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Created by:
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
About the instructor
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Massachusetts Institute of Technology
