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  

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