Look at the contents of this course, by Satyan Devadoss at Williams College: The Shape of Nature, 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.

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

Look at the contents of this course, by Satyan Devadoss at Williams College: The Shape of Nature, 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.