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Number theory is a wide field that concerns the study of certain sets of numbers. Principal among these is the set of positive integers. Number theory has a long and rich history, encompassing work by such important mathematicians as Euclid, Euler and Gauss, and it has been called the "Queen of mathematics". But fascinating work in number theory is still being done today. Fermat's Last Theorem was a famous centuries-old problem that has recently been solved. Many important unsolved problems still remain, like the twin prime conjecture, and the Riemann hypothesis. Number theory has practical applications as well. It provides the theoretical framework for our current standards of data encryption. Every time you make a purchase on the internet, you are using number theory!

This course will be a survey of elementary number theory. Here, "elementary" refers to number theory that does not rely on other fields such as algebra, analysis, or geometry. We will study primes and divisibity, congruences, arithmetic functions, cryptology, and other topics as time permits.

Stephanie Treneer

Last updated June 25, 2009 14:49:07 EDT