MTH 57715772: Algebra
Time: TR 5:307:30 PM
Prerequisites
Two semesters of undergraduate abstract algebra.
Textbook
There will be no textbook required. I will use my lecture notes as a textbook, which will be provided for free.
However, recommended books that you probably should have in your library, if you are planning to study algebra are:
 Algebra, Serge Land
 Abstract Algebra, Dummit & Foote
 Topics in Algebra, Hernstein
Grading
Homework will be assigned and will be collected to be graded. There will be no midterms. The final exam will be a take home exam.
Course policies
The course will be conducted in accordance to the Oakland University regulations and policies. Details can be found here
https://oakland.edu/provost/policiesandprocedures
Topics
 Basic properties of groups
 Quotient groups and homomorphisms
 Groups acting on sets
 Sylow Theorems
 Abelian groups
 Solvable groups
 Extensions and cohomology
 Rings and ideals
 Euclidean rings, PID's, UFD's
 Polynomial rings
 Local and Notherian rings
 Introduction to module theory
 Modules over PIDs
 Field extensions
 Splitting fields and algebraic closure
 Galois extensions
 Computing Galois groups of polynomials
 Abelian Extensions
 Finite fields
 Transcendental extensions
