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) |