In this class, we will be reading the book "In Code: a Mathematical Journey" by Sarah Flannery (with David Flannery) published by Workman Publishing Co. (2001). For each class, someone in the class will be responsible for taking good notes, writing them up, getting me to look them over, and handing them out to the class by the start of the next week.
For ages, number theory has been thought to be the purest area of pure mathematics, the mathematician's equivalent of Art for Art's sake. With the advent of computers, applications of number theory to cryptography, intelligence gathering, and the secure transmission of data have often thrust number theory into the public eye. For example, the National Security Administration has sought to preview and restrain the publication of research on the factorization of integers! See the recent book "Crypto" by S. Levy.
The properties of numbers have fascinated people since ancient times. This course will introduce students to the most important general concepts underlying the development of number theory over the last three thousand years. We will emphasize the beauty of the subject, how its ideas change what you can think about, and the pleasure it affords.
This course requires no formal background in mathematics. It should be of interest to prospective teachers, computer science students, mathematics majors, and anyone interested in mathematics as a cultural activity.