There are five general and overlapping areas of specialization within the department:
- Algebra, Algebraic Geometry, Combinatorics and Number theory
- Analysis, Differential Equations and Probability
- Applied and Computational Mathematics
- Geometry, Topology, and Dynamics
The requirements for the Ph.D. are the same in all areas. Students may also choose to specialize in Mathematics Education which has some different course and research requirements. Briefly, the requirements for a Ph.D. are:
Take a total of 51 graduate credits, or generally 17 courses. This includes courses in math and in a minor. In the Ph.D. program, math courses numbered above 700 are for graduate credit. Math courses below 700 must be approved by the Academic Advisor.
Complete a minor. A minor is usually 12 credits (4 courses), although this differs in some minors. The minor department determines what is required for a minor.
Pass any two of six qualifying exams. Exams are offered in Analysis, Algebra, Applied Mathematics, Computational Math, Logic, and Geometry/Topology.
Pass a Specialty Exam. This exam is constructed by your dissertation advisor in your chosen area of research.
Complete a dissertation. Once you have completed all of the requirements other than the dissertation (all courses, minor, qualifying exams, and specialty exam), you will be classified by the Graduate School as a Dissertator. Dissertators register for only three credits per semester.
When you begin studies at the UW Math Department a faculty member will be assigned as your academic advisor. You will consult with your advisor about your choice of graduate courses, requirements of the Math Department, how to find a dissertation advisor, and other issues. Students who have not reached dissertator status are required to meet with their academic advisor at least once each semester.
When you choose a dissertation advisor you must inform the Graduate Coordinator about your choice. Your dissertation advisor will then become your academic advisor.
You are required to meet with your academic advisor before you sign up for courses.
The Math Department requires a minimum of six credits per semester (except dissertators). However, most students take at least three courses (9 credits) each semester. At this rate you would finish your course requirements in three years. At least two of these courses must be at 700 level or above.
In selecting your courses, there are some things you should keep in mind:
Three 700-level or above courses (9 credits) can be a demanding load for students working as TAs. This is especially the case in your first year, when you may be adjusting to teaching, the general demands of graduate study, and life in general. Some students choose to take only 2 courses (6 credits) in a semester, while other students (usually those with fellowships) take four courses (12 credits).
The introductory 700 level classes are highly recommended. If you have already taken some of these classes at the program you previously attended then consult your academic advisor.
If you want to strengthen particular areas of your background in preparation for qualifying exams, there are some 500 and 600 level courses that may be helpful. A limited number of courses at this level may count for graduate credit. Consult with your advisor or the Director of Graduate Studies.
You may want to start thinking about your minor early. Since you are required to take 4 courses (12 credits) for most minors, it will speed things along for you if you start taking courses in your minor by the beginning of your second year.