Why elliptic curves?
Elliptic curves are the simplest possible curves after lines and conics. Lines and conics (which are usually given by linear and quadratic equations respectively) are fairly easy to understand. Curves more complicated than elliptic curves (e.g., defined by polynomials of higher degree than 3) are generally difficult to understand. Elliptic curves are “just right”. The fact that they can be dealt with is due to their very rich structure; in particular, they can be viewed as a group. Most of this course is about investigating this group structure.
