# Lecture Notes

These are directions suggested to students on how to prepare their lectures. (PDF)

Lecture Notes Table
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)