20230 Algebraic Structures 1

Credits: 3 intermediate and 3 advanced credits in Mathematics

Prerequisites: none

Required: Linear Algebra I, as well as having accumulated a total of at least 24 credits in Mathematics

Recommended: Introduction to Mathematics, Infinitesimal Calculus I, Infinitesimal Calculus II, Linear Algebra II

Author: Abraham Orenstein

This abstract algebra course is intended for Mathematics and Computer Science students and may also be of interest to students of Physics. The course requires considerable mathematical maturity. Therefore, it is recommended for veteran students who have already taken several Mathematics courses.

Topics: Sets, integers, relations, functions, semigroups, permutations; Groups and subgroups, quotient groups, isomorphism theorems, Sylow’s theorems, direct products, finitely generated abelian groups, normal series; Rings and ideals, extensions and imbedding of rings, polynomial rings, the ring F[x] (over a field F), unique factorization domains.

This is a year-long course, however, capable students may increase the pace and complete the course work by the end of the fall semester, or begin later, at any time prior to the beginning of the spring semester.

1A short non-credit seminar may be added to this course. See note under Mathematics seminars.