Contents

• Rational Right Triangles
• Congruent Numbers and Elliptic Curves
• Congruent Numbers and Elliptic Curves: II
• Elliptic Curve Groups
  • Elliptic Curves over $\mathbb{Q}$
  • Elliptic Curves Modulo $p$
  
  
• The Birch and Swinnerton-Dyer Conjecture (Monday)
• Square Triangles and Fermat's Last Theorem (Wed morning)
• An Elementary Criterion (Thursday)
• Square Triangles Revisited
• An Elliptic Curve Cryptography (ECC) Tutorial
  • Elliptic Curves Modulo $p$
  • Computing $nQ$
  • Diffie-Hellman - a way to create a shared secret
  • A serious cryptosystem that was deployed: MS-DRM

Goals:

• Learn about a major open problem in number theory.
• Learn to use SAGE to draw plots and do computations.
• Learn about elliptic curves: groups, public-key cryptography, the BSD conjecture.