week 1
M: Properties of divisibility and gcds. Induction. Division algorithm. Euclidean algorithm. GCD theorem.
T: Rings, primes, and composites. Euclid's Lemma. Fundamental theorem of arithmetic.
W: Linear diophantine equations. Prime number sieve. Infinitude of primes.
T:(mentioned Dirichlet's Thm, Chebotarev density Thm, Prime number Thm, Riemann Hypothesis)

week 2
M: Modular arithmetic.
T: Euler's Thm. Fermat's Thm. Wilson's Thm.
W: Chinese Remainder Thm.
T: phi is multiplicative. computing phi, inverses, and powers. Miller-Rabin test. AKS test.

week 3
M: Hensel's lemma
T: Root bound. (Z/p)* is cyclic
W: midterm 1
T: (Z/p^k)* is cyclic when p an odd prime

week 4
M: Public key cryptography. RSA cryptosystem. Review Hensel's lemma.
T: Diffie-Hellman. Attacking RSA given phi. Fermat factorization method.
W: Pollard p-1 method. Attacking RSA given decryption key.
T: Quadratic sieve. Factoring given two numbers that square to same thing.

week 5
M: Quadratic residues. Legendre symbol. Euler's Criterion.
T: Guass's lemma. Quadratic reciprocity.
W: Jacobi symbol. Jacobi version of quadratic reciprocity.
T: Finding square roots mod p.

week 6
M: Properties of Farey sequences. Existence of good rational approximations.
T: Continued fractions. Computing convergents.
W: midterm 2
T: Which numbers are a sum of two squares.

week 7
M: Periodic continued fractions are exactly quadratic irrationals
T: Pell's equation
W: Elliptic curves
T: Group law on the points of an Elliptic curve.

week 8
M: Lenstra's elliptic curve factorization method.
T: Elliptic curve cryptography
W: review
T: final