Introduction

Number theory is one of the oldest and most beautiful branches of mathematics. Apparently simple questions, such as whether a given number can be written as a sum of squares, are answered by deep and powerful theory.

This course provides an introduction to number theory. Our focus will be on integral and rational solutions to equations, and on the algebraic structures which explain the shape of those solution sets.

Prerequisites

The formal requirements for this course are minimal, but you should be comfortable with proofs. Although this course is self-contained, you may find that the first two weeks move especially quickly if you have not taken M360 or M366.

Logistics

Requirements and other expectations

As in any other 400-level class, you will need to work both diligently and creatively.

Help

This is challenging material; it's fully expected that sometimes you'll need a little help. Unless specifically noted, you're encouraged to work with other students in the class. (Please observe that the work you actually turn in must be your own.)

Questions directed to j.achter@colostate.edu will be answered swiftly. However, some questions are best answered in person. You can come by office hours or schedule an appointment.

This page is available at http://www.math.colostate.edu/~achter/400