Niven, Zuckerman, and Montgomery, An Introduction to the Theory
of Numbers, 5th edition. The book is out of print, but pdf versions can
be found.
Class Time: MWF 2:00--2:50, Pasq 109.
Course syllabus
Exams :
- Hour exam, approximately first week of October
- Final exam will be Monday, December 11, 4:15--6:15, TBA. You can substitute a project for the final exam.
- We will focus on solving Diophantine equations, including Pythagorean triples, finding which numbers are sums of two squares or variants of this problem,
and showing there are no solutions to the Fermat equation with n=3.
In order to do this, we will cover properties of primes, modular arithmetic,
quadratic reciprocity, algebraic number fields, and other topics,
time permitting. In the process, we will develop tools from abstract algebra as they are needed; this may mean people who already know a lot of algebra can skip a few classes.
- We will jump around the book, but the aim is to cover many topics in chapter 9 by the end of the semester.
Useful websites:
List of first 1000
primes
Modular arithmetic calculator by Ben Jones
Notes from class:
- 8-30 and 9-1: Notes on subrings of complex numbers and divisibility pdf file
- Notes on orders of elements of finite abelian groups (from 11-8 and 11-10) pdf file
- Proof of Fermat's last theorem for n=3 (12-4 and 12-6)
pdf file
- Review material on write gcd(a,b) as a combination of a and b pdf file
Assignments: Assignments with a date at the end are due on the date
specified.
In-class problems: These are problems that we considered during class. Most of them will eventually be on homework assignments.
- In-class Problems 1, considered Mon Sept 11 pdf file
- In-class Problems 2, considered Mon Sept 25 pdf file
- In-class Problems 3, considered Fri Oct 6 pdf file
- In-class Problems 4, considered Wed Nov 1 pdf file