This course is an introduction to both the classical and modern questions about numbers. Students explore the integers, examining issues such as primes, divisibility, congruences, primitive roots, quadratic residues, and quadratic reciprocity. They master a variety of number theoretic techniques and computations and apply these in applications such as cryptography and coding theory. Prerequisite: MAT 2880 Mathematical Rigor or MAT 2890 Introduction to Mathematical Rigor or permission of instructor.