Applications of Abstract Algebra:

Some people have asked about what abstract algebra is used for, so here are a few links to provide an introduction to the applications. 

Ethnomathematics: A Multicultural View of Mathematical Ideas
by Marcia Ascher   includes a chapter on using group theory to model kinship relations in (if I remember correctly) Australian aborigines.  This would also be a great Hudson River talk (as would many of the ideas in this book).  I worked on this briefly myself at one time, long enough to form a hypothesis about the group structure of the kinship relations forcing a prohibition on incest.  Working this out in detail would be a great undergraduate research topic. (peg solitaire and group theory—this could be a very cool Hudson River talk!) (a short note about applications in physics) (lots of applications in coding, eg error correcting codes)  (group theory in the cognitive sciences) (books on group theory in quantum mechanics) (group theory in chemistry) (group theory and design/psychology)