- The other mentors did the same thing. Â If you didn’t have a preference, you went to the bottom of my queue.
- A second REU doesn’t double the benefits of the first one; there are decreasing returns for each REU. Â So, to maximize the value to the participants, I looked for the students who would be participating in an REU for the first time.
- I know other mentors disagree with me on this item. Â They may try find one student with a prior research experience to act as a leader. Â Even I looked for students with some experience doing research, just not in an REU setting.
- A recommendation letter tells me the following: your mathematical ability, your persistence in the face of obstacles, and your role on a team. Â More generally, it tells me if you’re a person that I would like to work with. Â Sometimes letters highlight your weaknesses, too; this isn’t a bad thing. Â I wanted to find students that would work well together and learn something from the experience.
- An 8-week research experience is intense and requires persistence, problem-solving skills, and mathematical intuition. Â In many cases, these all come from exposure to mathematics. Â If you haven’t taken many math classes and your letters don’t address your preparation despite your lack of experience, then I would rather you apply when you have a little more experience. Â In short, I want to feel confident that you will be successful in the program.
- The theme this summer is algebra. Â That means that I wanted to find students who had taken classes that exposed them to the basics: vector spaces, linear transformations, groups, rings, fields, and homomorphisms. Â The more background in algebra, the better, because there’s not enough time for a crash course in 8 weeks. Â My group got a crash course that built on their foundation of coursework. Â If you haven’t had a lot of classes in the relevant subject, your letters should indicate that you are nevertheless prepared for the program. Â For instance: have you had a crash course with a professor? Â Have you sat in on a seminar on the topic?
- If you’re not excited about my project description, your application goes to the bottom of my pile.  The worst thing you can do is apply to a bunch of REUs with the same exact cover letter.  Yes, I know you are thinking about grad school and want to have an REU under your belt before you apply.  Yes, I know you like math.  But why are you applying to this REU?  What interests you about my project?
- Address any gaps in your transcript. Â Although your letter writers have a better perspective on your mathematical preparedness, your input is helpful, too.
- The following is my most adamant advice: don’t make mathematical errors in your cover letter.  It sounds obvious, but it can be subtle.  It’s clear if you’re just barfing up a bunch of facts and jargon to try to convince the reader that you’re an expert.  No one expects you to be an expert in any field (yet).  Real expertise is easy to discern because it comes from experience.  If you are well-versed in an area, write about your work in that field instead of merely describing the field of study.
- It’s no good to have three lone-wolf geniuses on the same project. Â I wanted to find a team that had a good balance of talent, expertise, organization, and persistence.
There you have it.  That was my process, and I ended up with a team of students that work well together.  They are pushing each other to be better mathematicians and learning from each other.  They’re using their different background preparation to come up with strategies for proving theorems.  And they all want to be working on the project.  So even though we have (temporarily) hit a road block with our theorem, the frustration isn’t compounding indifference to the math.  As I hope my team knows by now, I’m more than pleased with the results of my search.
Best of luck with your REU applications!
Related
- Can’t win every day, right?
- WMC REU: Stalking the Theorem
- The Linear Algebra of Voting
- WMC REU – Week 4, or, “To Prove a Lemma”
- A Weekend in Salem, OR
