Doctor of Philosophy (Ph.D.) in Mathematics

Departmental Requirements

(Pure Mathematics)

Pure Mathematics (Ph.D.)

The Ph.D. Degree in Pure Mathematics is designed to prepare a student for a career in university or industrial research and college instruction. Recipients of the Ph.D. degree in Pure Mathematics are expected to have signifigant breadth across the core areas of mathematics, as well as skills to undertake independent and original research in a particular area. More information is available in the "Guide to Graduate Study" and the "Graduate Program Handbook".

Credit Requirements:

A total of 90 hours above the B.S. degree or 60 hours above an M.S. is required, including 15-24 credit hours for the Ph.D. thesis.

Core Requirements:

All candidates for the Ph.D. in Pure Mathematics are required to complete 24 credit hours of core courses from the following list. A minimum GPA of 3.0 must be maintained in the core courses.

 Real Analysis I (Math 5143) & Real Analysis II (Math 5153)

 

 Complex Analysis I (Math 5283) & Complex Analysis II (Math 5293)

 

 Algebra I (Math 5613) & Algebra II (Math 5623)

 

 Six hours from General Topology (Math 5303), Geometric Topology (Math 5313), or Algebraic Topology I (Math 6323)

Additional Courses:

In addition to the core requirements, every plan of study must contain at least 12 hours of graduate courses in the Mathematical Sciences chosen from outside the major field of study.

Comprehensive Exams:

A Ph.D. student in Pure Mathematics must select three (3) of the areas from the core requirements, listed above, and for each must pass a comprehensive exam covering the content of the core courses taken in that area. The exams in Mathematics are given twice a year, in August and January. The comprehensive exams must commence within one year of residence after completing the required coursework. All exams must be completed within 25 months after the first exam is taken. A student may sit for an exam a maximum of three times. With the approval of the student's advisor, a student may substitute the writing of a paper, called a Minor Thesis, for one of the comprehensive exams (see below regarding the requirements for a Minor Thesis).

Minor Thesis: The minor thesis option must be approved by the student's advisor and after the student has successfully passed two written comprehensive exams. The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content that is:

In an area different from an area in which the student has passed a written comprehensive exam.

On a topic that is not covered completely in any prior coursework.

On a topic approved by the student's Advisory Committee.

Completed in one semester (fall, spring, or summer), from start to finish, (to encourage the ability to learn mathematics independently and write a suitable exposition in a timely manner). No extensions will be granted.

After completion of the written Minor Thesis, the student must pass an oral exam on the subject of the minor thesis, which is administered by three faculty members approved by the Advisory Committee. A grade of pass or fail on the Minor Thesis will be assigned following this examination. A public presentation is encouraged but not required. The Minor Thesis must be completed within the same 25 month period determined by the taking of the first comprehensive exam. A student who takes the Minor Thesis option and does not pass has no further option of a Minor Thesis.

Language Requirements:

Candidates for the Ph.D. in Pure Mathematics must pass an examination demonstrating reading knowledge of one foreign language, usually French, German, or Russian, before they take the Qualifying Examination. Other languages may be substituted subject to recommendation of the student's committee and approval of the Graduate Committee, including a working ability with a computer language or symbolic computation meeting the satisfaction of the student's committee.

Qualifying Examination:

The student must pass an oral qualifying examination over the area of specialization for their Ph.D. thesis. This exam covers the material on a reading list presented to the student by the advisory committee. Its purpose is to test the student's readiness to begin thesis work.

Thesis Proposal:

An outline of the proposed thesis research must be presented to the student's advisory committee for approval. A written proposal is then filed with the Graduate College.

Thesis:

A thesis must be written according to Graduate College guidelines. The thesis consists of an original research contribution in Pure Mathematics. It must be prepared according to the style required of doctoral theses and defended.

Graduate College Requirements:

All requirements listed in the University catalog must be satisfied.