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 NagellLutz 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 
Calendar
Instructor:  
Course Number: 

Departments:  
As Taught In:  Fall 2004 
Level: 
Undergraduate

Learning Resource Types
notes
Lecture Notes
group_work
Projects with Examples
assignment_turned_in
Problem Sets with Solutions