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 (at Columbia University and SMALL at Williams College) 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!
Disclaimer: Everything stated on this page is my personal opinion; it is not the opinion of any institution or REU program that I’m affiliated with. This advice is based on my own limited personal experience, was largely written when I was a graduate student, and has not been updated since—in particular it has not been updated for COVID-19. Any suggestions for improvements are very welcome.
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, REUs will often organize social events and fun excursions.
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!
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. You should ask for recommendation letters early (at least a month before the deadline) and order transcripts in advance, as it may take 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
Read the project descriptions carefully to see what kind of math is involved. 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. It’s important to be open-minded—don't limit yourself to topics and areas that fit your current interests. There is a huge amount of interesting math out there, and an REU provides a great opportunity to learn new things.
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?
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.
There is no “better” type of program—it all depends on what you want. The two descriptions listed above are very broad generalizations that do not exhaustively describe all programs. 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 by searching for their names.
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 specifically target students who have not taken any upper-level math. Some programs have minimum GPA requirements. Some programs are only open to students enrolled at the home institution.
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?
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.
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).
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 top choices (it’s ok if you aren’t 100% set on one specific program when you submit your applications!) and applying to no more than 10 total (all of which you are genuinely interested in and really do want to attend). Make sure you carefully follow the instructions for the programs that you apply to.
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 often a lot of luck involved, and sometimes 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. Keep in mind that REUs are not necessary for going to grad school or for doing math research in the future, and there are many other fulfilling activities that you can do over the summer.
This is the most important component of your application (in my opinion). 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 ok to ask for letters from 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!
Some potential letter-writers could include:
Please request your letters at least a month in advance of the deadline—your letter writers are busy people! Make sure you have your documents prepared in advance, since, to repeat Ravi Vakil’s advice, it is in your interest to make your busy letter writer's job as easy as possible. It is also helpful if your letters mention what you are like as a person, since teamwork and collaboration are important parts of an REU and so coordinators may be less likely to choose someone who does not work well with others. (Thanks for Colin Defant for this tip!)
If your letters haven’t been submitted close to the application deadline, send a friendly and polite reminder—it is your responsibility to remind your letter writers of the deadline. Be sure to thank your letter writers afterward, and keep them updated.
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:
Here are some real life examples of successful statements that have worked in the past:
If you have a personal statement that you are willing to share and would like for it to be posted to help other future REU applicants, please email me at lenaji [at] umich [dot] edu. (These essays can also be anonymized and have identifying information removed.)
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 (usually in early March). 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 have questions about a program and you cannot find the answers on the website, it may be reasonable to email the program administrator about them, especially if you've been accepted to the REU. If you’re waiting to hear back from somewhere else before giving a program a response, let the program director know this! In some situations it’s also appropriate to ask for updates on the status of your application, for example if you have to respond to an offer from another program by a certain deadline. 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’ve been admitted to an REU that you are certain you will not attend, you should decline it as soon as possible so that they can admit other applicants.
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 may be happy to reply and share their experiences or link you to the project that they worked on.
Good luck with your applications!!