Applying to Graduate School in Math

Note that this is not meant to be a guide on how to apply to graduate school, just a resource with some pointers.

Some students with adequate background (typically, equivalent to the background provided by the Honors Track of the math major at Rutgers) apply to Ph.D. programs in mathematics. In addition to transcripts, educational history, and previous experience, there are several important components to many Ph.D. applications, some of which are listed and described below.

  • Application statements: statements of purpose, personal statements
  • Recommendation letters
  • The mathematics GRE subject test, if required

Application Statements

Generally, you can expect to see two types of statements when applying to graduate programs.

Statements of Purpose

In a Statement of Purpose, your objective is to justify why you are a good fit for the program you are applying to. You should mention your research interests, your background and how it prepares you for the program, specifics about the program (including any professors you may be interested in working with), and a bit on your long-term goals (what do you hope to do after graduate school?). Certain programs may have specific guidelines on what to write here. Typically, a Statement of Purpose is under 1,000 words in length.

Personal Statements

In a personal statement, the focus is on your personal experiences and how they have led to you pursuing graduate study. You can use these statements to describe how you will contribute to your community while a student at the program. Some schools have specific prompts for personal statements (e.g., tell us about a time you’ve faced a challenge), and personal statements are usually shorter than a statement of purpose.

Recommendation letters

This is generally considered the most important part of your application, especially for Mathematics Ph.D. programs. You will need 3 professors to write letters of recommendation for your applications. These professors should know you well and be able to meaningfully comment on your mathematical abilities and potential to contribute to research (not “this student got an A in my class”). Typically, your recommendation writers are professors you came to know through experiences such as advanced coursework (400 or graduate level), research experience, or independent studies.

Professors are busy people and will need time to write a letter for you. Ask them for a letter as early as possible, even if that is months before your earliest deadline! It can be as easy as sending them a few emails. They may ask you for various materials to help them write a letter for you, such as your transcript, CV, or statement of purpose.

Some math professors have webpages about what to do when asking them for letters, which can give you an idea of what you need to do. You can find one such page (with links to other such pages) on A. J. de Jong’s website.

The GRE

There is a specific GRE subject test in mathematics, which is not to be confused with the math portion of the general GRE test (which is similar to the SAT/ACT standardized tests, but for graduate school). The material on the subject test is much more advanced than what is on the math portion of the general test. More information, as well as a practice test, can be found in the official practice book. Additionally, some resources for test preparation are posted online by Ian Coley.

The test is only offered during 3 months in the year—April, September, and October—and you can only take the test once every 14 days, so plan accordingly!

GRE requirements vary by school. It can help to refer to this spreadsheet, which is often updated with the latest information on general and subject GRE test requirements for graduate programs in mathematics. For some programs where submission of the is optional, you can send in your scores if you feel that it may boost your application. Note that some of the more selective programs typically accept students who score around the 80th percentile or above (as indicated by UCLA).

Funding

Generally, you can expect Math Ph.D. programs to fully fund students, waiving most costs associated with attending the institution and providing a stipend to be used towards living expenses. This funding may come through a source such as a teaching assistantship.

There are external sources of funding for graduate school you can apply to in your senior year of your undergraduate education. The most popular of these for mathematics graduate students is the NSF GRFP, which waives all institutional costs for you and provides a stipend of $37,000 for 3 years; while receiving the stipend, you will not be required to take on TA or other roles for your funding. Useful information for applying to the GRFP can be found on the websites of Kenneth DeMason and Alex Lang.