# 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. This program is the Philosophy Department component of the CMU Pure and Applied Logic program. As part of the program, students earn a Master of Science from the Department of Mathematical Sciences.

## Coursework

## Core Philosophy requirements (9 courses)

**80-600 Philosophy Core Seminar I**: Survey of crucial research in philosophy, logic, and related areas (12 units)**80-601 Philosophy Core Seminar II**: Continued survey of crucial research in philosophy, logic, and related areas (12 units)**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 (6 units each)

**80-611 Undecidability and Incompleteness**(half semester): The theory of computability, and Gödel's incompleteness theorems (6 or 12 units)

**80-811 Professional development seminar**: This class is for professional development of masters and PhD students in the philosophy department. All students who are in their first three years of graduate programs should enroll in this course. (18 units total)

## Mathematics requirements (8 courses**, sufficient to earn an MS in Mathematical Sciences**)

- One course in algebra (such as 21-610 Algebra I, 21-611 Topics in Algebra, or 80-713 Category Theory) (12 units)
- One course in topology (such as 21-651 General Topology) (12 units)
- One course in analysis (such as 21-720 Measure and Integration or 21-721 Probability) (12 units)
- Three courses in logic (such as 21-602 Set Theory, 21-603 Model Theory, 21-604 Recursion Theory, or 80-711 Proof Theory) (12 units)
- Two electives in mathematics or computer science (12 units each)

At most two of the eight courses can be taken outside of Mathematics. Students should contact the Director of Graduate Studies of the Mathematics Department to determine if courses taught outside of Mathematics will satisfy this requirement.

## Breadth (2 courses)

- One course in the analytic tradition (such as 80-605 Decision Theory, 80-612 Mathematical Revolutions, or 80-680 Philosophy of Language) (12 units)
- One course in the history of philosophy (such as 80-655 Pragmatism, or 80-612 Mathematical Revolutions) (12 units)

## Electives (4 courses)

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

## Research

## 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

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.

## Alumni

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.