The SUMRY program is a ten-week undergraduate research program run by the mathematics department at Yale University, usually between early June and early August. In a recent year, there were 15-20 funded positions for undergraduates to investigate open research problems in the mathematical sciences. Students work either individually or in small groups, directed by faculty members, postdoctoral fellows, and graduate students. The work pursued in this program will give participants an idea of what research in mathematics is like.
The Directed Reading Program pairs undergraduate students with graduate student mentors to read and work through a mathematics text over the course of one semester. The pairs meet once each week for one hour, with the undergraduates expected to do about 4 hours of independent reading per week. At the end of the semester, undergraduates either give a talk to their peers or prepare a short exposition of some of the material from the semester. Undergraduates are expected to have a high level of mathematical maturity and eagerness to learn the topic.
Math 470 is an individual studies course, it can be taken for graduation credit (but not applied toward undergraduate math major requirements). By default, it can be taken only once, though under exceptional circumstances, the DUS may permit it to be taken twice. Interested students must submit a proposal to firstname.lastname@example.org at least three days before the end of add / drop period, with the name of their adviser, and details about the proposed study (both its content and the structure of the course). Typically, the class will require weekly meetings with the adviser, it will have some assignments along the way (that are to be written up or presented to the adviser), and it will terminate with a final paper or project. Please note that university rules do not allow independent study on topics that are taught in existing courses (there can be a bit of overlap, but you cannot do independent study to learn Math 370, for example).