Prerequisites: Permission of instructor.
Course Outline:
We will cover many of the following: Primes, divisibility,
congruences, Euler's theorem (public key cryptography), primitive
roots (pseudo-random numbers), quadratic residues, primality testing
and factoring, arithmetic functions (multiplicative functions,
Dirichlet series), continued fractions, Diophantine equations
(linear equations, Pell equations, Pythagorean triples, infinite descent),
Diophantine approximation (Dirichlet's theorem, Liouville's theorem,
irrationality, algebraic versus transcendental numbers).
Grading Scheme:
There will probably be assignments (potentially weekly) worth 25%,
two mid-terms
(Monday February 7, Monday March 20)
worth 20% each and a final exam
worth 35%.
Assignments:
Write on only one side
of the paper and staple all pages together.
On the the first page summarise your answers (those not involving proofs!)
with no working (show your working and proofs on the subsequent pages).
Include a cover sheet with your name, the course number and date.
You will generally have about a week to complete the assignment.