Week 1


September 10

 Introduction, divisors, Euclidean algorithm.
 Read Section 1.1
 Homework for Week 1 can be found at Homework Week 1.

September 11

 Xhour, 12:00  12:50
 Euclidean algorithm, Bezout's identity
 Read Section 1.2

September 12


September 14

 Least common multiple, linear Diophantine equations
 Read Sections 1.3 & 1.4

Week
2


September 17

 Prime numbers, the fundamental theorem of arithmetic
 Read: Section 2.1
 Homework for Week 2 can be found at Homework Week 2.

September 19 
 Homework for Week 1 due today.
 Distribution of primes, Fermat and Mersenne primes
 Read: Sections 2.2 & 2.3

September 21 
 Primality testing and factorization.
 Read: Section 2.4

Week
3


September 24 
 Modular arithmetic.
 Read: Sections 3.1
 Homework for Week 3 can be found at Homework Week 3.

September 26 
 Homework for Week 2 due today.
 Linear congruences.
 Read: Section 3.2

September 28 
 The Chinese remainder theorem.
 Read: 3.3

Week
4


October 1

 A little group theory
 Read: Class notes
 Homework for Week 4 can be found at Homework Week 4.

October 3 
 Homework for Week 3 due today.
 Arithmetic of Z_p
 Read: Section 4.1

October 5 
 Pseudoprimes and Carmichael numbers, congruences modulo a prime power
 Read: Section 4.2, class notes

Week
5


October 8 
 Congruences modulo a prime power, the Fibonacci sequence
 Read: Class notes
 Homework for Week 5 can be found at Homework Week 5.

October 9

 Xhour, 12:00  12:50
 First midterm exam: inclass portion

October 10 
 Homework for Week 4 is due today.
 Units in Z_n
 Read: Sections 5.1

October 12 
 The Euler phi function
 Read: Sections 5.2

Week
6


October 15 
 Introduction to cryptography
 Read: Section 5.3
 Homework for Week 6 can be found at Homework Week 6.

October 17

 Homework for Week 5 is due today.
 Quadratic residues
 Read: Section 7.1 & 7.2

October 19

 The Legendre symbol
 Read: Section 7.3

Week
7


October 22 
 Quadratic reciprocity
 Read: Section 7.4
 Homework for Week 7 can be found at Homework Week 7.

October 24 
 Homework for Week 6 is due today.
 Quadratic reciprocity, finding square roots, solving quadratic congruences.
 Class notes

October 26

 Solving quadratic congruences, odds and ends from Chapter 6, multiplicative functions
 Read: Class notes & Section 8.1

Week
8


October 29 
 Multiplicative functions, perfect numbers
 Read: Sections 8.1 & 8.2
 Homework for Week 8 can be found at Homework Week 8.

October 30

 Xhour, 12:00  12:50
 Second midterm exam: inclass portion

October 31

 The Moebius inversion formula
 Read: Section 8.3

November 2

 Homework for Week 7 is due today.
 The Dirichlet product
 Read: Section 8.6

Week
9


November 5 
 Gaussian integers & sum of two squares
 Read: Sections 10.1, 10.2 & class notes

November 7 
 Pythagorean triples
 Read: Sections 11.1, 11.2 & 11.3

November 9

 Homework for Week 8 is due today.
 Classification of Pythagorean triples
 Read: Sections 11.4 & 11.5

Week
10


November 12

 LAST CLASS
 Questions, Comments, Discussion of Final Exam, etc.
