Mathematics 114 - Explorations in Number Theory

We will cover the arithmetic of whole numbers and of prime numbers, in particular, examining some of the earliest questions in mathematics from a modern perspective, finding whole number solutions to equations with several variables, deciding whether or not such solutions exist and if so, determining whether the solution set is finite or infinite. Topics include the theory of 'finite arithmetic,' converting questions about the infinite set of whole numbers to those involving just a small set of primes, using computers to examine problems numerically.