MATH 3890 - Algebra I

Goals: An introduction to algebraic structures. 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 ring of integers modulo n.

Content: Equivalence relations. Peano Axioms. Fundamental Theorem of Arithmetic. Diophantine equations. Prime numbers. Gaussian integers. The group of integers modulo n. Fundamental Theorem of Finite Cyclic Groups.

This course is the first in a two semester sequence, along with MATH 5980, in algebra.

Taught: Fall term.

Prerequisite: MATH 1180.

Credits: 4 credits