The Directed Reading Program (DRP) pairs undergraduate students with graduate student mentors to pursue an independent reading project throughout the semester. Typically, an undergraduate student follows a textbook or a paper and the graduate student plays the role of a mentor. It is up to each pair to decide how frequently to meet and discuss the content, but once a week is usual. At the end of the semester, each student is encouraged to give a presentation (or write a report) about the project in order to solidify their own understanding and to pass it on to others.
The first DRPs took place at the University of Chicago over a decade ago. These programs have had great success and have spread to many other math departments. The DRP at Brown began in Spring 2017.