semesters.

**This option is intended for students who will continue for a PhD at UW.**

 

Doctoral Program

The student must maintain a 3.0 cumulative GPA.

The student must teach two semesters of college mathematics.

The student must complete a combination of 72 hours of coursework and dissertation research. Within the 72 hours, a maximum of 12 hours can be at the 4000 level, and 42 hours must be formal courses at the 5000 level. The courses must be mathematics courses or courses with significant mathematical content, as approved by the department's graduate committee.

Within the 42 hours of 5000-level courses, the student must:

• Complete MATH 5200, 5230, 5310, 5400, 5500, and 5550 with a grade of B or better.

• Take two hours of MATH 5800-02, Seminars and Colloquia.

• Complete the courses distributed in three areas: algebra, analysis, and applied mathematics. The student must take at least two courses in each of two categories and at least one course from the third category. The department maintains a list of course categories.

In addition, the student must:

• Pass the foundation exam, the qualifying exam in the student's research area, and the preliminary exam.

• Write a dissertation containing the student's original mathematical results and present an oral defense of the research.

• Take one hour of the seminar 4970: Professional Development in Mathematics and one hour of the seminar 4970: Professional Development in Teaching.

Mathematics (MATH) Courses

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