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

Calendar

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