| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | The Projective Plane | |
| 2 | Curves in the Projective Plane | |
| 3 | Rational Points on Conics | |
| 4 | Geometry of Cubic Curves | Homework 1 due |
| 5 | Weierstrass Normal Form | |
| 6 | Explicit Formulas for the Group Law | |
| 7 | Points of Order Two and Three | Homework 2 due |
| 8 | The Discriminant Points of Finite Order have Integer Coordinates - Part 1 |
|
| 9 | Points of Finite Order have Integer Coordinates - Part 2 | |
| 10 | Points of Finite Order have Integer Coordinates - Part 3 The Nagell-Lutz Theorem |
Homework 3 due |
| 11 | Real and Complex Points on Cubics | |
| 12 | Heights and Descent | |
| 13 | Height of P + P_0 | Homework 4 due |
| 14 | Height of 2P | |
| 15 | A Useful Homomorphism - Part 1 | Homework 5 due |
| 16 | A Useful Homomorphism - Part 2 | |
| 17 | Mordell's Theorem - Part 1 | |
| 18 | Mordell's Theorem - Part 2 Examples - Part 1 |
Homework 6 due |
| 19 | Examples - Part 2 | |
| 20 | Examples - Part 3 | |
| 21 | Singular Cubics | |
| 22 | Rational Points over Finite Fields | |
| 23 | Gauss's Theorem - Part 1 | |
| 24 | Gauss's Theorem - Part 2 | Homework 7 due |
| 25 | Points of Finite Order Revisited | |
| 26 | Factorization using Elliptic Curves - Part 1 | |
| 27 | Factorization using Elliptic Curves - Part 2 | Homework 8 due |
| 28 | Integer Points on Cubics Taxicabs - Part 1 |
|
| 29 | Taxicabs - Part 2 Thue's Theorem - Part 1 |
|
| 30 | Thue's Theorem - Part 2 | Homework 9 due |
| 31 | Construction of an Auxiliary Polynomial | |
| 32 | The Auxiliary Polynomial is Small | |
| 33 | The Auxiliary Polynomial Does Not Vanish | |
| 34 | Proof of the DAT Further Developments |
Homework 10 due |
| 35 | Congruent Numbers and Elliptic Curves I: Koblitz - Part 1 | |
| 36 | Congruent Numbers and Elliptic Curves II: Koblitz - Part 2 |