The following is a tentative syllabus for this course, which will be ammended as necessary.

Lectures	Sections in Text	Brief Description
9/26	1.3, 1.4	Introduction, Induction and Fibonacci numbers
9/28	1.5, 3.1	Divisibility, Prime numbers
10/1	3.1, 3.2	Distribution of primes
10/3	3.3, 3.4	Greatest Common Divisor, Euclidean Algorithm
10/5	3.4, 3.5	Extended Euclidean Algorithm, Fundamental Theorem of Arithmetic
10/8	3.5, 3.6	Factorization and Fermat numbers
10/10	4.1	Introduction to congruences, Modular arithmetic
10/12	4.2, 4.3	Linear congruences, Chinese Remainder Theorem
10/15	4.6, 5.1	Pollard rho factorization, Divisibility tests
10/17	5.2, 5.5	Perpetual calendar, Check digits
10/19	6.1	Wilson's Theorem, Fermat's Little Theorem
10/22	6.2	Pseudoprimes and Carmichael numbers
10/24	6.3, 7.1	Euler's phi function, Euler's theorem
10/26	7.2, 7.3	Totient and divisor functions, Perfect numbers
10/29	7.3, 7.4	Mersenne primes, Mobius inversion
10/31	8.1, 4.5	Introduction to cryptography, Linear systems of congruences
11/2	8.1, 8.2	Character ciphers and Block ciphers
11/5	8.4	Public Key Cryptography (RSA)
11/7	8.5, 8.6	Knapsack cipher, Cryptographic protocols
11/9	11.1	Quadratic residues
11/12	11.2	Quadratic reciprocity
11/14	11.2	Quadratic reciprocity, Pepin's test
11/16	11.3, 11.4	Jacobi symbol, Euler pseudoprimes
11/19	3.7, 13.1	Diophantine equations
11/21	NO CLASS	Thanksgiving break
11/23	NO CLASS	Thanksgiving break
11/26	13.2	Fermat's Last Theorem
11/28	13.3	Sums of squares
11/30	Supplement	Introduction to partitions
12/3	Supplement	Partitions

Stephanie Treneer

Last updated June 25, 2009 14:49:07 EDT