Number Theory

This course is devoted to the study of the integers. Although the approach will be mainly axiomatic, consideration will be given to historical aspects of the subject. Special attention will be given to problem solving, both as a central device for exposing the development of the theory of the course and for its own sake. Topics will include divisibility properties of integers, prime numbers, modular arithmetic, Diophantine equations, and special-number theoretic functions. No prior experience with this material is necessary, although mathematical sophistication would be important.