When I was an undergraduate in mathematics, I was fortunate to have stumbled upon some opportunities which had a huge impact on my mathematical career. I am often amazed at the fact that such opportunities remain unknown to many undergraduates in mathematics, especially since these opportunities increase in number year after year. Of course, there are things you can do in college which are within your own school: talk to professors and pursue some sort of collaboration with them, take seminar courses outside of the usual curriculum, etc. But there are many opportunities outside of your department which are incredibly valuable. They allow you to travel to exciting places (sometimes for free or even for pay), meet other students in mathematics from around the world, talk to top notch professors, and, most importantly, learn lots of exciting mathematics. In addition, many of these programs are designed to give students an idea of what research in mathematics is like, which is something one usualy misses by taking courses (even very advanced courses) alone. Not to mention, if you decide to apply to graduate school in mathematics, having attended such programs will not only set you apart from other applicants, but will also most likely equip you with some good recommendation letters too.

Below are a few suggestions of where to start.

Nowadays there are MANY REU's around the country. Basically, these are summer programs which run for about 8 weeks and give students the opportunity to do original research in a variety of fields, from applied mathematics to combinatorics to number theory. Each REU usually lets in on the order of 20 students, and students who attend get free housing and some sort of salary.

- Penn State REU
- IPAM RIPS in Los Angeles
- DIMACS REU in New Jersey
- Ken Ono's REU in Georgia
- Berkeley Program in Geometry and Topology
- REU in Duluth, Minnesota
- Probability and Discrete Math REU in Tennessee
- Cornell REU
- LSU REU
- U Washington REU

- For students in their first 2 years of university: click here. This was in Lyon, France this past summer (the location changes from year to year).
- A program in analysis and geometry (follow link on main page): Princeton University Math
- A program aimed at women, but men can apply: IAS WAM in Princeton, NJ

These programs are very intensive, but also very rewarding. These are just some of the many opportunities that are available to you as an undergraduate. If you want more information, don't hesitate to talk to your professors and major advisors: they know about many of these programs and can help you decide which of them might fit you personally.