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