Mathematics, M.S.

5000-level Mathematics Courses

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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

Track #1: Master’s Thesis (Plan A)

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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)

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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)

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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)

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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: