2007-05-25
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1. Yi -- demo of ECM (first 25 min) with questions.

2. SAGE -- introduction to SAGE demo / talk, with examples 
   involving elliptic curves:

 Elliptic curve demo.  Key points:
    over QQ
     * examples of elliptic curves with pictures
     * examples of group law with pictures.
     * 3d graph of points on curve using tachyon
    mod p
     * some graphs
     * arithmetic on elliptic curve modulo a prime
     * diffie-hellman key exchance on an elliptic curve
    
3. Note -- Peter Clark will be giving a talk at 3:30 here about
   the "Sieve of Atkin" which is used for enumerating primes. 


Plan:
 
* Monday -- holiday
* Wednesday -- elliptic curve cryptosystems
* Friday -- the Birch and Swinnerton-Dyer conjecture
          and your projects are due -- paper version + email me the *pdf*.