The Distinguished Majors Program is the UVa mathematics departments version of an honors mathematics thesis. The principal component is performing directed study under the supervision of a faculty member and writing a thesis, which is then defended at a public lecture, much like a master's or PhD thesis. This program is an excellend opportunity to broaden one's horizons and to develop useful skills for further studies in mathematics and related disciplines. Some things to keep in mind:
Acceptance into the program is through application to the Director of the Undergraduate Program. Official guidelines are here.
You will need the support of a faculty member who will be willing to supervise your thesis. The earlier you start on cultivating this relationship, the better.
Get to know more advanced students who are writing DMP theses and attend their defenses.