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Last updated:

December 26, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This is a seminar for mathematics majors, where the students present the lectures. No prior experience giving lectures is necessary.

Course Curriculum

  • The Projective Plane Unlimited
  • Curves in the Projective Plane Unlimited
  • Rational Points on Conics Unlimited
  • Geometry of Cubic Curves Unlimited
  • Weierstrass Normal Form Unlimited
  • Explicit Formulas for the Group Law Unlimited
  • Points of Order Two and Three Unlimited
  • The Discriminant Unlimited
  • Points of Finite Order have Integer Coordinates – Part 2 Unlimited
  • Points of Finite Order have Integer Coordinates – Part 3 The Nagell-Lutz Theorem Unlimited
  • Real and Complex Points on Cubics Unlimited
  • Heights and Descent Unlimited
  • Height of P + P_0 Unlimited
  • Height of 2P Unlimited
  • A Useful Homomorphism – Part 1 Unlimited
  • A Useful Homomorphism – Part 2 Unlimited
  • Mordell’s Theorem – Part 1 Unlimited
  • Mordell’s Theorem – Part 2 Unlimited
  • Examples – Part 2 Unlimited
  • Examples – Part 3 Unlimited
  • Singular Cubics Unlimited
  • Rational Points over Finite Fields Unlimited
  • Gauss’s Theorem – Part 1 Unlimited
  • Gauss’s Theorem – Part 2 Unlimited
  • Points of Finite Order Revisited Unlimited
  • Factorization using Elliptic Curves – Part 1 Unlimited
  • Factorization using Elliptic Curves – Part 2 Unlimited
  • Integer Points on Cubics Taxicabs – Part 1 Unlimited
  • Taxicabs – Part 2 Unlimited
  • Thue’s Theorem – Part 2 Unlimited
  • Construction of an Auxiliary Polynomial Unlimited
  • The Auxiliary Polynomial is Small Unlimited
  • The Auxiliary Polynomial Does Not Vanish Unlimited
  • Proof of the DAT Unlimited
  • Congruent Numbers and Elliptic Curves I: Koblitz – Part 1 Unlimited
  • Congruent Numbers and Elliptic Curves II: Koblitz – Part 2 Unlimited

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Massachusetts Institute of Technology