Goals: An introduction to number theory. This course will develop the properties of integers, especially the properties of prime numbers, starting from the Peano Axioms and show how the structure of prime numbers is reflected in the structure of the group of integers modulo n. While not a prerequisite for MATH 5890, this course is the first in a two semester sequence, along with MATH 5980, in modern algebra. Content: Equivalence relations, Peano Axioms, Fundamental Theorem of Arithmetic, Diophantine equations, prime numbers, Gaussian integers, Fundamental Theorem of Finite Cyclic Groups. Taught: Spring term. Prerequisites: MATH 1180.