Things to do as a math undergraduate

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.

Research Experience for Undergraduates (REU's):
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. Often international students are not eligible for the salary, but in many cases if you contact the REU director he/she might let you participate and get free housing nonetheless. Applications are usually due in early February to early April. A good list of these is maintained on the AMS website here. As you can see, there are many of them to choose from, so I will list a few that I know about (in no particular order) here. It's a fairly good mix of competitiveness levels and mathematics topics.
Other Mathematics Programs for the Summer:
Semester Long Programs:
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.