Lecture No. 
Date 
Title 
Reading 
Lecture Notes 
1 
June 18 
Introduction. Divisibility. Ideals. 
1.1,1.2 
Lecture 1 
2 
June 19 
GCD and Ideals. 
1.2, notes 
Lecture 2 
3 
June 20 
LCM. Primes, Unique Factorization. 
1.2,1.3 
Lecture 3 
4 
June 21 
Congruences and Their Properties. 
2.1 
Lecture 4 
5 
June 25 
Fermat's Little Theorem. Wilson's Theorem. 
2.1 
Lecture 5 
6 
June 26 
Fermat's Thm on Sums of Squares 
2.1 
Lecture 6 
7 
June 27 
Chinese Remainder Thm 
2.3 
Lecture 7 
8 
June 28 
Algebraic Perspective: Rings 
2.10, 2.11, notes 
Lecture 8 
9 
July 2 
More Algebra 
2.10,2.11,notes 
Lecture 9 
10 
July 3 
Hensel's Lemma, Reduction of Modulus 
2.5,2.6 
Lecture 10 
11 
July 4 
Holiday  No Class 

12 
July 5 
Prime Modulus 
2.7 
Lecture 12 
13 
July 9 
Primitive Roots 
2.8 
Lecture 13 
14 
July 10 
Quadratic Residues 
3.1 
Lecture 14 
15 
July 11 
Gauss' Lemma 
3.1 
Lecture 15 
16 
July 12 
Quadratic Reciprocity 
3.2 
Lecture 16 
17 
July 16 
Quadratic Forms 
3.4 
Lecture 17 
18 
July 17 
Review 

19 
July 18 
Midterm Exam 

20 
July 19 
Quadratic Forms II 
3.4,3.5 
Lecture 20 
21 
July 23 
Quadratic Forms III  The Reduction Theorem 
3.5,3.6 
Lecture 21 
22 
July 24 
Applying the Reduction Theorem 
3.7 
Lecture 22 
23 
July 25 
Diophantine Eqns  Linear Equations 
5.1,5.2 
Lecture 23 
24 
July 26 
Pythagorean Triples 
5.3 
Lecture 24 
25 
July 30 
The "Method of Descent" 
5.4, notes 
Lecture 25 
26 
July 31 
Rational Points on Curves 
5.6 
Lecture 26 
27 
Aug 1 
The Projective Line 
5.6, notes 
Lecture 27 
28 
Aug 2 
The Projective Plane 
5.6, notes 
Lecture 28 
29 
Aug 6 
Elliptic Curves I 
5.7 
Lecture 29 
30 
Aug 7 
Elliptic Curves II 
5.7, notes 
Lecture 30 
31 
Aug 8 
Review 

32 
Aug 9 
Final Exam 
