Joint Mathematics and Computer Science Ph.D.

Draft, March 24, 2005

Program Overview
This program is designed to allow a student to earn an interdisciplinary Ph.D. in the fields of Mathematics and Computer Science. The degree is one where the student makes meaningful research contributions to both ends. The program will be overseen by a four-person committee (Oversight Committee), comprised of 2 faculty members from each department. The committee is a subcommittee of the Graduate Advisory Committee of each Department.

Entrance to the Program
A student may apply to the program by request, either as a new student or as a current student. Admission must be approved by the Graduate Chairs of both Departments.  As a general guide, students considered for the program should demonstrate backgrounds of sufficient strength
to warrant admission and financial support for the Ph.D. program of both departments.
Students entering the joint Mathematics/Computer Science Ph.D. program must have adequate background to successfully take the Qualifying Examination within a year.  Background courses must include (equivalent UNL courses shown within parentheses):

• Mathematics Courses: At least 15 semester credit hours of mathematics past calculus.
• Computer Science Courses: computer organization (CSCE 230), discrete structures (CSCE 235), data structures and algorithms (CSCE 310), and programming language concepts (CSCE 322).

Qualifying Examinations
Students are required to pass a Qualifying Examination. This exam consists of three 3-hour long exams. A student may take two mathematics portions and one computer science portion or two computer science and one mathematics portion. The mathematics portions must be drawn from: algebra (Math 817-818), analysis (Math 825-826), applied mathematics (Math 842-843), combinatorics/graph theory (Math 850-852). The computer science portions must include systems in the situation where only one CS exam is taken and both systems and theory when two exams are taken. The student must pass at the \Qualifying level" on at least one part from each department. Variations on this may be made with the approval of the Oversight Committee and the Graduate Advisory Committees of each Department.

Supervisory Committee
The graduate chairs of each department, shall jointly appoint a supervisory committee, thus both graduate committee chairs must sign the Appointment of Supervisory Committee form.

The committee must consist of an equal number of faculty from each department. An outside representative must be chosen from a department other than mathematics or computer science. (Computer Science does not see the need for an outside representative since two departments are involved anyway. Graduate College rules seem unclear on this point, thus we should check with the Graduate College for clarification.) The supervisory committee must have two co-chairs and two readers, with one co-chair and one reader from each department. A faculty member cannot serve as both a reader and a co-chair on the committee.

Program of Study
The program of study should consist of at least 90 hours, with at least 24 hours of course work from each department. No graduate level courses with 200 or 300 level counterparts are permitted. In addition, the program of study must include the following breadth requirements:

• Mathematics Breadth Requirement:
  The student must complete at least one of the following sequences:  817-818, 825-826, 842-843 AND at least 15 hours chosen from the following courses: 850, 852, 901, 902, 921, 922, 924, 925, 928, 929, 935, 936, 958.
• Computer Science Breadth Requirement:
  At least two courses in each of the systems and theory tracks and at least one course in the applications track.

Comprehensive Examinations
Students have two options for the comprehensive examination, as determined by the student's supervisory committee.

• Option 1: Under this option, the supervisory committee gives the student a topic new to the student. The topic must have significant content from both disciplines. After 4 weeks time, the student submits a written report on the topic, and then gives an oral presentation on the report.

• Option 2: Under this option, the student takes two examinations, one in each discipline. One of the examinations must be a four-hour written examination, and the other is either another four-hour written examination or a two-hour oral examination.  The examination is to be administered by the supervisory committee, and will be consistent with the current practices of each department.

Language Requirements
The student must demonstrate reading knowledge of at least one of French, German or Russian. Computer Science does not have a language requirement, and recommends deleting the language requirement from the joint degree. Mathematics has an extensive literature, hundreds of years old, and in several languages, hence sees some need for a language requirement. This is a point which will need resolution. 

Dissertation
Under the guidance of the supervisory committee, the student engages in research which culminates in a thesis which is expected to use significant tools from each discipline to make an original contribution to both areas. The student will prepare a written proposal outline of the proposed thesis research. The Supervisory Committee will meet to approve this proposal. If the research deviates significantly from the proposal, the student will submit a revised proposal for the Supervisory Committee's approval.

Final Oral Examination
After the dissertation is completed, the student takes an oral examination according to the procedures described in the Graduate Bulletin.