Number theory is one of the most beautiful and ancient parts of mathematics, and is still a vibrant area of modern research. It is concerned with properties of whole numbers, especially how numbers break down into primes and which equations admit whole-number solutions. This course will introduce the basic ideas of number theory. One of the most striking applications of number theory from the past century is its use in cryptography; a signicant part of the course will develop the material needed to discuss a famous cryptosystem called RSA. The course will end with a selection of topics, possibly including sums of squares, Diophantine equations, continued fractions, and the use of imaginary and complex numbers in number theory.
There are two optional bonus assignments: a programming assignment and an essay assignment. Only one will affect your grade, but if you wish to complete both of them I will use the higher of the two scores.
Essay assignment description.
Programming assignment description.
|Programming task||Submission Deadline|
|Phi||SAMPLE (not for credit)|
|Dirichlet||Friday 10 April, 2pm|
|LeastNR||Friday 17 April, 2pm|
|Remainders||Friday 24 April, 2pm|
|Cracking||Friday 1 May, 2pm|