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) |