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Created on Wednesday 19 March 2003 by

Table of Contents
  1. Solving Cubic Equations
  2. Two Types of Equations
  3. Pythagorean Theorem
  4. Babylonian (1800 - 1600B.C.)
  5. Pythagorean Triples
  6. Enumerating Pythagorean Triples
  7. Enumerating Pythagorean Triples
  8. Integer & Rational Solutions
  9. Elliptic Curves
  10. The Secant Process
  11. The Tangent Process
  12. Mordell's Theorem
  13. The Smallest Solution Can Be Huge
  14. The Height
  15. Slide 15
  16. Tate Canonical Height
  17. Tate Picture
  18. Central Question
  19. Mazur's Theorem
  20. Solutions Mod p
  21. Counting Solutions
  22. The Error Term
  23. More Primes
  24. Guess
  25. A Differentiable Function
  26. Birch and Swinnerton-Dyer Conjecture
  27. Slide 27
  28. Gross-Zagier Theorem
  29. Zagier
  30. Thank You
  31. Quadratic Formula
  32. Roots of Cubic Polynomials: