Summer provides students with a lot of time and freedom, resources which may be best spent on mathematical pursuits. REUs (Research Experience for Undergraduates) definitely seem to be the most well-known summer math opportunity, so we will devote our first to other options. Some thoughts and information about REUs will then be presented in a Q&A format.

**Conferences**

Strictly speaking, conferences are a phenomenon not restricted to the summer (an example being one of the largest math conferences known as the Joint Mathematics Meetings or simply JMM). Information about conferences is often presented alongside that for REUs at mathprograms.org. Further information can be found by checking the bulletins on floors 9-12 of RLM as well as, of course, talking with math grad students and professors.

**Independent Study**

Conference courses (discussed on the Opportunities at UT tab) are an option for the summer as well as the regular academic year. Some professors stay in town for large portions of the break, and others are available through Skype or by email. If your goal is to conduct a reading project or some other form of independent study then we recommend you try to setup a conference course in order to stay motivated and have more accountability. All you need to do is ask a professor who you think might be interesting to work with.

**Summer Camps**

Summer math camps offer undergrads the chance to serve as mentors to younger students while also learning cool math and networking with others. A few of the more well known programs include:

- Program in Mathematics for Young Scientists (PROMYS): apply to be a counselor
- Ross Mathematics Program: apply to be a counselor at either the US or China branches of the program

The US and China branches of the Ross program differ in that the China program is five weeks long rather than six and offers less pay, while at the same time reimbursing travel expenses and offering a free one week stay with a host family before the start of the program. Contact Zachary (zacharygardner137@utexas.edu) for personal anecdotes and other inside info on the Ross program.

**REU FAQ**

**What are good websites for finding out about REUs?**

- mathprograms.org
- ams.org/programs/students/emp-reu
- nsf.gov/crssprgm/reu/list_result.jsp?unitid=5044
- sites.google.com/view/mathreu

**What opportunities are there for international students who do not have
citizenship?**

Many REUs do not offer funding/stipends to international students, while others bar international students from applying at all. Here are a few programs for international students to consider.

- Park City Math Institute (PCMI)
- Fields Institute
- Institute for Pure and Applied Mathematics (IPAM)
- Mathematical and Theoretical Biology Institute (MTBI)
- National Institute for Mathematical and Biological Synthesis (NIMBioS)
- Institute for Computational and Experimental Research in Mathematics (ICERM)

**Are there any parts of the application process that may be unexpected or not obvious?**

Some programs, such as SMALL, have rolling admissions. Others, such as the Purdue PRiME REU, require three letters of recommendation instead of the more typical one or two. Watch out for programs that require cover letters, and be sure to pay close attention to any length requirements. A good rule of thumb is to apply well in advance of any deadline.

**Who should I choose as a recommender and why?**

Ask professors whose classes you have taken (and done well in) to write reference letters. In many instances, a good grade in a course whose content is relevant to the content of the REU is worth a lot more than a bad/mediocre grade in an unrelated course. Draw attention to your good grades in relevant classes when talking with your (potential) letter writers. In general, recommendations and transcripts will be most important.

Note: Conference courses are a good way to build closer relationships with professors.

**What are some of the more prestigious REUs, and what makes them prestigious?**

REUs are typically described as prestigious due to

- word of mouth and reputation;
- high pre-print/publication output; or
- selection of high-quality topics suited for undergrads.

The following REUs are grouped roughly by the amount of prestige they seem to have (admittedly with some bias toward algebra and combinatorics).

- Duluth (combinatorics / number theory), Emory (number theory), Williams College / SMALL (topology / number theory / probability)
- Minnesota Twin Cities (algebraic combinatorics), DIMACS (Rutgers; theoretical computer science), Cornell, UChicago, UMichigan
- Oregon State, Auburn (algebra / graph theory), IPAM (UCLA; applied industry math), Fields Institute (Canada; math with theoretical computer science), A&M, SUNY Potsdam, Park City Math Institute, ICERM (Brown, topological data analysis), UMaryland (CS)

**Do all REUs follow the same administrative setup?**

No. UChigaco and UMichigan, for example, are different from most other REUs in that they require students to somewhat independently organize projects with specific professors. UChicago also tends to focus more on reading courses than original research.

**How hard is it to get into an REU?**

REUs seem to be becoming more and more difficult to get into as time passes. Many programs prioritize juniors who are applying for their last shot at an REU, so freshmen and sophomores will have a harder time. In general, REU applicants should apply to many places and expect only a small number of acceptances. Freshmen and sophomores may be best served applying to 10-20 places. However, students should only apply to programs that they can honestly see themselves doing (otherwise they will probably have trouble finding sufficient motivation).

**What can I expect to get out of an REU?**

While there are many ways to ensure you have strong letter writers when applying for graduate school, working hard and exhibiting passion/knowledge during a summer REU can mean that you can have a good letter of reference for your grad school apps. If you are lucky enough to be working with a tenured (or tenure track) professor (whose words mean a lot when read by admission committees), seize the opportunity by building a good rapport.

Because the research projects tend to be toy problems / dissimilar to current research topics (although more prestigious REUs have somewhat better quality in this respect), they aren’t as helpful as learning theory in the long run. However, they are helpful for informing career decisions and meeting peers as well as being one of the better ways to show grad schools that your summers are productive. It’s also worth noting that grad schools are increasingly looking for ways to distinguish among applicants and gauge whether admitted students will successfully complete their PhDs, aims which are both partially served by REU experience.

Also, don’t forget to have fun and go a bit outside of your comfort zone!