1. Take at least 60 hours beyond the bachelor’s degree - 45 hours, excluding MATH 7300.

There must be 30 hours of mathematics courses numbered 6000 or above, excluding MATH 7300. It is required by the University that the dissertation hours and 30 hours of course work be completed after admission to the doctoral program. The 60 hours will include the following courses:

• MATH 5220 - Introduction to Topology Credits: 4 hours
• MATH 5700 - Advanced Calculus I Credits: 4 hours
• MATH 6760 - Complex Analysis Credits: 4 hours
• MATH 6300 - Abstract Algebra I Credits: 4 hours
• MATH 6400 - Graph Theory I Credits: 4 hours
• MATH 6460 - Combinatorics Credits: 4 hours
• MATH 6700 - Real Analysis I Credits: 4 hours

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  Select one of the following three courses:

• MATH 5100 - Applied Matrix Algebra Credits: 3 hours
• MATH 5300 - Linear Algebra Credits: 3 hours
• MATH 5310 - Linear Algebra with Applications Credits: 3 hours

2. Take two comprehensive examinations.

• A student must pass two comprehensive examinations, one in Analysis and one in the research area of a doctoral student. The Analysis exam will be given in years following the course Math 6760. The exam in the research area will be given by the end of student’s third year in the program. Any alteration to the timeline must be approved by the Graduate Committee.
• A student must successfully complete a given examination by the second attempt and will be notified in writing of the results of each comprehensive examination within two weeks of its administration.

3. Demonstrate competency in research tools.

Candidates must demonstrate proficiency in mathematical typesetting, presentations, and mathematical literature search tools. In addition, in consultation with the candidate’s advisor, candidates must choose one of the following tools: foreign language or mathematical research software.

4. Complete a teaching practicum including teaching an approved undergraduate mathematics course.

5. Complete a dissertation that is a significant new contribution to mathematics.

The dissertation must be defended before the student’s doctoral committee. Completing the dissertation requires at least 15 hours of the following course:

• MATH 7300 - Doctoral Dissertation Credits: 1 to 15 hours

6. The following courses may not be included in the required 60 hours.

• MATH 6150 - Intermediate Analysis Credits: 3 hours
• MATH 6160 - Survey of Algebra Credits: 3 hours
• MATH 6170 - Survey of Discrete Mathematics Credits: 3 hours
• STAT 6120 - Data Analysis Credits: 3 hours