We will commence this subject with an introduction to number theory. In the later parts of the subject we will treat topics such as congruences, residues, continued fractions, diophantine equations, transcendental numbers, and/or primality and factoring. We will also touch on tantalizing connections to cryptography and/or one or more of the recent analytic and algorithmic advances in the areas of Mersenne primes, the Riemann hypothesis, and primality proving. This subject will be accessible and interesting to a varied audience, including students with interests in applied mathematics, pure mathematics, or computer science.
