By Alvaro Carbonero, Brittany Gelb, Amaury Miniño, Vanessa Sun, and Lee Trent
Introduction
What is an REU? REU stands for “Research Experience for Undergraduates.” REU’s are typically 6-10 week long summer programs hosted at colleges or universities. To be officially considered an REU, the program generally has funding from the National Science Foundation or the National Security Agency, but there are other research programs that are very similar which are supported through other funding sources. REU’s invite undergraduate students to apply to their program to spend the summer at their college or university (although the pandemic has changed this) and work on an individual or group research project advised by mathematicians with research and mentoring experience Undergraduates are paid to participate in these programs, and are typically housed on campus or nearby (with the costs often covered by the program directly). The faculty members will have carefully selected and curated problems that they believe are accessible to undergraduates and they provide the necessary background. If an REU would be your first research experience, not to worry, that’s what they’re designed to be and your REU advisor will know how to support and mentor you!
The authors of this blog post have successfully applied to REU programs in the recent past and some of us have been involved in multiple REU’s or other similar summer programs. In fact, we recently organized the Online Undergraduate Resource Fair for the Advancement in Academia of Marginalized Mathematicians (OURFA2M2) to bring together faculty representatives of undergraduate career-advancement opportunities, students who have recently participated in such programs, mathematicians whose career trajectories were impacted by such programs, and others within the mathematics community to discuss and share resources related to these opportunities. Given our experiences along with the information we learned from our conference participants, we now share some advice with those applying to an REU.
First piece of advice: You should NOT rule yourself out from applying to REUs.
We truly believe that the only failure is the failure to try. There are a myriad of reasons that we or people we know considered not applying to REU programs. These include:
- You never participated or succeeded in a math competition.
- You have only completed a few math classes or have not taken many (or any) upper-division mathematics classes.
- You have never done research before or don’t know what the research process in mathematics entails.
- You don’t know anybody from your school who has gone to an REU program.
- Your school is not nationally recognized for their math department.
- Your overall GPA is not high.
- You don’t feel confident in your mathematical abilities.
- You believe you will be rejected (for any reason above or others).
If you have considered not applying to REU programs for one of these reasons, we want you to know that there have been many successful applicants in your shoes before (including us) so you can and should apply!
Finding an REU
Here is a presentation from our conference, OURFA2M2, that includes information on how to find REU’s and other research programs. Past eMentoring Network blogs also provide a list of REUs aimed at first and second year undergraduates. You can find that blog here. When you visit an REU program’s website you’ll likely find descriptions of the individual project topics they are planning for the upcoming summer. We encourage you to be willing to work in areas of mathematics that you may not have much background in. What’s perhaps most important is that you choose a topic you find interesting, so that if progress is especially slow or difficult you are still fueled by your interest in the topic of investigation.
Selecting programs
When we asked our fellow recent REU participants about application advice to share with you, one recommendation was repeated multiple times: Start as early as possible and be organized. You can use a spreadsheet to keep track of your applications, with columns for due dates and each individual piece of the application. Likely you will need a personal statement, two letters of recommendation, and a CV/resume. A past eMentoring Network Blog contains advice on asking for letters of recommendation, which you can find here. You can note down when parts of the application are completed and submitted and which you still have to finish.
Another piece of advice that was emphasized is that fit is very important. It should be possible to tell from the REU website what the target audience is in terms of mathematical experience. Ask yourself what you want to gain from an REU and make sure that the programs where you apply align with those goals. You should be excited to join the program, even if the research area is largely unfamiliar to you. If in doubt of whether a particular program might be the best suited for your goals, speaking with a trusted mentor could be very helpful.
REU programs are highly competitive and you should apply to several programs to maximize your chances of an acceptance. Most students apply to around 10-15 programs, and at least 8 is reasonable. Because these programs are competitive, it’s wise to apply to a wide range of opportunities, like counselorships, internships, and research programs that are not REU’s — Some alternatives are provided in the presentation linked here.
Advice on application materials
After selecting the programs that you will apply to, you will have to start working on the application materials they require. Here we provide advice about some of the most common application materials.
Personal Statement
In the personal statement, you should demonstrate the skills and experiences you have that would make you a successful participant in this research program. These skills do not necessarily need to come from previous mathematics research experiences. Depending on whether the proposed REU projects are individual or collaborative, you can talk about experiences you’ve had working independently or on a team. For example, maybe you have persevered to solve a particular problem or understand the material from a challenging class, or you have developed collaboration skills by working on homework or projects with other students. Articulating your interest in a specific project offered by the REU can be beneficial. For example, did you take a class related to the research area? If so, what did you enjoy about it? Did you listen to a lecture on the topic that caught your interest? One of us knew nothing about graph theory beyond an hour-long research talk she attended, but she made connections between the visual nature of the subject and how she generally enjoyed visual mathematical problems.
