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 |
|