MATH 404A     Spring, 2011  

Solutions for the Final Exam







INSTRUCTOR:  Ralph Greenberg,   Padelford C-553,    543-7648,    greenber@math.washington.edu


OFFICE HOURS:  Monday 11:00 -12:00,   Wednesday, 1:00 - 2:00,   Friday, 2:00 - 3:00,   other times by appointment.


TEXT:   Abstract Algebra, 3rd edition, by D.S. Dummit and R.M. Foote

GRADING:   The grade will be based on the homework assignments (which count 30% altogether), the midterm (which counts 30%), and the final (which counts 40%). The midterm will be on Friday, April 29th. The final will be on Wednesday, June 8th, 8:30 - 10:20.



Math 404 is devoted to field theory and Galois theory. We will cover most of chapters 13 and 14 in the text. This topic originated in the study of polynomials and their roots. The underlying idea is that we study the roots of a polynomial by studying the fields generated by those roots. We study relationships between those fields by studying their groups of automorphisms.


MATH 403A Webpage



PROBLEM SETS:       1,       2,       3,       4,

SOLUTIONS:             1         2,       3       4


Sample Midterm,       Solutions for the Sample Midterm


Galois Theory Problems,       Solutions for the Galois Theory Problems


HANDOUTS
Reducibility and Irreducibility of Polynomials over a Field
The Fundamental Lemma
Vector Spaces
Field Extensions and Their Degrees
The Primitive Element Theorem
Isomorphisms, automorphisms, and embeddings of fields
The discriminant of a polynomial
Galois Theory
Solvable Groups