Lena Ji (SMALL ’15) is a second-year graduate student studying algebraic geometry at Princeton. She was sort of clueless when applying to REUs and hopes this post can be somewhat helpful to anyone else in the same position.

[Editor’s Note:  Lena is one of the smartest mathematicians I know, no matter what she tells you.]

How to Apply to Math REUs

For undergraduates potentially interested in going to graduate school for math or just curious about math research in general, REUs are a great way to gain research experience. I attended two REUs in the past and had a great experience, so I’ve put together this page in hopes that it might be helpful to anyone who’s considering applying. A lot of inspiration for this page came from Alex Lang’s NSF GRFP page, which is an excellent resource if you are a junior and plan to apply for the NSF next year!

Contents:

1. What is an REU?
2. Outline of Application Process and Components
3. Factors to Consider When Applying
4. General Tips
5. Recommendation Letters
6. Personal/Research Statement
7. What to Do After You’ve Been Accepted

Disclaimer: All information on this page is based on my limited personal experience, and I make no claims to objective accuracy. If you disagree with anything I’ve written or think I’m wrong about something, please let me know! Any feedback is welcome, and if you want to share personal statements you’ve used in the past that would be super appreciated!

What is an REU? 

An REU (research experience for undergraduates) is a summer program designed to introduce undergraduates to mathematical research. They typically run for about 6-8 weeks, and usually pair an undergraduate or a small group of undergraduates with a mentor (faculty member or postdoc or grad student) to work on a project. REUs are a full-time commitment – a stipend is provided (usually restricted to US citizens or permanent residents), and most places will provide housing and/or meals. In addition to research, most REUs will organize social events and fun excursions (so you won’t be spending all summer just working).

There are several websites listing the REU programs running each year. Be aware that these lists may not be complete and the programs listed might not necessarily take place every year!

• Math REU Programs
• NSF REU Sites
• AMS List of Math REU Programs

Outline of Application Process and Components 

Most REU application deadlines are in February, but it’s important to start early and not wait until the last minute. Winter break is a good time to work on applications, but most applications should be up by November and it never hurts to start thinking about them earlier. Recommendation letters should be requested early (at least a month in advance is better if possible), and transcripts should also be ordered in advance as it sometimes takes a while to process them.

Many programs have moved to using MathPrograms.org to apply, which simplifies the process a lot. An application usually consists of

• Personal information and CV – not all programs require a CV but it’s generally useful to have, especially if you’re applying to grad school
• Transcript (usually unofficial ones are ok) – some programs also ask for a separate list of math classes you’ve taken (with grades and textbooks listed)
• Personal/research statement
• 1-3 letters of recommendation (usually 2) – in my opinion this is the most important part of your application

Factors to Consider When Applying 

• What kind of research do you want to do?  Read the project descriptions carefully to see if you’re interested in the type of math they involve. Looking at projects from previous years is helpful, and it’s also useful to look into what kind of research the project leader does, as the REU project they supervise is often related to their own research. Many projects are in combinatorics, graph theory, and elementary number theory, but many programs are branching out into other topics – a lot of these projects involve problems in various fields that can be tackled using more elementary methods.The mentor’s style is also an important factor to consider. Do you want someone more hands-on or do you want to be more independent? How often do you want to meet your mentor and the rest of your research group? Do you want a one-on-one experience or do you want to be in a larger group? Do you care if you’ll mostly be working with a grad student or with a professor?
• What do you want to get out of the REU?  Do you want to get a taste of what math research is like? Do you want to be published? Do you want to learn a lot of new math? Do you want to attend conferences? Different REUs have different focuses, and it’s important to know what you want to get out of your experience.
  • Some programs focus on an immersive learning experience, where you pick one topic and study it in depth. The level of the material and the extent to which you learn about it are both greater than what is covered during the ordinary school year. One example of this type of program is the UChicago REU.
  • Some programs focus on original math research, which otherwise students typically don’t experience until after the first few years graduate school (unless you do a senior thesis or some other project). The REU mentor will usually provide a lot of guidance, and I think it’s useful to see what research is like before applying to grad school. These programs typically don’t teach much theory beyond what is immediately needed for the research problem. One example of this type of program is the Duluth REU.

  There is no “better” type of program – it all depends on what you want. If possible, look at the work that people from previous years have done – sometimes this is posted on the REU website, and sometimes past participants will put their work up on the arXiv, which you can find if you search for their names.

• Eligibility requirements.  Make sure you’re eligible before you apply! Many REUs will not accept international students due to funding restrictions, and some will take international students but ask them to find their own funding (for example through their home institution). It might still be worth applying since some programs do have the funding to admit some students who are not permanent US residents – just be honest about your status and see whether or not they are flexible.It’s important that you meet the requirements for background knowledge. Some programs do not require any background, some explicitly state that they require a linear algebra and proof-based class, and some (such as St. Mary’s College of Maryland) specifically target students who have not taken any upper-level math. Some programs have minimum GPA requirements. Also, some programs are only open to students enrolled at the home institution.
• Location.  As you’ll be living here for several weeks over the summer, location can be an important factor – what is the weather like in the summer? How close is it to your home and/or home institution? How are you going to get here, and is transportation covered by the program? Are you interested in attending graduate school here.
• Timing.  Make sure you don’t have any conflicts with the start and ends dates of the program. Some REUs are more flexible about this than others, and it doesn’t hurt to ask.
• Finances.  REUs have stipends that vary depending on the program. Some cover housing and/or food costs, and some provide support for transportation to/from the program. Some programs that are not NSF-funded are able to provide financial support to international students.

