Mathematics, M.A.

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A comprehensive mathematics degree, with training in the fundamentals of analysis, abstract algebra, computation, and mathematical modeling. Provides a strong foundation for teaching, work in industry, and continued study in graduate-level programs.

Common Requirements

The following requirements are common to all four tracks:

The student must maintain a 3.000 cumulative GPA.
The student must complete 30 hours of formal mathematics coursework at the 5000 level.
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 MATH 4970 : Professional Development in Mathematics and one hour of the seminar MATH 4970 : Professional Development in Teaching.

5000-level Mathematics Courses

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:

MATH 5200 - Real Variables I Credits: 3
MATH 5230 - Complex Variables I Credits: 3
MATH 5310 - Computational Methods in Applied Sciences I Credits: 3
MATH 5400 - Methods of Applied Mathematics I Credits: 3
MATH 5500 - Advanced Linear Algebra Credits: 3
MATH 5550 - Abstract Algebra I Credits: 3

Tracks:

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 mathcontent 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.

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.

The oral component of this Track will consist of a defense of the student’s written answers to qualifying exam.
Pass one of the department’s qualifying exams in: