Number Theory
Last updated May 31, 2008 12:24:21 EDT

Lectures	Sections in Text	Brief Description
9/25		Introduction to Number Theory
9/27	1.4, 3.1	Divisibility and Primes
9/30	3.1	Distribution of Primes
10/2	3.2, 1.2	GCDs, Induction
10/4	1.2, 3.3	Induction and Euclidean Algorithm
10/7	3.3, 3.4	Euclidean Algorithm and Fundamental Theorem of Arithmetic
10/9	4.1	Intro to modular arithmetic, equivalence relations, partitions
10/11	4.1	Intro to congruences
10/14	4.2, 4.3	Linear congruences, Chinese Remainder Theorem
10/16	4.3, 4.6	Examples CRT and Pollard rho factorization
10/18	4.6, 5.2	Examples of Pollard rho, and calendar problems
10/21	5.2, 5.5	Calendar Problems, Check Digits
10/23	6.1	Wilson's and Fermat's Little Theorem
10/25	8.1	Cryptography Introduction
10/28	8.1	Character ciphers
10/30	4.5, 8.2	Linear systems of congruences and block ciphers
10/31 (x-hour)	8.2	DES, AES
11/4	6.3, 7.1(part)	Euler phi function
11/6	8.4	Public Key Cryptography (RSA)
11/8	8.4	Public Key Cryptography (authentication issues)
11/11	6.2	Pseudoprimes and Carmichael numbers
11/13	6.2, 7.1	Strong Pseudoprimes and Miller-Rabin test
11/15	7.2	Euler totient and divisor functions, multiplicative functions
11/18	7.3	Perfect numbers, Mersenne primes, Lucas-Lehmer
11/20	7.4	Mobius Inversion
11/22	9.1	Orders of elements modulo n
11/25	9.1, 9.4	Primitive roots and Indices
12/2	9.4	kth power residues and Miller's test
12/4	9.4, 9.5	Miller's test (other primality tests?)

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