# MATH-UA 348 Honors Algebra I

4 points. Offered in the fall.

## Course Description

Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, group actions, homomorphisms and quotient groups, direct products, classification of finitely generated abelian groups, Sylow theorems. Rings, ideals and quotient rings, Euclidean rings, polynomial rings, unique factorization.

## Prerequisites

MATH-UA 123 Calculus III or MATH-UA 213 Math for Economics III (for Economics majors) and MATH-UA 140 Linear Algebra with a grade of C or better or the equivalent. Recommended: the honors section of MATH-UA 123 Calculus III and MATH-UA 148 Honors Linear Algebra.