mathematical logic phd programs

Department of Philosophy

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Philosophy and Mathematics

The Departments of Philosophy and of Mathematics together offer a joint Ph.D. degree in Philosophy and Mathematics. Students in this program submit a single dissertation prepared under the supervision of members of both departments. Students enrolled in the Philosophy PhD program at Notre Dame can apply to the joint-degree program (typically during their third year of study). The joint-degree program does not accept applications from students outside of Notre Dame or admit students to the University.

The joint Ph.D. program continues a long tradition of the advanced study of formal logic at the University of Notre Dame.

Tim Bays (Philosophy) Jc Beall (Philosophy) Patricia Blanchette (Philosophy) Peter Cholak (Mathematics) Natasha Dobrinen (Mathematics) Curtis Franks (Philosophy) Joel David Hamkins (Philosophy and Mathematics) Julia Knight (Mathematics) Anand Pillay (Mathematics and Philosophy) Nicholas Ramsey (Mathematics) Sergei Starchenko (Mathematics)

Philosophy students interested in the joint program begin preparing to apply immediately upon beginning their studies at Notre Dame. In addition to philosophy coursework, they take at least the two-semester logic sequence, and sometimes other courses, in the Mathematics Department in their first year. They also take part in the Mathematics Department's research seminars. By the second year, they have taken several courses in the Mathematics Department and become integrated into the research group of a Mathematics faculty member whom they intend to be their mathematics supervisor.

Most students will then choose to apply to the Master of Science in Interdisciplinary Mathematics (MSIM). This application describes a list of courses and a research project that the student and his or her mathematics supervisor propose. While working towards the MSIM, the student decides either to complete the degree as initially described or to expand the project into a joint program dissertation. In the latter case, the student applies to the joint-degree program.

Requirements

Students in the joint program are required to take only 27 credits in Philosophy. Joint Program students need to take only two of the three seminars in the history of philosophy that are required for the regular Philosophy PhD. program, and the 3-credit seminar "Intermediate Logic" is not required. Students are required to take the two-course logic sequence, and two other basic courses in mathematics (students can complete a basic course by taking or testing out of the basic course). Philosophy graduate students doing the MSIM degree or the joint PhD are expected to complete ten total courses in mathematics, but up to four of them can be mathematics-intensive courses outside the mathematics department.

Joint program students take the Mathematics Department's oral candidacy exam instead of the Philosophy Department's oral exam. This consists of both the basic and advanced exams in logic and the basic exam in one other area.

Matteo Bianchetti, MSIM: "Infinite Time Computation: Strong and Weak Infinite Time Turing Machines" (C. Franks, J. Knight); Ph.D. in Philosophy: "Geometric representations in mathematical problem-solving. Intuition and creativity" (C. Franks), Current Placement: non-academic

Paul Trần-Hoàng , MSIM: "Model-Theoretic Galois Cohomology" (A. Pillay, C. Franks); Ph.D. in Philosophy: "Model-Theoretic Approaches to Theoretical Equivalence and Reduction" (T. Bays, C. Franks). Current placement: Visiting Assistant Professor, Vassar College

Graham Leach-Krouse , Joint Ph.D.: "Conceptions of Absolute Provability" (T. Bays, M. Detlefsen, P. Larson). Current placement: Associate Professor, Department of Philosophy, Kansas State University.

Chris Porter , Joint Ph.D.: "Mathematical and Philosophical Perspectives on Algorithmic Randomness" (P. Cholak, M. Detlefsen, C. Franks). Current placement: Assistant Professor, Department of Mathematics and Computer Science, Drake University.

Sean Walsh , Joint Ph.D.: "Arithmetical Knowledge and Arithmetical Definability: Four Studies" (P. Cholak, M. Detlefsen). Current placement: Associate Professor, Logic and Philosophy of Science, UCLA

Andy Arana , Joint PhD: "Arithmetical Investigations: A Study of Models of Arithmetic and Purity of Methods" (M. Detlefsen, J. Knight). Current placement: Professor of Philosophy, University of Lorraine and Archives Henri-Poincaré.

Graduate Study in Logic at Berkeley

The Ph.D. Program in Philosophy . Students who choose to specialize in logic within the context of this program are expected to obtain a broad education in philosophy.

The Group in Logic and the Methodology of Science administers a program leading to the degree of Ph.D. in Logic and the Methodology of Science. The Group is not a part of the Department of Mathematics or of the Department of Philosophy; rather, it is an independent program staffed by faculty members from Mathematics and Philosophy, along with several from Electrical Engineering and Computer Science. Students who want to pursue the Ph.D. in Logic and the Methodology of Science should apply directly to the Graduate Program in Logic and the Methodology of Science, rather than to Mathematics or Philosophy.

Students in the L&M program are expected to study both mathematics and philosophy, though they need not meet all the breadth requirements for a Ph.D. in either field. They must pass one examination in the foundations of mathematics, one examination in philosophy (Area I), and a third in either mathematics or philosophy. Although there are no graduate instructorships in Logic and Methodology of Science, students in this program may, if qualified, hold graduate student instructorships in the Department of Mathematics or in the Department of Philosophy.

The Department of Mathematics administers a program leading to a Ph.D. in Mathematics. Students in this program may specialize in the foundations of mathematics, but are also expected to study other aspects of mathematics. In particular, they must pass departmental qualifying examinations in two other areas as well as in the foundations of mathematics. The Department of Mathematics also has a program leading to an M.A. degree.

Logic Events

Logic colloquium.

The Group in Logic and the Methodology of Science sponsors a biweekly logic colloquium , with talks by mathematicians, computer scientists, and philosophers.

Working Group in the History and Philosophy of Logic, Mathematics, and Science

The Working Group in the History and Philosophy of Logic, Mathematics, and Science , jointly sponsored by the Philosophy Department and the Doreen B. Townsend Center for the Humanities , sponsors monthly talks, many of them on topics connected to logic.

Berkeley-Stanford Circle in Logic and Philosophy

The Berkeley-Stanford Circle in Logic and Philosophy brings together graduate students from UC Berkeley and Stanford University to discuss research at the intersection of Logic and Philosophy.

Mathematical Sciences

Mellon college of science, 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 page .

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.

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