Be sure to detail why you are applying to an REU and why you want to do research. Do you want to figure out if a research career is right for you? Do you want experience in one specific field to decide if you like it and would potentially pursue that area in graduate school? Do you already find the subject fascinating? If so, why?
Do not forget to personalize your statements to each of the programs you are applying to — we know that this means you will have to work longer on your materials and we believe this will lead to a more favorable outcome. Explain what you expect to get out of that specific program and why and how you will benefit from those experiences. Additionally, be sure to speak about why you and the program you’re applying to will mutually benefit each other. This means that you should speak about how you will be an asset to the program. What experiences, interests, personality traits, technical or “soft” skills, or combinations thereof do you have that make you a uniquely qualified person that they definitely want on their team? As we stated previously, these experiences don’t need to have come from previous research experiences. For example, many university classes ask students to do a final project or a presentation. What did you learn while doing it that would benefit an REU team?
In the personal statement, you can discuss any challenges or barriers that have influenced your academic journey and the opportunities you have had access to. For example, are you a first generation college student, or do you come from a low-income family? If appropriate, mention that research opportunities are limited at your home institution, as likely this makes you the target audience of many REU programs. You can also discuss how aspects of your identity and life tie into your mathematical journey, and how an REU might help you overcome challenges or barriers.
Lastly, have multiple people review your writing if you can. You can ask professors, mentors, friends, and past summer program participants to provide feedback on your personal statement. Different people will have different perspectives, and it is generally helpful to clarify what feedback you are looking for, such as typos, grammar, organization, style, or content. Ask people who know you well to edit, as they know your strengths (and weaknesses) and which of your past experiences you can use to make the most compelling case that you are a good candidate for the program you’re applying to. Many universities also have resources to help you create applications, such as career centers and writing centers. We encourage you to make use of those offices and the resources they provide.
Supplemental application materials
Some programs ask for the answers to multiple specific questions. If the application also requires your personal statement, see this as an opportunity to be more specific about why you should be selected to participate in the program. Even if you feel you answered a question in your personal statement, don’t answer a question with, “see my personal statement,” follow the directions and include the information they ask for in the places they ask for it. Of course, do make your best effort to take these questions seriously and your answers should also implement feedback if at a minimum for grammar and typos.
Some applications ask you to mention your favorite mathematical theorem or concept. Such questions are there to gauge your interest in math and your ability to communicate about math, not to pick an impressive theorem or to prove that you have specialized knowledge. It’s okay to speak about something complicated if it’s something you’re interested in but don’t understand well — as long as you are honest about your level of understanding. You could also talk about what you are intrigued by and what new theorems or concepts you hope to learn in your coming courses. We encourage you to not try to appear more knowledgeable than you are. Be honest and genuine.
Recommendation Letters
When you apply to an REU, you will likely need to ask college professors for recommendation letters for the first time. You should ask professors who know about your mathematical ability, work ethic, ability to collaborate with other students, perseverance, intellectual curiosity, enthusiasm for learning, and/or personality to write your recommendation letters. If you’re reading this well in advance of when you first plan to apply to programs, start thinking about building those relationships with your professors. Most programs require at least one letter from a mathematics professor.
Tell your recommenders the different programs and their deadlines. Give them plenty of time — at a minimum a few weeks. You should consider having a draft of your application materials ready before or soon after you ask, since these can be helpful documents for your recommenders. Sometimes a recommender will request that you share these materials with them before they write the letter, but if they don’t, you may offer it anyway. Just as you tailor your personal statements to particular programs, consider using different recommenders for different programs. If you have multiple strong relationships with recommenders, you can match your recommenders to programs by their professional connections or research interests. If not, though, that’s okay, too! Remember that finding good recommendation letter writers may not always be an easy task. It can be hard to establish healthy and close professional relationships with professors.
The presentation we linked in the beginning of this blog post has an entire section (Networking/Mentoring) with advice that can help you establish good relationships with potential recommendation letter writers. We emphasize that this needs to be done with ample time so as to be able to request the letter in time for your application deadlines.
CV/Resume
There is already much advice on the internet about putting together an effective CV or resume. Career centers at colleges and universities can often provide templates, advice, and feedback. Consider tailoring your CV to emphasize skills or subjects you think will most appeal to each program. Here we provide copies of our current CVs as examples.
