MATH 3809, WEEKLY OUTLINE, FALL 2005

# WEEK OF ~ SECTIONS TOPICS
~ Sep 8 ~ 2.1 An overview of the course. Divisibility.
1 Sep 12-16 ~ 2.1-2.2 Divisibility. Primes.
2 Sep 19-23 ~ 2.3-2.4 Unique factorization. Elementary factoring methods.
3 Sep 26-30 ~ 2.5-2.6 GCD and LCM. Linear Diophantine equations.
4 Oct 3-7 ~ 3.1-3.3 Congruences. Inverses mod p. Chinese remainder theorem.
5 Oct 10-14 ~ 4.1-4.4 Fermat's theorem. Euler's Phi function. Euler's theorem. Lagrange's theorem.
6 Oct 17-21 midterm 1; assg. 1 due 5.1 Classical cryptosystems.
7 Oct 24-28 ~ 5.2-5.3 Public-Key cryptography. The RSA scheme.
8 Oct 31-Nov 4 ~ 6.1, 6.3-6.4 Pseudoprimes and Carmichel numbers. Pollard's p-1 and rho factorization methods.
9 Nov 7-11 ~ 7.1-7.4 Order. Discrete logarithm. Lucas-Lehmer test.
10 Nov 14-18 midterm 2 8.1, 10.1 ElGamal cryptosystem. Identification schemes.
11 Nov 21-25 assg. 2 due 8.2, 9.1 Signature schemes. Quadratic residues.
12 Nov 28-Dec 2 ~ 17.1-17.3 or 12.2 Quadratic reciprocity law or quadratic sieve. Review.
The above weekly outline is subject to change depending on the progress of the course.
Last modified: September 6, 2005