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