Math graduate schools almost always pay students a stipend, but this can vary from program to program. For example, a program might only cover the school year, and not the summer months. Stipends are also often dependent on teaching. Fellowships have three main benefits. First, they typically pay more than the university's stipend. Second, fellows have fewer teaching requirements. Thirdly, being a fellow looks good on your resume.
The most common fellowship is the NSF Graduate Research Fellowship Program (GRFP). The NSF GRFP is only available for US citizens, nationals, and permanent residents. If you qualify, you should apply! The NSF awards GRFPs by field depending on what percentage of applicants are from that field. So, applying is helping out the math community.
The National Science Foundation Graduate Research Fellowship Program (NSF GRFP) is a three year fellowship with a $34,000 yearly stipend. Applying requires writing a personal and graduate research plan statement. Both statements are judged on "intellectual merit" and "broader impact." Broader impact means two things: how your proposed research impacts the real world, and how you've helped others in your community. For example, if you took an active role in an affinity group, you can discuss that experience. Mentioning you are interested in collaboration and cross-disciplinary study, makes the NSF happy.
The research proposal can be tricky to write. Most people applying for math grad school haven't done research, so coming up with a project to do in grad school seems out of reach. Keep in mind, no one is going to make you carry out the research you propose. Deciding what research to write about is something your advisor or a grad mentor can help you with.
- You may apply again for the NSF GRFP in the first or second year of graduate school.
- While on the NSF GRFP, you typically don't teach/TA/grade etc.
- The NSF GRFP application is due in October. That means you should try to ask your letter writers around September.
- You can choose which years you use the NSF. For example, some schools offer first-year fellowships that relieve you of teaching duties. If you wanted to avoid teaching, you could then use the NSF for the second through fourth years of grad school.
Personal TestimonyBelow is a more personal experience of a current MIT graduate student with the NSF GRFP:
"I would strongly recommend that any U.S. student applying for math graduate school first apply for the NSF GRFP fellowship. Even if you do not get the fellowship on your first try, it helps organize your thoughts about your goals and gives you a good corpus of material to draw from in your personal statements for individual schools’ applications. It can also be useful to send NSF application materials to potential recommenders to remind them of the chronology of your academic career and some of your major accomplishments. Moreover, many graduate school applications ask if you have applied for external fellowships, and if you have applied for fellowships like the GRFP it shows that you have taken initiative.
If you have trouble narrowing down what you want to study, do not let this dissuade you from applying for the NSF graduate fellowship as a senior. If you awarded the fellowship, you can change your field of interest within math even after accepting the fellowship.
Regarding the project proposal: a research proposal is not a firm commitment to do a particular project. Particularly in pure math, students’ interests may evolve during graduate school if they are exposed to new areas through their coursework or discussions with professors in their new department. It is most important for reviewers to see that you are interested in a mathematical problem, that you have taught yourself about it, and that you have ideas for techniques that may be relevant."
The Department of Defense's National Defense Science and Engineering Graduate Fellowship Program is also a three year fellowship. Unlike the NSF GRFP, you cannot defer the NDSEG. Another difference between the NSF and the DoD fellowships, is that the NDSEG is only given to people whose area of study relates (very loosely speaking) to things the military cares about. For example, most areas of applied math, probability, combinatorics, and number theory if you can make a connection to cryptography. You can't have both the NDSEG and the NSF GRFP.
If you are in applied math and plan on working on computational research, consider applying for the Computational Science Graduate Fellowship, which is available to U.S. citizens or permanent residents. It's renewable up to four years, and has a yearly stipend of $38,000 with a yearly $1,000 academic allowance. There is a annual "program review" held in Washington, D.C. every July. There is a "program of study" requirement, which consists of six courses broadly in areas of computing, math, and applied fields.
The fellowship encourages interaction with US National Laboratories. One of the program requirements is to complete as 12-week long practicum (internship) with a National Lab on a research topic outside of your direct research area.
- You may apply for the DOE CSGF as an undergraduate senior, the year before matriculating into a Ph.D. program, or during your first of graduate school.
- While on the DOE CSGF, you typically are not allowed to teach/TA/grade etc.
- The DOE CSGF application is due in January, which is later that most fellowships and graduate school applications.