Week | Class | Section covered | Remarks |
1 | R Aug 31 | Introduction to the course; well-ordering principle, divisibility and division theorem | 1.1, 1.3, 1.5 |
2 | T Sept 5 | GCD, Euclidean Algorithm, and linear Diophantine equations | 3.3, 3.4, 3.7 PRIMES is in P |
2 | R Sept 7 | primes numbers and unique factorization and Twin prime conjecture. | 3.1, 3.2, 3.5 Erdos-Selberg Dipute |
3 | T Sept 12 | Congruence | 4.1 |
3 | R Sept 14 | Congruence equations | 4.2, 4.3, 4.4 |
4 | T Sept 19 | Congruence system and congruence classes | 4.1, 4.4 |
4 | R Sept 21 | Reduced system of residues and Wilson's Theorem | 6.1 (part) and 6.3 (part) |
5 | T Sept 26 | Euler's Theorem and Euler-phi function | 6.3, 7.1 |
5 | R Sept 28 | Euler phi-function and sum and number of divisors | 7.1, 7.2 |
6 | T Oct 3 | multiplicative functions and Perfect numbers and Mersenne Primes , (GIMPS) | 7.2, 7.3 prime page |
6 | R Oct 5 | Mobius Inversion | 7.4 |
7 | T Oct 10 | partition | 7.5 |
7 | R Oct 12 | Applications Cryptography---Caesar Cipher and RSA Journey to Cryptography | 8.1 and 8.4 |
8 | T Oct 17 | Fall break | |
8 | R Oct 19 | order of elements | 9.1-9.2 |
9 | T Oct 24 | primitive root | 9.2 |
9 | R Oct 26 | existence of primitive roots, and Discrete Logarithm | 9.3-9.4 |
10 | T Oct 31 | Quadratic residues and nonresidues | 11.1 |
10 | R Nov 2 | The Law of quadratic reciprocity | 11.1-11.2 |
11 | T Nov 7 | the Jacobi Symbol | 11.2-11.3 |
11 | R Nov 9 | Continued fractions I | 12.2-12.3 |
12 | T Nov 14 | Continued fraction II | 12.3-12.4 |
12 | R Nov 16 | Periodic continued fractions and Pell equation | 13.4 |
13 | T Nov 21 | Pythagorean triples and Fermat's Last Theorem | 13.1-13.2 |
14 | R Nov 23 | Thanksgiving Day | |
13 | R Nov 28 | Sum of squares and congruent numbers | 14.1-14.2 |
14 | T Nov 30 | Gaussian Integers, GCD | Circles and squares...and Primes |
15 | T Dec 5 | Prime factorization, sums of squares | 14.2-14.3 |
15 | R Dec 8 | Review (of homework problems) | |
16 | W Dec 20 | Final exam | 9-12 |