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.

http://www.cut-the-knot.org/proofs/PegsAndGroups.shtml (peg solitaire and group theory—this could be a very cool Hudson River talk!)

 

http://www.math.hmc.edu/math171/applied_algebra_papers/henage.pdf (a short note about applications in physics)

 

http://web.usna.navy.mil/~wdj/book/node269.html (lots of applications in coding, eg error correcting codes)

 

http://www.rci.rutgers.edu/~mleyton/GT.htm  (group theory in the cognitive sciences)

 

http://store.doverpublications.com/0486432475.html (books on group theory in quantum mechanics)

 

http://store.doverpublications.com/0486432475.html (group theory in chemistry)

  

http://www.nexusjournal.com/Leyton3.3.html (group theory and design/psychology)