Research Experiences for Undergraduates, or REUs, are typically 6-8 week long summer programs designed to expose undergraduates to mathematics research. Participation in an REU is a fantastic way to get a feel for what research is like, and to help decide if pursuing graduate studies is right for you. Such programs usually accept a small number of applicants, and are usually in-person (with a notable exception being the online Polymath Junior REU). The following are things to keep in mind about REUs:
Admission to an REU is often extremely competitive, with acceptance rates <5%.
Participation is usually limited to US citizens and permanent residents. This is due to federal funding sources. Some REUs are funded by private gifts and may accept international students.
REUs will typically provide housing and a living stipend.
Directories of REUs are maintained by the NSF, as well as by some mirror lists: here, and here, for example. UVa hosts a topology REU.
Application formats may differ. Many applications are done through the AMS MathPrograms site.
Be sure to read the descriptions of REUs to make sure you meet the qualifications and that they are what you are looking for.
Advice on writing personal statements from John Layne ('26), Mandy Unterhalter ('25), and Samir Fridhi (PhD student) for summer 2025
REU Panel Summary from Sam Goldberg ('24) for summer 2024
REU Advice from Gennady Uraltsev for summer 2023
There's already a lot of good information about what an REU is and how to get into one. I'm going to share some details about my personal experience at REUs to provide more insight and to hopefully make you more excited about participating in one. I have done math REUs at Ursinus College, Texas A&M University, and the Einstein Institute of Mathematics. I have had fantastic experiences at all of them, I learned a ton of new math, and I am still in touch with the friends I have made.
Ursinus College:
I participated in the Ursinus College math REU in the summer after my first year at UVA. I applied to ten REUs, and Ursinus was the only one that accepted me (I also had an interview from another program, but was ultimately rejected). I got help from my DRP mentor in applying for REUs. It is uncommon for students to get accepted into math REUs after their first year, but it is possible, and I know several other people who have done it. No matter how qualified you might be as a first-year student, many programs simply prefer to take second and third-year students. I know people who were far more qualified than I was, yet didn't get into an REU their first summer. Figuring out which programs require less specialized knowledge probably helps your chances if you are applying as a first-year student (ask people who know more math than you).
All of the REU students lived in one big house (separate bedrooms) with a big common room, and we had meals provided to us at the on-campus dining halls (we all ate together), which contributed to a great social environment. Some of the students brought their cars, so we were able to travel. After the program, many of us presented our research at math conferences and had our travel supported by the REU.
I worked with two other undergraduate students and a professor on a research project about integer partition identities. An integer partition is just a way to write a number as the sum of smaller numbers. For example, we can write 4=3+1=2+2=2+1+1=1+1+1+1, and so there are five partitions of the number 4. There are lots of questions you can ask from here. What if we are only allowed to partition our numbers into parts satisfying certain properties? For example, the partitions of 5 into entirely odd parts are 5=3+1+1=1+1+1+1+1, and the partitions of 5 into entirely distinct parts are 5=4+1=3+2. In both cases, there are exactly three ways to partition 5 according to these rules. It turns out that this holds for any positive integer n. That is, the number of ways to partition a number into odd parts always equals the number of ways to partition a number into distinct parts. We call this a partition identity. My research project was to provide a new proof for a vast generalization of this kind of situation, and we ultimately published a paper, which you can find online if you're interested. This project was unusual in that we roughly knew how the proof was supposed to go from the start because there were already several papers that used the same strategy of proof for related partition identities.
Texas A&M University:
I participated in the Texas A&M math REU in the summer after my second year at UVA. This time, I applied to seven REUs and was accepted to four of them. My application was significantly stronger this time for a few reasons. The first reason is that I had way more experience, as I took 8 math classes my second year, one of which was an independent study on analytic number theory (I only applied to projects in this area). The second reason is that I got a significant amount of help with my applications from Sam Goldberg (24'), who sent me his application materials from prior years and who informally taught me a lot of the math related to the projects I was applying for.
All of the REU students lived on the same floor of a dorm, and we had a large common room with a TV, which contributed to a great social environment. We frequently watched movies and played card games together there. Some of the students brought their cars, so we were able to travel. We had to deal with getting food on our own. The program funded a multiday trip to the University of North Texas. After the REU, many of us went to conferences to present our research, and the REU provided funding to do so.
I essentially worked one-on-one with my project mentor. There were other undergraduate students in the number theory group under this mentor, but I was working on a different project from theirs. Overall, it was a lot more independent than my first REU. I usually met with my mentor twice a week, compared to at Ursinus, where we met most weekdays. I studied the distribution of a certain object, called the newform Dedekind sum. Understanding properties of classical Dedekind sums arises when one wants to count the number of partitions of an integer (as above). These newform Dedekind sums combine the classical Dedekind sum with something called Dirichlet characters, which appear, for example, when one wants to show that there are infinitely many primes p of the form p=a+qn for a and q coprime. Unlike at the Ursinus REU, we had no idea how this project was supposed to go from the start. As a result, I learned a lot of new math along the way, compared to at Ursinus, where I was able to get by with my prior knowledge. I read various research papers, learned common techniques in the area, and collected lots of new book references. Another consequence of not knowing how things were supposed to go was that my result fell through at the very end of the program! In the end, I ended up salvaging my result, but it took me a few months after the program ended to do so.
Einstein Institute of Mathematics:
I participated in the Einstein Institute math REU in the summer after my third year. I applied to seven REUs, and was only accepted to this one. I was admittedly overconfident from the prior year. I was primarily looking for REUs with ergodic theory/dynamics projects, of which there were only two or three out of the many programs. And the other programs I applied to were complete shots in the dark because, instead of applying to the listed projects, I tried to apply directly to people in the department who worked in the area I wanted to. This is sometimes an option, but it is probably only viable if you already know someone on the inside who is willing to take you. Don't do what I did.
All of the REU students lived on the same floor of a hotel with a roommate, and we had breakfast provided daily at the hotel. We had to figure out the remaining meals on our own. The school was a 25-minute walk or a 10 to 15-minute bus ride away. The REU students shared an office at the school. There were many things to do within walking distance of the hotel, and we also sometimes used the train.
I worked entirely one-on-one with my mentor for this project. The level of independence was similar, if not more than, that at Texas A&M. I was studying what happens when you multiply generators of a group according to the trajectory of a point in a dynamical system. Suppose you are rotating around the circle by an irrational number, and that you assign a group element g to the top half of the circle and a group element h to the bottom half of the circle. If g and h generate the group, do you hit every group element when you multiply g and h according to the trajectory of the irrational rotation? Such a setup is called a group extension. I was considering this setup where the underlying group was SL_2(Z), and I was interested in whether every group element was hit when you take the matrices modulo large primes. So, my project was a mixture of dynamical systems and what's called the strong approximation property. This project was incredibly broad in terms of the math that it related to: topological dynamics, ergodic theory, continued fractions, algebraic geometry, number theory, strong approximation, expander graphs, cohomology, representation theory, functional analysis, harmonic analysis, and so on.