| Week | Class | Section covered | Remarks |
| 1 | R Aug 30 | Introduction to the course; well-ordering principle, divisibility and division theorem | 1.1, 1.3, 1.5 |
| 2 | T Sept 4 | GCD, Euclidean Algorithm, and linear Diophantine equations | 3.3, 3.4, 3.7 PRIMES is in P |
| 2 | R Sept 6 | primes numbers and unique factorization and Twin prime conjecture. | 3.1, 3.2, 3.5 Erdos-Selberg Dipute |
| 3 | T Sept 11 | Congruence | 4.1 |
| 3 | R Sept 13 | Congruence equations | 4.2, 4.3, 4.4 |
| 4 | T Sept 18 | Congruence system and congruence classes | 4.1, 4.4 |
| 4 | R Sept 20 | Reduced system of residues and Wilson's Theorem | 6.1 (part) and 6.3 (part) |
| 5 | T Sept 25 | Euler's Theorem and Euler-phi function | 6.3, 7.1 |
| 5 | R Sept 27 | Euler phi-function and sum and number of divisors | 7.1, 7.2 |
| 6 | T Oct 2 | multiplicative functions and Perfect numbers and Mersenne Primes , (GIMPS) | 7.2, 7.3 prime page |
| 6 | R Oct 4 | Mobius Inversion | 7.4 |
| 7 | T Oct 9 | partition | 7.5 |
| 7 | R Oct 11 | Applications Cryptography---Caesar Cipher and RSA Journey to Cryptography | 8.1 and 8.4 |
| 8 | T Oct 16 | Fall break | |
| 8 | R Oct 18 | order of elements | 9.1-9.2 |
| 9 | T Oct 23 | primitive root | 9.2 |
| 9 | R Oct 25 | existence of primitive roots, and Discrete Logarithm | 9.3-9.4 |
| 10 | T Oct 30 | Quadratic residues and nonresidues | 11.1 |
| 10 | R Nov 1 | The Law of quadratic reciprocity | 11.1-11.2 |
| 11 | T Nov 6 | the Jacobi Symbol | 11.2-11.3 |
| 11 | R Nov 8 | Continued fractions I | 12.2-12.3 |
| 12 | T Nov 13 | Continued fraction II | 12.3-12.4 |
| 12 | R Nov 15 | Periodic continued fractions and Pell equation | 13.4 |
| 13 | T Nov 20 | Pythagorean triples and Fermat's Last Theorem | 13.1-13.2 |
| 14 | R Nov 22 | Thanksgiving Day | |
| 13 | R Nov 27 | Sum of squares and congruent numbers | 14.1-14.2 |
| 14 | T Nov 29 | Gaussian Integers, GCD | Circles and squares...and Primes |
| 15 | T Dec 4 | Prime factorization, sums of squares | 14.2-14.3 |
| 15 | R Dec 6 | Review (of homework problems) | |
| 16 | T Dec 18 | Final exam | 9-12 |