MATH 418 D14 - Intro to Abstract Algebra II
Rings of quotients of an integral domain. Euclidean domains, principal ideal domains. Unique factorization in polynomial rings. Fields extensions, ruler and compass constructions. Finite fields with applications. Modules. Structure theorem for finitely generated modules over principal ideal domains. Application to finitely generated abelian groups and canonical forms of matrices. Introduction to error-correcting codes. Course Information: 3 or 4 undergraduate hours. 3 or 4 graduate hours. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance. Prerequisite: MATH 417 or consent of instructor.
Graduate students requesting the 4 credit hour section must first register for the 3 hour section. If the instructor is willing to offer extra work to graduate students for the 4-hour section, students can follow the instructions to request a switch to the 4-credit section between the FIRST DAY of the semester and the 8th week of the semester. Instructions are available at https://go.math.illinois.edu/3to4credit
Option 1Number of Required Visit(s): 0
Course Level: Graduate