# Admission to SPUR: A General Description

In SPUR/SPUR+, we take many factors into account during the admissions process. In our application form, we ask you to list the courses you've taken and the ones you're planning to take in the upcoming semester. We pay a lot of attention to advanced courses because those are some of the strongest indicators of whether we'll be able to find a suitable research project for you. Finding a research project is tough because it has to be a research-level question that your graduate student mentor can't readily figure out. Additionally, the summer program is only six weeks long and you spend the last week and a half polishing up your paper and preparing your talk. So we can't afford to give you a project that you can't get started on right away.

It may seem strange that we don't ask for grades, but that's because we have access to all your grades anyway. We get all the information we can. When we have students without too much of a track record at MIT, we ask faculty who taught difficult math classes you took how you performed in the class. Math research is also about persistence and hard work, so we keep a lookout for students who might not have had a strong background coming into a class, but made up ground quickly and had scores with an upwards trajectory.

We also look for different things depending on your areas of interest. If you're interested in combinatorics, there's a good chance we can find a project for you that doesn't require you to have taken any graduate classes in the area. But if your project is in algebraic topology, it's much harder. You probably need a deep background in it and some of the surrounding areas.

But there's a lot more to how we evaluate applications than just looking at the grades and coursework. That's why we have an open-ended question about your past experience. It's hard to give a comprehensive list of all the things that might stand out to us. Students often tell us about summer programs they've been involved in (e.g. PROMYS and the Ross program). They might tell us about past research experience, even if it's in an area other than math. Basically, we're looking for whether you've had experience working independently on an open-ended project. In research, most of the time you're stuck and don't know where you're going, which can be quite frustrating. We pay attention to your experiences outside of the classroom because they can be a big component of whether you're ready for research and would enjoy the experience.

Some students also tell us about how well they did on math competitions. But we want to emphasize that this is not necessary. None of us are believers that you have to go this route to be successful in math (in fact, most of the math faculty are counter-examples). But we do use this information because participating in programs like MOP means that you've been exposed to a lot more math outside of the classroom.

We also have an open-ended question about your mathematical interests. We try to assemble a group of students that cover most of the main areas, like analysis, algebra, topology, number theory, representation theory, combinatorics, theoretical computer science, numerical analysis, and physical applied math. We pay attention to how well this part is written. It's not a requirement, but if a student writes something very mature and thoughtful about their interests, it stands out. Students also tell us about whether they'd prefer an individual or joint project. Having two students work together has had a lot of success in the past, but we can only do this if we can find a match in terms of interests and how advanced the students are. We don't want to partner anyone with anyone else who's much further along, because that is a recipe for an un-fun summer.

And finally, being a great mathematician is not about fitting into any particular mold. We try our best to assemble a diverse group of students. This is something that we take very seriously, and we are as interested in looking at the numbers (to see how we're doing and to figure out if there are ways to improve) as you are. But just a word of caution: Final numbers don't always tell the full story. In fact, a trend we've seen in recent years is that a disproportionately large fraction of the offers we make to women or under-represented minorities are declined. In the last three years, we made four times as many offers to members of these groups as were accepted. Our summer research program is part of a larger ecosystem, and it turns out that many of these applicants got numerous offers, some from programs that were either more prestigious or in some way better tailored to their research interests.