Contents
Diophantine equations, rational points on elliptic curves, Nagell-Lutz Theorem, Mordell’s Theorem.
We will cover the first three chapters of the book of Silverman and Tate. These three chapters consist of the context of a series of lectures of Tate at Haverford College in 1961. The audience of Tate’s lectures were advanced undergraduate students 50 years ago. These lectures use some knowledge of complex analysis, but it is not absolutely indispensable.

Course prerequisite:
Complex analysis of one variable, which is a beginning of

Reference material (textbook(s)):
Silverman and Tate, Rational points on elliptic curves, Springer-Verlag, 1992
Husemoller, Elliptic curves, Springer-Verlag, 1987.

Grading scheme:
20%, attention;
80%, final examination.

Course Goal:
Mordell’s Theorem on rational points of elliptic curves. The students may continue to read the remaining three chapters of the book of Silverman and Tate, which is a beginning of a fascinating and deep chapter of modern number theory. Alternatively they may go ahead to study the famous theorem of Mordell-Weil conjecture (Faltings’s Theorem).