|The text for the course is Elementary Number
Theory by David M. Burton, McGraw-Hill Publishing Co. The first four
chapters of the book, encompassing Mathematical Induction, the Theory of
Divisibility, Primes and their role, and the Theory of Congruences,
constitute the core of the course.
Beyond that, and as time and participant interest allows/dictates, we will select topics from among Chapter 8, Primitive Roots and Indices; Chapter 9, Quadratic Reciprocity; Chapter 10, Cryptography; Chapter 15, Continued Fractions. We hope to provide also a glimpse into algebraic number theory through an examination of the beautiful theory of the Gaussian Integers. A variety of applications will be discussed along the way.
Any background material needed by the audience will be cheerfully provided. Starting at a point where everyone is comfortable and proceeding through material of significant mathematical and historical interest, we hope to arrive at an understanding of the theory of numbers in some reasonable depth.