Math 42 spring 2015

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 signi cant 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.


Textbook and readings


Problem sets and solutions

Solutions will be posted after class on the due date of each assignment.

Exams and solutions

Bonus assignments

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