Doctor of Philosophy in Mathematics

Advisor: See Mathematics Office,
Room 3319, Everett Tower

Admission Requirements

A student may enter this program with a master’s degree or directly upon completion of a bachelor’s program. In addition to satisfying the general admission requirements of The Graduate College, the student must have acquired a sufficient level of mathematical background as determined by the Mathematics Faculty of the Department.

A student entering the program in Collegiate Mathematics Education must have sufficient background in mathematics and education as determined by the Collegiate Mathematics Education Committee, a joint committee of the Mathematics and Mathematics Education faculty.

Program Requirements

Mathematics

A student must complete the following requirements:

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.

A two-semester graduate sequence in Algebra (MATH 6300-6310)
A two-semester graduate sequence in Analysis (MATH 6700-6710)
A two-semester graduate sequence in Topology (MATH 6210-6240)
A course in Complex Analysis (MATH 6760)
An approved course in applied mathematics or probability/statistics

2. Take three comprehensive examinations.

A student in Algebra, Analysis, or Topology must take comprehensive examinations in each of these areas.
A student planning to do a dissertation in any other area of mathematics may, with approval of the advisor and the Mathematics Graduate Committee, replace either the Algebra or Topology examination with one in the student’s specialty.

3. Demonstrate competency in two research tools, including at least one foreign language.

The foreign language research tool may be satisfied by completing courses numbered 4000 in foreign languages with a “B” or better or by demonstrating the ability to read mathematics in foreign languages as certified by the Mathematics Graduate Committee. Competence in computer usage as a research tool is usually demonstrated by completing 3 hours of MATH 6880 with a “B” or better.

4. Teach an undergraduate mathematics class at the 2000-level or higher.

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

And defend the dissertation before the student’s doctoral committee. This requires at least 15 hours of the following course:

MATH 7300 - Doctoral Dissertation Credits: 15 hrs.

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

MATH 6110 - Mathematical Applications Credits: 3 hrs.
MATH 6120 - Data Analysis Credits: 3 hrs.
MATH 6150 - Intermediate Analysis Credits: 3 hrs.
MATH 6160 - Survey of Algebra Credits: 3 hrs.
MATH 6170 - Discrete Dynamical Systems Credits: 3 hrs.
MATH 6190 - Computer Methods in Secondary School Mathematics Credits: 3 hrs.

Collegiate Mathematics Education

This degree program requires a minimum of 80 hours beyond the bachelor’s degree — 65 hours, excluding MATH 7300. The basic requirements of the program are as follows.

1. Complete at least 65 hours of course work, including the following:

Introduction to Topology (MATH 5220), Linear Algebra (MATH 5300), and Advanced Calculus I & II (MATH 5700 and 5710)
A two-semester graduate sequence in Algebra (MATH 6300-6310)
A two-semester graduate sequence in another approved area of mathematics in which a comprehensive examination is offered
A semester course in Complex Analysis (MATH 6760)
Five additional courses, including at least one in Applied Mathematics and at least two in Probability or Statistics (usually STAT 5620 and 6620)
Fifteen graduate hours in mathematics education

2. Pass three comprehensive examinations in

Algebra
Mathematics Education
One other approved area in Mathematics

3. Demonstrate competence in two research tools.

This may be satisfied by demonstrating competence in computer usage, usually through 3 hours of MATH 6880, and in educational research methods, usually through EMR 6400 and EMR 6480.

4. Teach an undergraduate course in mathematics at the 2000-level or above.

5. Complete and successfully defend a dissertation.

This requires 15 hours of:

MATH 7300 - Doctoral Dissertation Credits: 15 hrs.

Procedures

Upon admission every student will be assigned an advisor. The advisor and student will, within the student’s first calendar year, design a tentative program for completing a Ph.D. This plan must be approved by the committee supervising the Ph.D. program in Mathematics (or Collegiate Mathematics Education for students in that program). Any changes in the student’s program must be approved by the supervising committee.
A student must take the comprehensive examinations as soon as possible. After completing a course sequence leading to a comprehensive examination, a student must take the corresponding comprehensive examination the next time it is offered. Each exam will be offered twice a year as demand requires. If a student fails a comprehensive examination, the student must retake the examination the next time it is offered. A student who fails a comprehensive examination twice will be dismissed from the program at the end of the semester when the exam was taken.

A full-time student must take all the comprehensive examinations by the beginning of the student’s fourth year and must pass the examinations by the end of the fourth year. Part-time students must follow a similar schedule adapted to the number of classes they can take each year.
A full-time student will start taking reading courses from potential dissertation advisors as soon as the student has passed one comprehensive examination. As soon as a student finds a dissertation advisor, the dissertation advisor becomes the student’s advisor.
As soon as a student passes the comprehensive examinations and completes the research tools, the student will, in consultation with the advisor, form a dissertation committee and apply for candidate status. The dissertation committee will consist of the dissertation advisor, a second reader, at least one other faculty member, and a member from outside the department. This committee must be approved by the committee supervising the Ph.D. program. A student will not be allowed to take MATH 7300 hours until these requirements are completed.
At least one year before the final oral defense of the dissertation, each student will give an open oral presentation of their proposed dissertation and answer questions on the proposal. The dissertation committee will consider the merits of the proposal and either allow the student to continue with the proposed problem, require the student to expand the scope of the research, or require the student to find a new topic.
After completing a dissertation and all other requirements for the Ph.D., a student will present an oral defense of the dissertation. This will be an open presentation with an open question period. The committee will then decide to accept or reject the dissertation and defense. All committee members must agree on acceptance for the student to pass.