Doctor of Philosophy (Ph.D.) in Mathematics

Departmental Requirements

(Applied Mathematics)

Applied Mathematics (Ph.D.)

The Ph.D. Degree with emphasis in Applied Mathematics is designed to prepare a student for a variety of careers in industry, in government research laboratories and in university research and teaching. Application of mathematics is an important skill to be cultivated by students based on an ability to discern occurrences of mathematical structures in the human environment. Recipients of the Ph.D. degree in Applied Mathematics are expected to have signifigant breadth across the mathematical sciences, 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 Applied Mathematics are required to complete 24 credit hours of core courses. These must include three of the following 4 options (presumably the 3 options over which a student will take the Comprehensive Exams) plus an additional 6 credit hours from other courses in the approved "Electives" given below. A minimum GPA of 3.0 must be maintained in core courses taken from Real Analysis and Complex Analysis. In all other courses, which are to satisfy the core requirements, a student must have a grade of A or B. If the Minor Thesis option is elected, students should complete 2 of the following 4 options plus an additional 12 credit hours from other courses in the approved electives given below.

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

 

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

 

 Numerical Anaylsis fro Differential Equations (Math 5543) and Numerical Analysis for Linear Algebra (Math 5553)

 

 Six hours from Fourier Analysis (Math 5213), Partial Differential Equations (Math 5233), or Ordinary Differential Equations I (Math 5243)

 

 Electives: Any of the courses in the above four options, Math 5303(General Topology), Math 5613(Algebra I), Math 5623(Algebra II), Math 5113(Probability Theory), Math 5133Stchastic Processes), Math 5523(Calculus of Variations and Optima Control), Math 5580(Case Studies in Applied Math), Math 5593(Methods of Applied Math).

 

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:

The students Advisory Committee must be satisfied that the student has a strong working ability with a computer language or symbolic computation.

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.