Look at the contents of this course, by Satyan Devadoss at Williams College: [The Shape of Nature][1],
a.k.a., the *Geometry and Topology of Nature*.  It was just released the The Teaching Company. [Disclosure: Satyan is a coauthor.]  To quote Herbert Wilf from the *Notices of the AMS*,

>"A mind is a fire to be kindled, not a bucket to be filled."  The job of the teacher is to light that fire...

I think material such as that in this course is suitable kindling.


  [1]: http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1460

<b>Addendum</b>:
In that course, Satyan manages to touch upon: The Poincaré conjecture, Voronoi diagrams, the Jones polynomial, the Seifert algorithm, and
Dehn surgery.