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

Students seeking a Ph.D. in Mathematical Sciences 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 most important requirement for the Ph.D. degree is timely
completion and public defense of an original Ph.D. 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 regard to the thesis. The D.A. thesis is not
expected to display the sort of original research required for a
Ph.D. thesis, but rather to demonstrate an ability to organize,
understand, and present mathematical ideas in a scholarly way, usually
with sufficient innovation and worth to produce a publishable
work. Whenever practical, the department provides D.A. candidates with
the opportunity to use materials developed to teach a course. While a
typical Ph.D. recipient will seek a position that has a substantial
research component, the D.A. recipient will usually seek a position
where research is not central.

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

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

ACO Website.

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

This is an interdisciplinary program with faculty from the Department
of Mathematical Sciences, the Department of Philosophy, and the School
of Computer Science. The participating units evaluate applicants
separately and set their own program requirements. Students
who have been admitted to the PAL program, and who complete the
requirements for the Ph.D. in Mathematical Sciences with a thesis in
the area of logic, can choose to receive either a Ph.D. in Pure and
Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which
degree to receive is usually based on the intended career path.