A computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
While this is an introductory course, we will (gently) work our way up to some fairly advanced material, including an overview of the proof of Fermat's last theorem.
See the course outline for further details.
Prerequisites: A first course in algebra covering groups, rings, and fields. May be taken concurrently with 18.702 or 18.703.
05-13-15 Note: in part 2 of problem 1 on Problem Set 12 you are asked to find a single elliptic curve E/Fp whose j-invariant simultaneously satisfies (a)-(f).
05-13-13 Problem Set 12 has been updated to correct a typo in part 2 of problem 2.
05-13-13 There will be no lecture on Thursday 5/16. Instead, watch this BBC documentary on the proof of Fermat's Last Thoerem.
05-13-13 The notes for Lecture 24 have been posted.
05-13-13 An updated version of Problem Set 12 has been posted that corrects an error in part 3 of problem 1.
05-10-13 Problem Set 12 has been posted. It is due Thursday 5/16.
05-09-13 The notes for Lecture 23 have been posted.