## COURSE DESCRIPTION

Arithmetic geometry lies at the intersection of algebraic geometry and number theory.
Its primary focus is the analysis of diophantine equations (*x ^{n}* +

*y*=

^{n}*z*, for example), both from an algebraic and a geometric perspective. See the

^{n}**course outline**for a list of planned topics.

Note: 18.782 and 18.783 both cover material on elliptic curves, but there is essentially no overlap; the courses are complementary and may be taken in either order.

**Prerequisites:** 18.702.

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## RECENT UPDATES

**12-15-13** The notes for **Lecture 26** have been updated.

**12-14-13** The notes for **Lecture 26** have been posted.

**12-12-13** The notes for **Lecture 25** have been posted. They include a section on height functions that we did not cover in class.