Don’t worry if you don’t know all the specifics at the time you’re applying though – your goals and priorities might change between the time you apply and the time you have to accept an offer (usually around early March).

General Tips 

The application process is free, so don’t limit yourself to just a few programs. At the same time, applying is time-consuming and a lot of work, and it’s a bad idea to just blindly submit the same application to a bunch of different programs. I would recommend picking 1-2 specific programs that you really want to attend and applying to no more than 10 total (all of which you are genuinely interested in).

You can contact faculty members ahead of time to tell them that you’re interested in working with them, as they can often influence application decisions. Be sure to actually spend time looking into their work though – don’t just send some generic email and expect a response. Oftentimes you may not get any response, but this is normal as they are extremely busy too; don’t let this discourage you from sending more emails to other faculty members whose research you’re interested in.

REUs are extremely competitive, with hundreds of students applying for a very limited number of spots. Don’t be discouraged if you don’t get into one your first try! These programs are very competitive, and this is by no means a comment that you’re somehow not “good enough” – there’s a lot of luck involved and often there might be something specific that the coordinators are looking for. If you don’t get into an REU, you can ask a faculty member at your home institution if they would be willing to oversee a summer project or reading course with you (such as a reading course or helping with their research). When you reapply the next year, you’ll have a stronger application.

Recommendation Letters 

This is the most important component of your application. Most REUs require 1-2 letters of recommendation, and some will require a letter from a previous REU advisor if you’ve done one before. It’s very important that you find someone who can write you a detailed and enthusiastic letter, and it’s useful to show them your application before they write the letter so they know how you’re presenting yourself. It is better to have a glowing letter from a less senior person who knows you well than it is to have a lukewarm letter from a famous person who doesn’t know you.

It’s okay to ask for letters from non-senior faculty (e.g. postdocs), but I would avoid asking graduate students for letters. Don’t ask for letters from people whose classes you didn’t excel in – you want someone who can speak positively about your mathematical ability and potential to do research! In my limited view, I think you should ask for letters from the following people:

1. Someone who you have directly done research with already – e.g. previous REU mentors, someone at your institution who you did a project with during the school year. This doesn’t have to be limited to math, for example if you’ve worked in a lab before a letter from the PI would be good. According to a professor I talked to before writing this, “People want to see the ability and drive of the applicant. In some sense, math knowledge is not as important as these things.”
2. Instructor of a math class who you directly interacted with and who remembers you – e.g. a class where you asked a lot of questions or went to office hours, someone who oversaw an independent reading course
3. Other faculty members who you know and have interacted with, if they have something concrete to say.

Your letter writers will likely ask for your CV and transcript, or some other document about your academic background, so prepare these in advance. If your letters haven’t been submitted close to the application deadline, send them a friendly and polite reminder a few days before the letter is due. Remember, your letter writers are busy people and they are doing you a favor! Be sure to thank your letter writers afterward, and keep them updated.

Personal/Research Statement 

This is the only part of your application that you can completely control, so while it doesn’t matter as much as your letters, it’s still important to have a compelling and informative essay. These are usually around 1-2 pages long (single spaced), and should describe why you’re interested in the project and the background and qualifications you have. Some programs have an outline of what you should write, and generally my impression is that they should include the following:

• Why do you like math? Be specific about why you find it interesting and how you became interested in it. Citing specific examples (e.g. a class or a theorem) is better than something generic and broad like “math is beautiful”; presumably everyone applying for the REU thinks so too.
• Why do you want to do research this summer? Don’t write a generic statement that doesn’t mention any of the specific projects and why you are interested in those projects in particular. It’s ok to reuse most of the same statement for different programs, but at least have a few sentences about the particular REU you’re applying to.
• Talk about your previous research experience (if any) – what did you get out of the experience, what was the problem studied, what results did you get, and how did you go about solving the problem?
• Mention any previous coursework and independent reading you’ve done that directly relates to the research project. Specifics are good.
• If you’ve had previous experiences where you’ve worked with others on a research team, it’s good to mention this teamwork. Most REUs have students working together in groups with one another, so it’s important for the organizers that you be able to work the other participants.
• What are your plans after graduation? How will this REU contribute to them?
• This (and potentially letters) is the place on your application where you can explain poor grades if needed, but don’t spend too much space on it.
• Ask another person to proofread it!

Here are some real life examples of successful statements that have worked in the past:

• Sarah Fleming, Emory REU 2016 [cover letter] [research statement]
• Lena Ji, SMALL 2015 [personal statement] (Disclaimer: it’s fluffy and nonspecific and not that good.)

What to Do After You’ve Been Accepted 

Many programs have agreed to the Common Reply Date agreement, which means that students accepted to these programs will not be required to accept or to decline an offer until a fixed date that’s the same for all REUs in the agreement (March 8, 2018). This means you have until this date to make a decision – it’s a bad idea to accept an offer and then back out later.

If you’re waiting to hear back from somewhere else before giving a program a response, let the program director know this! Also, don’t give up hope if you don’t hear back for a while – sometimes more offers will be sent out if the initial ones aren’t all accepted. On that note, if you’re sure you don’t want to attend an REU, you should decline it as soon as possible so they can accept other students who might actually attend.

If you’re having difficulty deciding where to go, don’t hesitate to talk to people who’ve participated in the past or attend the institution where the program is hosted. Emailing is a good way to get specific information too – some people might ignore your email but others would be happy to reply and share their experiences or link you to the project that they worked on.

Good luck with your applications!! 

Any and all comments and suggestions are welcome at lji [at] math.princeton.edu.