The following is a tentative syllabus for the course.
Week  Lectures  Sections in Text  Brief Description  Suggested Practice 

1  9/16  1.1  Introduction, Division and Euclidean Algorithms  Prove divisibility facts 5, 7, and 9. Read over the proof of Thm 1.1 in the text, and note any questions you have. 
9/18  1.2, 1.3  Bezout's identity, least common multiples  Write gcd(1485, 1745) in the form 1485u+1745v. Find lcm(1485, 1745). Show that ca and cb iff cgcd(a,b). 

9/20  1.3, 1.4  LCMs, Linear Diophantine Equations  Find the general solution to 1066x+1492y=8. Exercise 1.25 on p. 17 of the text. 

2  9/23  2.1, 2.2  Fundamental Theorem of Arithmetic, Distribution of primes  Prove the following: if a positive integer n is not a perfect square, then the square root of n is an irrational number. 
9/24  (xhour) Appendix A  Induction practice  Solutions to practice problems  
9/25  2.2, 2.4  Distribution of primes, primality testing  Exercise 2.7 on p.29 of the text. Use the Sieve of Eratosthenes to find all the primes less than 100. 

9/27  3.1  Modular arithmetic  Find the least absolute and least nonnegative residues of 19*14 mod (23). // Prove the divisibility rule for 5.  
3  9/30  3.2  Linear Congruences (Clarification)  Exercise 3.7 on p.52 of the text. 
10/1  (xhour) 10 ways  Proof techniques  Solutions to practice problems  
10/2  3.3, 3.4  Chinese Remainder Theorem  Exercises 3.9, 3.11, and 3.12 on p.5557 of the text.  
10/4  No class today  
4  10/7  3.4, 4.1  CRT, arithmetic modulo p  Exercises 3.18 and 3.20 on p.63 of the text. Exercise 4.1 on p.67 of the text. 
10/9  Exam 1 inclass portion  Material through Section 3.4. Take home portion due 10/11.  
10/11  4.1, 4.2  Pseudoprimes and Carmichael Numbers  Exercises 4.4 and 4.5 on p. 73 of the text.  
5  10/14  5.1, Appendix B  Units and groups  
10/15  (xhour) 5.2, class notes  Euler's function, intro to cryptography  Try out some examples with p=5 and q=7.  
10/16  class notes  More cryptography, RSA  Exercise 5.7 on p.90 of the text.  
10/18  6.1, 6.2  The group of units and primitive roots  Exercise 6.26(b) on p.118 of the text. Exercise 6.5 on p.101 of the text. 

6  10/21  6.36.5  Primitive roots for composite moduli  Read the proof of Theorem 6.7. Exercise 6.10 on p. 106 of the text. 
10/23  6.6  Applications of primitive roots  Exercise 6.16 on p. 112 of the text.  
10/25  7.1, 7.2  Quadratic residues  Exercise 7.4 on p. 121 of the text. Find the set of quadratic residues mod 60. 

7  10/28  7.3  The Legendre symbol and properties  Determine if [72] is a quadratic residue mod 41. Determine if [2] is a quadratic residue mod 29. 
10/30  Exam 2 inclass portion  Material through Section 6.6. Take home portion due 11/1.  
11/1  7.3  Gauss's Lemma  Exercise 7.10 on p.129 of the text.  
8  11/4  7.4  Quadratic reciprocity  Exercise 7.12 on p.132 of the text. Read the proof of Theorem 7.11 on p.133 of the text. 
11/5  (xhour) 8.1, 8.2  Arithmetic functions  Exercise 8.1 on p. 144 of the text. Exercise 8.5 on p. 147 of the text. 

11/6  8.38.5  The Mobius function  Exercise 8.15 on p. 156 of the text.  
11/8  8.6, 9.1, class notes  The Dirichlet product, the Riemann Zeta function  Note: This material is not covered on the final exam.  
9  11/11  11.111.5  Fermat's last theorem and Pythagorean triples  Exercises on p.220 of the text. Read Section 11.8. 
11/13  10.1, 10.3  Sums of squares I  Exercises 10.2, 10.3 on p.195 of the text.  
11/15  10.3, 10.4  Sums of squares II  Exercises 10.13, 10.14 on p.205 of the text.  
10  11/18  Wrapup  Final Exam Study Guide 