# Math/Philosophy Math Graduate Programs

### MSIM PROGRAM FOR PHILOSOPHY PhD STUDENTS, MAMP PROGRAM FOR MATHEMATICS PhD STUDENTS, AND JOINT MATH/PHILOSOPHY PhD PROGRAM

In collaboration with the Philosophy Department, the Mathematics Department at Notre Dame offers several joint programs for students interested in Mathematical Logic as well as Philosophy. The acronym MSIM stands for Master of Science in Interdisciplinary Mathematics, and this degree is given by the Mathematics Department. The program is available also to students from fields besides Philosophy. See this link: https://math.nd.edu/graduate/msim-degree/ for more information about joint Mathematics/Philosophy graduate degrees at Notre Dame. If you are a PhD student at Notre Dame interested in the MSIM degree with your primary area of interest not in Mathematical logic and Philosophy, the MAMP (Master of the Arts in Mathematical Philosophy) program may be of interest. See https://philosophy.nd.edu/graduate-program/mathematical-philosophy-minor/ for additional information about MAMP. This page gives instructions for how to apply for the MSIM, MAMP, or the joint PhD program in Mathematical Logic and Philosophy. Please contact the Math or Philosophy DGS if you have additional questions.

Admission to either of these degree programs requires the approval of both the Mathematics and Philosophy Departments. Similarly, any extension of the deadlines discussed below need the approval of the Mathematics and Philosophy Departments. Approval by the Philosophy Department requires primary approval by the Logic Group within that department, and final certification by the Philosophy DGS. Approval by the Math department requires approval by the Logic Group within that department in consultation with the Math DGS and if necessary, the graduate committee. As these degrees are additional degrees beyond the student’s Ph.D. program, they are not funded separately. We expect that the students earning these degrees will be exceptional.

A student in the joint PhD program will have to find a Mathematics adviser and a Philosophy adviser. The student will write a single PhD thesis, but it may have separate parts with a Math or Philosophy focus.

#### Philosophy Primary

An essential criterion for admission to the MSIM or Joint Degree for a Philosophy graduate student by the mathematics department is the approval of a mathematics department faculty member who agrees to oversee the student’s work. This will normally require that the student has become integrated into that faculty member’s research group, and has proposed a viable area for research. It is the student’s responsibility to find their own advisor. Given that, the path towards admission to the MSIM or Joint Degree is as follows:

- Year 1 and 2 (coursework): In addition to Philosophy coursework, the student takes the Mathematics department’s Logic Sequence Math 60510 and Math 60520 in Year 1. The student is also required to take two additional basic courses in mathematics. Basic Algebra I and II is a common choice, but other choices are possible. These courses should be completed in the first two years. S/he also, in this period, plays an active role in some part of the Mathematics department’s on-going research seminars, lectures, etc.
- Year 2: The student finds a faculty member willing to supervise some advanced work in that faculty member’s area. This might be over the first summer, during the second year, or during the second summer. The student should become well-integrated into the research group of the intended supervisor and take topics courses in Logic.
- Application to the MSIM program is made prior to the start of Year 3, and we encourage applicants interested in continuing to do the joint PhD program to apply well before the start of year 3. The application will include a description of the courses to be taken for the degree, and of the proposed Master’s thesis topic, both of which will have been designed in consultation with the proposed advisor along with letters of support from their advisors. It is expected that the student’s work in Mathematics classes outside Logic will be above average and similarly with their work in philosophy.
- If the student is admitted to the MSIM program, s/he will work during Year 3 with the Mathematics advisor on their thesis topic.
- Students interested in pursuing the joint PhD program should take the oral exam in Mathematics by the beginning of Year 4. This oral is understood to be similar to the one taken by students pursuing a Ph.D. in Mathematical Logic. Passing this oral exam is required to earn the Joint Ph.D.
- While working towards the MSIM degree, a student interested in pursuing the joint PhD program must express an intention to apply by the end of May of Year 3 and apply by the beginning of Year 4. An application consists of a description of the courses to be taken for the degree, a research proposal, hopefully some completed research and letters of support from their advisors. If the decision at that stage is that the student needs further work, then the student may submit a revised application during Year 4. In any event, if a philosophy student is to be accepted to the joint PhD program, this must happen by the first day of classes in the 5th year.
- If the student in the MSIM program is not admitted to the Joint PhD program, s/he will normally finish the requirements for, and be awarded, the MSIM degree on route to completion of the Philosophy PhD. In this case we expect the MSIM thesis to be completed by the end of Year 4. A public defense of the Master’s thesis is expected. The defense should happen by early in Year 5.
- If the student is admitted to the Joint PhD program, s/he need not complete the requirements for the MSIM degree. Research completed in pursuit of the MSIM thesis might be incorporated into the research for the joint PhD dissertation. We do expect this degree to be completed within 6 years.

#### Mathematics Primary

An essential criterion for admission to the MAMP or Joint PhD. for a mathematics graduate student by the Philosophy Department is the recommendation of a Philosophy Department faculty member who agrees to oversee the student’s work. This will normally require that the student has articulated a viable area for research and demonstrated to the satisfaction of the faculty member relevant competence to undertake a research project in the area. It is the student’s responsibility to find their own advisor.

- Years 1 and 2: The student should enroll in approximately 1 research seminar in the Philosophy Department each semester. [Generally, four philosophy seminar courses with a heavy writing component are needed for a student applying to the MAMP or joint PhD program.] Knowing that the application to the MAMP includes the submission of a sample of philosophical writing, it is wise to make sure to take seminars with substantial writing components so that by the time of application the student will have experienced several episodes of writing and rewriting in light of instructor feedback. Students should check with the instructor whether the course has a substantial writing component. Most seminars will fit this description, but some Logic seminars will not. Note that all seminars taken prior to application to the MAMP will be retroactively counted towards fulfillment of the MAMP (and/or Joint PhD.) degree. For students interested in MAMP or the joint PhD program,the Mathematics department can delay two of the required basic courses to the second year to allow students time to complete their philosophy seminars.
- An application to MAMP or the joint PhD program should consist of a transcript, the written work from Philosophy seminars, and a research paper, together with faculty evaluations.
- Year 2 or 3: Application to the MAMP should be made at the end of year 2 or during year 3. Students with a definite expectation to eventually apply to the Joint PhD program are strongly advised to apply before the start of year 3. Students with no plan to apply to the Joint PhD. program should in any event apply to the MAMP before the end of their 3rd year of study, so that the commencement of their MAMP thesis research does not disrupt the timely completion of their Mathematics dissertation research.
- Applications for the Joint PhD. will only be considered for students in their first four years of graduate study, and admission to the Joint PhD. must happen before the start of the student’s 5th year. A student applying to the Joint PhD. program need not complete their MAMP thesis; in many cases the work going towards that thesis will be further elaborated as the Philosophy component of their PhD. dissertation.
- A student who does not apply to the Joint PhD should submit their MAMP thesis by the end of their 4th year.
- A student admitted to the Joint PhD program should have a research plan suited for completion of the degree by the end of their 6th year.