Carnegie Mellon University

Doctorate Program in Pure and Applied Logic

The Doctorate Program in Pure and Applied Logic is an interdisciplinary program designed to support students seeking a career in Mathematics, but interested in working in an area of logic supported by the Department of Philosophy. As part of the program, students earn a Master of Science from the Department of Mathematical Sciences.

The program's course requirements are designed to provide students with a shared introduction to basic tools of philosophical analysis, a shared background of philosophical issues, significant interdisciplinary competence and an introduction to research topics in the department.

Core Philosophy requirements (4 courses)

  • 80-600 Philosophy Core Seminar: Survey of crucial research in philosophy, logic, and related areas
  • 80-601 Philosophy Core Seminar II: Continued survey of crucial research in philosophy, logic, and related areas
  • Formal Methods: Students should choose three different "mini" (i.e., half-semester) courses from among the available options.  These courses cover a range of formal frameworks including Bayes Nets, Decision Theory, Game Theory, and Formal Learning Theory
  • Topics in Logic I OR II (one half-semester course): The theory of computability or Gödel's incompleteness theorems
  • Professional development seminar: Students must enroll in the professional development seminar in the spring semester of each of their first three years

Mathematics requirements (8 courses)

Students are required to earn an MS in Mathematical Sciences. To earn this degree, a student must successfully complete at least 96 units of graduate courses (600 level or above) in the Department of Mathematical Sciences, at least which 48 of which are at the 700 level or above, with a B- or better average. The courses must reflect a reasonable level of breadth in Mathematical Sciences.

Graduate courses in other departments that have significant mathematical content can be applied towards the MS degree, with permission. The Director of Graduate Studies in Mathematical Sciences must approve the choice of courses used to fulfill the requirements. Students in the PAL degree program are encouraged to contact the Director of Graduate Studies in Mathematical Science early on and keep them apprised of their plans.

Breadth (2 courses)

  • One course in the analytic tradition (such as 80-605 Rational Choice, 80-612 Philosophy of Mathematics, or  80-680 Philosophy of Language)
  • One course in the history of philosophy (such as 80-254 Analytic Philosophy, or 80-255 Pragmatism)

Electives (4 courses)

  • Four unconstrained electives (including directed reading and dissertation research)

These requirements can be filled in three years by taking three courses each semester. Coursework must be completed by the end of the fourth year, at the latest. Electives should be chosen in consultation with the Director of Graduate Studies and the student's advisor, to ensure that the courses chosen will support the student's career goals.

Research areas include:

  • automated deduction and automated reasoning
  • category theory and categorical logic
  • computability and computable analysis
  • constructive logic and type theories
  • homotopy type theory
  • proof theory

Students are advised to do supervised reading and research with a member of the faculty in the spring of their first year, to explore possible research topics for the master's thesis. In the spring of the second year. The master's thesis itself should be completed by the end of the second year.

In the third year, students choose a dissertation topic and committee. Students must present and defend a prospectus by the end of the fourth year, at the latest, and are expected to complete their doctoral dissertation by the end of the fifth year.

Teaching experience is an essential component of the doctoratal program. It provides fundamental professional skills for those pursuing academic careers and broadens the focused expertise of pure researchers. Students are required to serve as an assistant or instructor each semester, with the following exceptions: students are exempt from teaching one semester in their first year, and one semester later on, while they are carrying out research on their thesis.

Students serving as principal instructors are mentored by a faculty member. Each foreign student whose native language is not English must take a proficiency exam with the ESL Center prior to teaching.

The department's interdisciplinary research thrust affords an unusually broad range of career possibilities. Graduates of the program have been offered positions in Philosophy, Mathematics, Psychology, Computer Science, and Statistics, as well as research positions in industry. This wide range of interesting career opportunities reflects the department's unique dedication to serious, interdisciplinary research ties.

For a complete listing of our graduates and placement record, see our Ph.D. alumni page.