The Bayer and Diaconis paper, "Trailing the Dovetail Shuffle to its Lair" is a classic and Brad Mann gave a [very readable exposition][1] of it.

Many people have heard, "seven shuffles are necessary to mix up a deck of cards."  But it is great for undergraduates to learn what exactly is meant mathematically by *shuffle*, and especially what is meant by *mix up*.


  [1]: http://www.dartmouth.edu/~chance/teaching_aids/Mann.pdf