| Week | Monday | Tuesday | Thursday |
|---|---|---|---|
| 1 (Sept 12-16) | Preliminaries, Combinatorial Proofs (Chapter 1) HW (due Sept 22): Give 2 proofs to (2,2)+(3,2)+...+(n,2)=(n+1,3) |
Divisibility, Greatest Common Divisor (2.2, 2.3) HW (due Sept 22): (1.2) 3f, 10, (2.2) 1, 8, 10 (2.3) 13, 14b, 20bd |
Euclidean Algorithm, Linear Diophantine Equations (2.4, 2.5) HW (due Sept 22): (2.4) 4bd, 10b, 12 (2.5) 2ac, 5b, 6, 8b |
2 (Sept 19-23) | Student Activity 1 | Primes (3.1, 3.2) HW (due Sept 29): (3.1) 6b, 6c, 16 (3.2) 3, 7, 12c |
Observations on Primes (3.3), Prime Number Theorem (16.4) HW (due Sept 29): (3.3) 2, 18, 28 |
3 (Sept 26-30) | Student Activity 2 | Congruences, Bases Representation (4.2, 4.3) HW (due Oct 6): (4.2) 2, 4a, 6c, 8b, 10, 12a (4.3) 1, 2a, 3, 15 |
Linear Congruences and the Chinese Remainder Theorem (4.4) HW (due Oct 6): (4.4) 4ad, 5, 11 |
4 (Oct 3-7) | Student Activity 3 | Fermat's Theorem, Wilson's Theorem (5.2, 5.3) HW (due Oct 13): (5.2) 2c, 9, 11, 15, 19 |
Wilson's Theorem, Factoring Methods (5.3, 5.4) HW (due Oct 13): (5.3) 4, 9 |
5 (Oct 10-14) | Student Activity 4 | Multiplicative Functions (6.1) HW (due Oct 20): (6.1) 6, 7, 8, 16b, 18, 19, 23 |
Möbius Inversion Formula, Greatest Integer Function (6.2, 6.3) HW (due Oct 20): (6.2) 1, 3 (6.3) 2c, 5a, 10 |
6 (Oct 17-21) | Student Activity 5 | Class Cancelled | Midterm Test | 7 (Oct 24-28) | Euler's phi-function (Chapter 7) HW (due Nov 3): (7.2) 1, 4be, 7a, 13 (7.3) 2, 4 (7.4) 1, 11 |
Primitive roots, Polynomial congruences (8.1, 8.2) HW (due Nov 3): (8.1) 1b, 3, 5 (8.2) 1 |
Class Cancelled | 8 (Oct 31-Nov 4) | Student Activity 6 | Primitive Roots (8.2, 8.3) HW (due Nov 10): (8.2) 8, 11 (8.3) 1 |
Hensel's Lemma, Quadratic Residues (9.1) HW (due Nov 10): (8.3) 7 (9.1) 1ac, 2, 5, 10 |
9 (Nov 7-11) | Student Activity 7 | Class cancelled | Legendre Symbol (8.2), Quadratic Reciprocity (8.3) No homework |
10 (Nov 14-18) | Student Activity 8 | Jacobi Symbol, Electronic Coin-toss, Introduction to Cryptography (supplement) | Public-key Cryptography (supplement), RSA Encryption System, Zero-knowlegde Proofs |