Submission
When creating your materials, be sure to be consistent with your formatting. Font type/size, paper margins, writing style, etc., should be consistent for everything that you submit. Even though you must submit multiple files, think about them as part of one application package which will be viewed together and should look like they belong together. Include your name and the program you’re applying to on each document, and be consistent in how you name files. One naming convention we recommend is to include your name and the document type: LastName_CV, LastName_transcript, LastName_personal_statement, etc.
To reiterate the earlier advice, start your applications early enough so that you can submit on time. If you are late, do request an extension, especially if you can articulate a specific reason for the delay. However, note that even though some programs may not grant extensions as they are highly competitive, moving from guess culture to ask culture can be beneficial as you learn to advocate for yourself within math spaces. Also, if you do not have the full application materials at the ready, offer to share the materials you do have prepared with them so they can begin looking over your application while you finish the rest.
Be aware of the deadline for your letter writers (which may be different from the application deadline) and feel free to check in with them about whether they’ve submitted. Sending a short email with a friendly reminder of upcoming deadlines a few days in advance is often very welcomed by professors. In most cases, you should receive confirmation that your application or letters of recommendation were received. Feel free to ask for confirmation if you don’t receive it automatically.
Accepting an offer
If you’re accepted to a program and it is not your top choice, you can contact the directors of the other programs to inquire about your application’s status. Once you have an offer from an REU, we highly recommend scheduling a meeting (either via a phone call or video call) with your potential REU mentor to determine if the program is a good fit. If such a meeting is not offered with the acceptance letter, know that it is very normal to ask. We think that this bank of REU/grad fair questions is a good starting point for questions you can ask during that meeting. Don’t forget to learn about the living/housing situation of the program, since this can have a lot of impact on your personal wellbeing, and you need to be happy and well to do good research. With this in mind, here are some additional questions you can ask: Will REU participants live together in a house or in dorms? Can students access the gym? Are there restaurants nearby? Is there a quiet place where you can practice your musical instrument? Does the program have activities to provide social interactions among participants and to build community? Alternatively, if the program is fully online, you should ask questions relating to your participation virtually. For example, you could ask: Will the program supply needed technology? Will the program be flexible with your schedule given that others within your household share internet/devices?
If you need it, you can also ask for extra time to make your final decision, particularly if you’re waiting on a decision from other programs. Some but not all REU programs are in agreement that you do not have to accept an offer before the Common Reply Date, which is typically on March 8th. It is courteous to other applicants and important to decline an offer as soon as you know you will not attend the program. Once you have accepted an offer, you should withdraw your remaining applications or immediately decline any other offers that you receive.
Preparing for the REU
Don’t stress! You generally won’t be expected to do much to prepare for the REU before it begins, but it’s a good idea to check with your REU project mentor if they have specific skills that you can work on or review before the program begins. It will be useful to know some LaTeX as you participate in an REU and, in fact, throughout your mathematical career. Your program may give you specific tasks to help you learn but if not, you can consider learning some on your own. We recommend using overleaf.com, which is a free LaTeX program online with many templates to get you started.
If you are rejected…
Some REU programs only send out acceptances and don’t send out rejections. This means you might not get an email from programs that are rejecting you. If you’re not sure about your status, you can ask. Remember that not everyone can get into their top choice, as most REU programs receive hundreds of applications. Do keep in mind that we know of many successful students with bright mathematical careers ahead of them that never participated in an REU. If you are rejected, know that you are not alone. An REU rejection does not say anything about your future in mathematics! If you do not get into an REU this year, seek other opportunities and if possible, apply again next year. Your application will only get stronger with one additional year of math courses and experiences.
Acknowledgments: We are grateful to many people for their advice throughout our careers which has made this post possible, including the speakers at OURFA2M2 2020, the 2019 Lafayette College REU cohort, the 2019 and 2020 MSRI-UP cohorts, and many professors at our institutions and elsewhere.
Author biographies:
Alvaro Carbonero is an undergraduate at the University of Nevada, Las Vegas. He has participated in the REU programs at Lafayette College and Rochester Institute of Technology.
Brittany Gelb is an undergraduate at Muhlenberg College. She has participated in the REU programs at Lafayette College and DIMACS.
Amaury Miniño is a first-year PhD student at Colorado State University. He graduated from Florida Atlantic University and has participated in the F-LEARN program and the Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP).
Vanessa Sun is an undergraduate at Macaulay Honors College at Hunter College, City University of New York (CUNY). She participated in the Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP).
Lee Trent is pursuing her undergraduate degree at Rose-Hulman Institute of Technology. She has been a counselor at Rose-Hulman AMP and PROMYS and participated in the REU at Grand Valley State University.
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