Lectures	Sections in Text	Brief Description
9/22	1.2, 1.4, and parts of 3.1, 3.4	Induction, Divisibility, Fundamental Theorem of Arithmetic
9/24	3.1	Primes: Euclid's and Euler's Proofs of Infinitude, Chebyshev's Estimates
9/27	3.2, beginning of 3.4	GCDs, the Fundamental Theorem Revisited
9/29	3.3, remainder of 3.4	Uses of the Fundamental Theorem, the Euclidean Algorithm
10/1	3.6, 13.1	Some Diophantine Equations: Linear Equations, Pythagorean Triples
10/4	13.1, 13.2, 4.1	Pythagorean Triples (cont.), a Special Case of Fermat's Last Theorem, Intro to Congruences
10/6	4.1	Intro to Congruences (cont.)
10/8	4.2	Primes in Progressions, Linear Congruences
10/11	4.3	Chinese Remainder Theorem
10/13	Supplemental and 4.4	Reclusive Primes, Solving Polynomial Congruences
10/15	4.4	Hensel's Lemma
10/18	5.1, 5.2	Applications of Congruences: Divisibility Tests, The Perpetual Calendar
10/20	5.2, 5.5	The Perpetual Calendar (cont.), Check Digits
10/22	6.1 and Supplemental	Wilson's Theorem, Formula for the nth Prime Number
10/25	4.6, 6.1	Fermat's Little Theorem, Pollard Rho and Pollard p-1 Factorization
10/27	6.2	Primality Tests, Pseudoprimes and Carmichael Numbers
10/28 (x-hour)	6.2, 6.3	Miller's Test and Rabin's Probabilistic Primality Test, Euler's Theorem
11/1	8.1, 8.2	Intro to Cryptography: Character and Block Ciphers
11/3	4.5, 8.2	Hill Ciphers and Systems of Linear Congruences
11/5	Supplemental	A Little Bit of Cryptanalysis
11/8	8.2, 8.3	Cryptanalysis Continued, Stream Ciphers, Exponentiation Ciphers
11/10	8.4	Public Key Cryptography and RSA, Cryptographic Protocols and Applications
11/12	Supplemental	Arithmetic Functions, Dirichlet Convolutions, Formal Dirichlet Series
11/15	7.1, 7.2	Euler's Phi-function, Sum and Number of Divisors
11/17	7.3, 7.4	Perfect Numbers, Mersenne Primes, Lucas-Lehmer Test, Mobius Inversion
11/19	Supplemental	Average Orders of Multiplicative Functions, Counting Square-Free Integers, Farey Fractions
11/22	11.1	Quadratic Residues, the Legendre Symbol
11/29	11.2	Quadratic Reciprocity
12/1	Supplemental	Wrap up

Ryan Daileda
Last updated May 31, 2008 12:24:21 EDT