T. R. Shemanske
Last updated June 17, 2015 12:57:00 EDT
| General Information | Syllabus | HW Assignments | Course Resources |
|---|
| Lectures | Sections in Text | Brief Description |
|---|---|---|
| 1/4 | Introduction, Elliptic curves in Fermat's Last Theorem, Congruent Numbers, and Cryptography | |
| 1/6 | Congruent numbers and rational points on conics; algebraic versus geometric structure on sets | |
| 1/9 | Rational curves and intersections; Bachet's duplication formula | |
| 1/11 | Rational points on the unit circle: Pythagorean triples, congruent numbers | |
| 1/13 | Well ordering, division algorithm, greatest common divisors and divisibility properties | |
| 1/16 | No Class Martin Luther King day (class moves to x-hour) | |
| 1/17 (x-hour) | Euclid's algorithm, Bezout's theorem, congruences | |
| 1/18 | congruences and equivalence relations; Caesar cipher | |
| 1/20 | Affine ciphers, general linear congruences | |
| 1/23 | Z_n as a ring, U_n as a group | |
| 1/25 | Groups, orders of elements | |
| 1/27 | More on groups, Euler's theorem, Fermat's little theorem | |
| 1/30 | Applications, fast modular exponentiation | |
| 2/1 | Public Key Cryptography, RSA | |
| 2/3 | Public Key Cryptography | |
| 2/6 | More about groups | |
| 2/7 (x-hour) | Fundamental Theorem of Finite Abelian Groups, Projective space | |
| 2/8 | Projective space and relating points on affine and projective curves | |
| 2/10 | No class: Snow Day (aka Winter Carnival) | |
| 2/13 | Elliptic curves and the addition law | |
| 2/15 | Elliptic curves and the addition law | |
| 2/17 | Pollard p-1 factoring algorithm | |
| 2/20 | Lenstra's elliptic curve method of factorization | |
| 2/22 | Congruent number problem and elliptic curves | |
| 2/24 | Congruent numbers and Tunnel's theorem; some complex analysis | |
| 2/27 | Elliptic Curves over C | |
| 2/29 | Student Presentations | |
| 3/2 | Student Presentations | |
| 3/5 | Student Presentations | |
| 3/7 | Student Presentations |
T. R. Shemanske
Last updated June 17, 2015 12:57:00 EDT