I will ask that you write a paper (10-20 pages typically) on a subject related to the material of Calculus III, but outside the scope of the class. Some possible topics
I will also ask that you learn the mathematical typesetting language TeX (pronounced "tech" as in "technology") to write it in. Even if you don't do the honors option, you will benefit enormously from learning TeX. It is a better system than most for any sort of writing (poetry, linguistics, philosophy, letters to the editor, etcetera), and is vastly superior in its handling of mathematics and graphical content.
The definitive site for all things Tex is the Comprehensive TEX Archive Network . You can find (links to and/or copies of) the major Tex distributions for different systems together with an enormous number of useful packages. I particularly recommend having a look at
Here is the Wikipedia page on CTAN.
I use TeXShop, a comprehensive TeX installation designed for the Mac, and like it a lot.