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Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves >> Content Detail



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Calendar

LEC #TOPICSKEY DATES
1The Projective Plane
2Curves in the Projective Plane
3Rational Points on Conics
4Geometry of Cubic CurvesHomework 1 due
5Weierstrass Normal Form
6Explicit Formulas for the Group Law
7Points of Order Two and ThreeHomework 2 due
8The Discriminant

Points of Finite Order have Integer Coordinates - Part 1
9Points of Finite Order have Integer Coordinates - Part 2
10Points of Finite Order have Integer Coordinates - Part 3

The Nagell-Lutz Theorem
Homework 3 due
11Real and Complex Points on Cubics
12Heights and Descent
13Height of P + P_0Homework 4 due
14Height of 2P
15A Useful Homomorphism - Part 1Homework 5 due
16A Useful Homomorphism - Part 2
17Mordell's Theorem - Part 1
18Mordell's Theorem - Part 2

Examples - Part 1
Homework 6 due
19Examples - Part 2
20Examples - Part 3
21Singular Cubics
22Rational Points over Finite Fields
23Gauss's Theorem - Part 1
24Gauss's Theorem - Part 2Homework 7 due
25Points of Finite Order Revisited
26Factorization using Elliptic Curves - Part 1
27Factorization using Elliptic Curves - Part 2Homework 8 due
28Integer Points on Cubics

Taxicabs - Part 1
29Taxicabs - Part 2

Thue's Theorem - Part 1
30Thue's Theorem - Part 2Homework 9 due
31Construction of an Auxiliary Polynomial
32The Auxiliary Polynomial is Small
33The Auxiliary Polynomial Does Not Vanish
34Proof of the DAT

Further Developments
Homework 10 due
35Congruent Numbers and Elliptic Curves I: Koblitz - Part 1
36Congruent Numbers and Elliptic Curves II: Koblitz - Part 2

 








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