Week  Chapters  Topics 
1  Introduction  Introduction

2  1.1  Rational Points on Conics

3  1.23  Geometry of Cubic Curves, Weierstrass Normal Form

4  1.4  Explicit Formulas for the Group Law

5  2.1  Points of Order Two and Three

6  2.2  Real and Complex Points on Cubic Curves

7  2.34  Points of Finite Order have Integer Coordinates

8   Midterm Exam

9  2.5  The NagellLutz Theorem

10  3.13  The Group of Rational Points, Height and Descent

11  3.4  A Useful Homomorphism

12  3.5,4.1  Mordell's Theorem, Rational Points over Finite Fields

13  4.2  A Theorem of Gauss (*)

14  4.4  Factorization Algorithm using Elliptic Curves

15   Final Exam
