Ph D Programs
**Doctor of Philosophy in
Mathematical Sciences**

Students seeking a Ph.D. are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all doctoral programs.

After being admitted to graduate status by the Department, a student seeking a Ph.D. must be admitted to candidacy for this degree by fulfilling the appropriate program requirements.

The only remaining requirement for the Ph.D.degree is timely completion and public defense of an acceptable thesis. The Ph.D. thesis is expected to display depth and originality and be publishable by a refereed journal.

### Doctor of Arts in Mathematical
Sciences

The Doctor of Arts Degree shares all requirements and standards with the Ph.D., except with respect to the thesis. The D.A. thesis is not expected to display the sort of original research required for the Ph.D. thesis, but instead to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient originality and worth to produce publishable work. Whenever practical, the Department provides D.A. candidates the opportunity to use materials developed to teach a course. While the typical Ph.D. recipient will seek a position which has a substantial research component, as at a large university or in an industrial or governmental research laboratory, the D.A. recipient usually will seek a position where research is not central.

### Doctor of Philosophy in Algorithms, Combinatorics, and Optimization (ACO)

This program is jointly administered by the Department of Mathematical Sciences, the School of Computer Science, and the Tepper School of Business. It focuses on algorithmic issues arising in computer science and operations research, particularly the mathematical analysis of these issues. The requirements for this degree and information on participating faculty are available on the ACO web site.

### Doctor of Philosophy in Pure and Applied Logic (PAL)

This is an interdisciplinary program with faculty from the School of Computer Science, the Department of Mathematical Sciences, and the Department of Philosophy. The participating units evaluate applications separately and set their own program requirements. Additional information, including answers to frequently asked questions and recent course offerings can be found at the Pure and Applied Logic webpage. Students doing thesis research in mathematical logic eventually choose between the Ph.D. in Mathematical Sciences and the Ph.D. in Pure and Applied Logic based on their interests and intended career paths.