Why to be involved Working on a research project in mathematics is an experience like no other. You get to totally immerse yourself in a problem, learn exciting new mathematics, and expand the frontiers of mathematical knowledge. Who will be involved Research is often done individually (although large projects may be worked on by groups), and it requires you to be motivated and independent, but there will be people to help you along the way (such as your research mentor). When to become involved Typically research is undertaken during the junior/senior year, after having completed some basic coursework (it helps to have taken lots of mathematics courses, and sometimes even computer science courses if possible). Projects may require a semester, a full academic year, or a summer. How to get involved Talk to your professors! Stop by during their office hours and say "I'm interested in math research." Professors usually have multiple ideas for projects they can share. It is important to choose a topic that matches your interests, so be prepared to talk about what mathematics courses you have enjoyed in the past and why, and what style of research you are interested in - theoretical (also known as "pure") mathematics, or applied mathematics (that is, applications of mathematics to the "real world"). It is important to talk to profs as early as possible, because there may be preparatory background work necessary before you actually begin working on the project. You will also need to find a research mentor - this may or may not be the same professor who suggests your topic of interest in the first place. They can assist you in various ways: help you identify what you need to do to prepare for a topic, such as reading particular books or journal articles, or complete additional coursework. They can suggest directions to pursue or modifications to your problem if you get stuck (although they may not know if a given direction will work out, and they won't do the work for you - that is the nature of research!), and they can let you know about opportunities for presentation and publication. Another way to get involved in mathematical research is to participate in an REU: a Research Experience for Undergraduates. These are research groups that are sponsored by the National Science Foundation and are based at various colleges and universities across the country. There is an application process and it is competitive, but the experience is well worth it. For more information, check out:
One important aspect of the research process is sharing your results with the mathematical community. The primary ways to do so are:
Here are some useful resources, advice, and examples:
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