Hello, I have a few questions that I feel would help me better understand a few things. The first set of questions relate to the type of research opportunities some of you guys will be involved with this summer. The second set of questions are a bit different and are related to math courses in preparation for Algebraic Topology/Category Theory. First how common is it for undergraduate students to get involved in research? I was under the impression some undergraduate research topics are topics that professors feel can be completed within a few semesters. Nothing as serious as research at the graduate level, is this generally true, despite the field (ie math, physics)? I know some research conducted at the undergraduate level is very serious. Any research period must look good on an applicant's transcript! But would it hinder the transcript if the applicant conducted research for a few semesters but not publish anything? How hard is it to get your results published if you feel like you made substantial progress? This leads to my second question, what summer REU/Internships will some of you be doing this summer? What kind of math/physics background do you guys have course wise? What do you feel made you stand out over the other applicants, and what kind of various research projects will you guys be working on? I'd like to eventually study Algebraic Topology and Category Theory. I am thinking about taking a group theory, a real analysis and a topology course. Would this be the natural progression one would need to have under their belt before they study AT? What books would you guys recommend to study AT with? I figure once I learn group theory I can go back and learn the basics of ring theory by myself. Basically I am wondering what mathematical foundations do I need to have in order to study AT and Category Theory? Are these courses generally taught at the undergraduate level? Thanks!