** 1. Qualifying Exams**

- Pass qualifying exams in two of six areas. The areas are algebra, analysis, applied mathematics, computational mathematics, logic, and geometry/ topology. These exams are written exams. They are given one or two weeks before the beginning of classes each semester. The time allowed for each exam is six hours. The exams are based on the first year graduate curricula and prerequisite undergraduate courses. Qualifying exams may be taken as often as necessary. There is a deadline by which students must pass their exams. (See exam section C2.) Passing grades may vary from year to year according to the difficulty of the exams.

** 2. Specialty Exam**

- Pass a specialty exam in the intended area of research. This exam is given by a committee of three faculty, usually one of whom is or will be the dissertation advisor. The exam may be written or oral (but is almsot always the latter).

** 3. Research and Dissertation**

- Under the guidance of a faculty member of this department, complete a significant piece of original research and render it in a written form that others can easily understand.

** 4. Minor**

- There are two different options.
*Option A*is a minor in a single department, either the mathematics department or an outside department. Option A requirements are set by the host department and typically call for 12 credits. The internal Math minor requires 12 credits in courses numbered above 700, in an area different from those of two qualifying exams. If the specialty exam is taken in an area different from those of two qualifying exams, then the minor area may be chosen in the area of one of the qualifying exams.*Option B*requires a minimum of 12 credits in one or more departments (which may include the mathematics department). Option B requirements are set by the Graduate Program Committee of the mathematics department. To avoid disallowed courses students should obtain approval in the early stages, by submitting a four course plan to the Director of Graduate Studies.- Please note, the following per Graduate School Policy, minimum course requirements for the minor include:

- An average GPA of 3.00 on all minor course work.
- Coursework must be graduate level, no audits, no pass/fail.
- Maximum of 3 credits of independent study (e.g. 699, 799, 899, 999)
- Research and thesis credits credits can't be used to satisfy the minor (e.g. 790, 890, 990).
- No more than 5 credits of course work completed more than 5 years prior to admission to the Phd; coursework taken 10 years ago or more may not be used.

** 5. Courses and Grades **

- Complete 51 credits of graduate work (typically in mathematics or an approved minor) to obtain dissertator status.
- Under certain circumstances, credit for graduate level courses taken prior to the enrollment in the PhD program may count towards the total of 51. Any waiver of credits based on prior work has to be approved by the Director of Graduate Studies. Such waivers cannot count towards the 32 credit residence requirement.
- Courses outside mathematics can be counted towards the 51 credits, up to a maximum of 12 credits, if approved by the Director of Graduate Studies or the Graduate Program Committee. If the 12 credit minor is inside the Mathematics Department the outside courses should be in a field directly related to the student's dissertation research.
- Achieve a grade point average of 3.0 or better.

** 6. Residence**

- The Graduate School requires a minimum of 32 graduate level credits (no audits or pass/fail courses) taken as a graduate student at UW Madison.

See the Ph. D. with Specialty in Mathematics Education about somewhat different requirements concerning courses, the specialty exam, the minor and a dissertation proposal.

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