2010 Spring MATH 201-01
Bulletin Course Description Fields and field extensions, modules over rings, further topics in groups, rings, fields, and their applications. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title ALGEBRAIC STRUCTURES II Department MATH Course Number 2010 Spring 201 Section Number 01 Primary Instructor Pardon,William L Prerequisites Prerequisite: Mathematics 200, or 121 and consent of instructor.
Synopsis of course content
This course will introduce Galois theory, one of the most
basic and vital ideas of "modern" algebra. The main goal is to prove that the roots of a polynomial p can be expressed "in radicals" involving the coefficients of p (a la the quadratic formula) if and only if a certain group G(p) ("the Galois group") associated to the polynomial is "solvable". The latter is a group-theoretic condition which can be checked in many cases, in particular showing that p is always solvable in radicals if its degree is less than 5; and that there are quintics which are not so solvable.
Textbooks
Abstract Algebra, by Dummit and Foote
Assignments
Weekly homework assignments
Exams
Midterm and final
Grade to be based on
exams and homework
