MATH 3003 - Schedule

 Day Topics/events Sections in text 1/17 There are infinitely many primes (proof), Prime Number Theorem (discussion) 1.1.1, 1.2.1, 1.2.5 1/19 GCD, Euclid's theorem, Fundamental Theorem of Arithmetic 1.1.2, 1.1.3, 1.1.4 1/24 Prime Sieve, Dirichlet's Theorem, zoo of conjectures about primes 1.2.2, 1.2.3, 1.2.4 1/26 Arithmetic modulo n, groups and rings 2.1 1/31 Linear congruence, sets of residues 2.1.1 2/2 Wilson's and Euler's theorems 2.1.2, 2.1.3 2/7 Euler's phi-function, Chinese remainder theorem 2.2 2/9 Snow day N/A 2/14 Extended Euclidean Algorithm, computing large powers modulo n 2.3 2/16 Polynomial equations (modulo n), primitive roots 2.5 2/21 Existence of primitive roots modulo a prime, review 2.5 2/23 Test 1 1.1 - 2.3 2/28 Primality tests 2.4 3/2 Simple ciphers, Diffie-Hellman key exchange 3.2 3/7 RSA 3.3, 3.4.1, 3.42 3/9 Law of Quadratic Reciprocity (statement and examples) 4.1 3/21 Euler's criterion and Gauss Sums 4.2, 4.4 3/23 Proof of the Law of Quadratic Reciprocity using Gauss sums 4.4 3/28 Gauss' lemma and Euler's version of Quadratic Reciprocity 4.3 3/30 Second proof of Quadratic Reciprocity 4.3 4/4 Finding square roots modulo n 4.5 4/6 Test 2 2.5 - 4.4 4/11 Ellipic curves, addition rule 6.1, 6.2 4/13 Ellipic curves over Z/pZ, examples 6.2 4/18 Pollard's p-1 method, Lenstra's factorization 6.3 4/20 Lenstra's factorization examples, Elliptic curve Diffie-Hellman 6.4 4/25 Congruent numbers 6.5