| Lectures | Sections in Text | Brief Description |
|---|---|---|
| 9/11 | 1.1, 1.2 | Introduction, Division and Euclidean Algorithms |
| 9/13 | 1.2, 1.3 | Bezout's identity, least common multiples |
| 9/15 | 1.3, 1.4 | LCMs, Linear Diophantine Equations |
| 9/18 | 2.1, 2.2 | Fundamental Theorem of Arithmetic, Distribution of primes |
| 9/20 | 2.2, 2.4 | Distribution of primes, primality testing |
| 9/22 | 3.1 | Modular arithmetic |
| 9/25 | 3.2 | Linear Congruences |
| 9/27 | 3.3, 3.4 | Chinese remainer theorem |
| 9/29 | 3.4, 4.1 | Polynomials and polynomial congruences |
| 10/2 | 4.1 | The Arithmetic of ${\mathbb Z}_p$ |
| 10/3 (x-hour) |
4.2 | Pseudoprimes and Carmichael Numbers |
| 10/4 | Midterm I | In class part; all material through $\S3.4$; takehome part due 10/6 |
| 10/6 | class notes | Strong pseudprimes and Miller's test |
| 10/9 | 5.1, 8.1 | Euler's function |
| 10/11 | 5.2, class notes | Multiplicative functions;
Euler's function, General remarks about cryptography and public key cryptosystems, signatures, authentication |
| 10/13 | class notes | Cryptography review, RSA |
| 10/16 | 6.1, 6.2 | $U_n$ and primitive roots |
| 10/18 | 6.3-6.5 | Primitive roots for composite moduli, indices |
| 10/20 | 6.6+supplement, 7.1 | Indices, applications of primitive roots, discrete logs, quadratic residues |
| 10/23 | 7.1, 7.2 | Quadratic residues |
| 10/24 (xhour) |
7.3 | The Legendre symbol and properties |
| 10/25 | Midterm II | In class part; all material through $\S6.6$; takehome part due 10/27 |
| 10/27 | 7.3 | Gauss's Lemma |
| 10/30 | 7.4 | Quadratic Reciproicity |
| 11/1 | 7.4 | Road Trip (Connections) |
| 11/3 | 7.4, 8.2, 8.3 | Mersenne numbers, Pepins' test, Perfect numbers, Dirichlet convolution |
| 11/6 | 8.2-8.6 | Mobius inversion; Dirichlet convolution |
| 11/8 | 8.6, class notes | Congruent Numbers, Pythagorean Triples, Rational Points on the unit circle |
| 11/10 | Chapter 11.5, class notes | Congruent Numbers, Pythagorean Triples, Rational Points on the unit circle |
| 11/13 | Class notes | Congruent Numbers, Pythagorean Triples, Rational Points on the unit circle |
| 11/17 | Final Exam | 8-11am, 007 Kemeny |