| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Introduction to Elliptic Curves | |
| 2 | The Group Law, Weierstrass and Edwards Equations | |
| 3 | Finite Fields and Integer Arithmetic | |
| 4 | Finite Field Arithmetic | |
| 5 | Isogenies | Problem Set 1 Due |
| 6 | Isogeny Kernels and Division Polynomials | |
| 7 | Endomorphism Rings | Problem Set 2 Due |
| 8 | Hasse's Theorem, Point Counting | |
| 9 | Schoof's Algorithm | Problem Set 3 Due |
| 10 | Generic Algorithms for Discrete Logarithms | |
| 11 | Index Calculus, Smooth Numbers, Factoring Integers | Problem Set 4 Due |
| 12 | Elliptic Curve Primality Proving (ECPP) | |
| 13 | Endomorphism Algebras | Problem Set 5 Due |
| 14 | Ordinary and Supersingular Curves | |
| 15 | Elliptic Curves over C (Part 1) | Problem Set 6 Due |
| 16 | Elliptic Curves over C (Part 2) | |
| 17 | Complex Multiplication | Problem Set 7 Due |
| 18 | The CM Torsor | |
| 19 | Riemann Surfaces and Modular Curves | Problem Set 8 Due |
| 20 | The Modular Equation | Problem Set 9 Due |
| 21 | The Hilbert Class Polynomial | |
| 22 | Ring Class Fields and the CM Method | Problem Set 10 Due |
| 23 | Isogeny Volcanoes | |
| 24 | The Weil Pairing | Problem Set 11 Due |
| 25 | Modular Forms and L-series | |
| 26 | Fermat's Last Theorem | Problem Set 12 Due |