| Week | Class | Section covered | Remarks |
| 1 | R Aug 27 | Introduction to the course; well-ordering principle, divisibility and division theorem | 1.1, 1.3, 1.5 |
| 2 | T Sept 1 | GCD, Euclidean Algorithm, and linear Diophantine equations | 3.3, 3.4, 3.7 |
| 2 | R Sept 3 | primes numbers and unique factorization | 3.1, 3.2, 3.5 Erdos-Selberg Dipute |
| 3 | T Sept 8 | Congruence | 4.1 |
| 3 | R Sept 10 | Congruence equations | 4.2, 4.3, 4.4 |
| 4 | T Sept 15 | Congruence equations and congruence classes | 4.1, 4.4 |
| 4 | R Sept 17 | Reduced system of residues and Wilson's Theorem | 6.1 (part) and 6.3 (part) |
| 5 | T Sept 22 | Fermat's Little Theorem and Euler's Theorem | 6.1, 6.3 |
| 5 | R Sept 24 | Applications of Congruences | Chapter 5 |
| 6 | T Sept 29 | Euler-phi-function, and sum and number of divisors | 7.1, 7.2 |
| 6 | R Oct 1 | multiplicative functions and Mobius Inversion | 7.4 |
| 7 | T Oct 6 | Perfect numbers and Mersenne Primes (GIMPS) | 7.3 |
| 7 | R Oct 8 | Cryptography---Caesar Cipher and RSA Journey to Cryptography | 8.1 and 8.4 |
| 8 | T Oct 13 | Fall break | |
| 8 | R Oct 15 | order of elements | 9.1-9.2 |
| 9 | T Oct 20 | primitive root | 9.2 |
| 9 | R Oct 22 | existence of primitive roots, and Discrete Logarithm | 9.3-9.4 |
| 10 | T Oct 27 | Quadratic residues and nonresidues | 11.1 |
| 10 | R Oct 29 | The Law of quadratic reciprocity | 11.1-11.2 |
| 11 | T Nov 3 | the Jacobi Symbol | 11.2-11.3 |
| 11 | R Nov 5 | Continued fractions | 12.2-12.3 |
| 12 | T Nov 10 | Periodic continued fraction | 12.4 |
| 12 | R Nov 12 | Pell equation | 13.4 |
| 13 | T Nov 17 | Pythagorean triples and Fermat's Last Theorem | 13.1-13.2 |
| 13 | R Nov 19 | Gaussian Integers, Gaussian primes, GCD | 14.1-14.2 |
| 14 | T Nov 24 | Review (of homework problems) | |
| 14 | R Nov 26 | Thanksgiving Day | |
| 15 | T Dec 1 | Prime factorization, sums of squares | 14.2-14.3 |
| 15 | R Dec 3 | Sum of squares and congruent numbers | 13.3, 13.5 |
| 16 | W Dec 16 | Final exam | 2-5pm |