Introduction

The theory of numbers long enjoyed a reputation as gorgeously useless, a creation of the mind unsullied by application. This reputation was decisively shattered in the second half of the twentieth century by the advent of modern cryptography. In this course you'll learn the mathematics necessary to keep a secret, share one, break one, or forge one. Broadly speaking, the topics are: In addition to this material, you'll learn how to handle unfamiliar problems with creativity, insight and rigor.

Prerequisites

Although the only formal prerequisite is M229, matrices and linear algebra, there are certainly other prerequisites; you'll need a flexible mind and a willingness to work hard.

Logistics

Requirements and other expectations

This may well be the first non-calculus class you take. You'll find the rhythm and demands of this class significantly different from those of the calculus sequence. Both in class and outside it, you'll be expected to generate and explore patterns. As a second step, you'll need to write down clear statements (and proofs!) of your assertions. If you miss an exam without a note from a doctor or dean you will receive a zero for that exam. You must take the exam during the scheduled time; no make-ups will be given. You must pass the final in order to pass the course.

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/360