Math 42: Introduction to Number Theory (Spring 2015)

This course introduces the basic ideas of number theory. It is aimed at non-majors and has no prerequisites.

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. 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.


  • The last required day of class will be Wednesday, April 22. There will be an optional meeting on Friday, April 24 (in the usual classroom), but the material discussed will not appear on any assignments or the final exam.
  • My office hours have changed. They will now be Wednesday from 3:00 to 4:20 and Thursday from 1:45 to 3:15. My dog Charley will be with me at my Thursday office hours unless requested otherwise.

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