Math 230B
Winter 2011
FINAL
RESULTS: I will finish grading tomorrow (Friday) morning and
post the results on eee around 9am. I will be in my office from 1pm on
for a couple of hours so please stop by to see your work and discuss
the final with me.
Time:
M-W-F Rh 340P
Instructor:
Martin Zeman
Grading
policy: 30% Homeworks, 30% Midterm (Date: Wednesday Week 6), 40%
Final
(Wed, Mar 16, 1:30-3:30pm)
Syllabus
Midterm
topics
Discussion:
I wold like to offer discussion session on Thursdays 11am-12noon in RH
440R. (If you prefer different time/date let me know; we may try to
find something.) The participation at the discussion is entirely
voluntary and will have no effect on grades. I just feel that some of
you may find helpful to have a session where we could go over the
homework problems and discuss the solutions. I will expect that
you will come with questions and problems to discuss.
Text:
Dummit & Foote: Abstract Algebra 3rd edition
Topics:
The goal is to cover Galois Theory. If time permits, we will discuss
some basic material on dual modules, tensor products, and injective and
projective modules.
Homeworks
(Instructions for Homeworks)
HW 1 (due Jan 12)
9.2:1,2,4; 9.5:5 Please do both
arguments indicated in the hint;
13.1:1,3
Please
turn the
homework in with Casey in the department office.
HW 2 (due Jan 19) 13.2:1,3,4,7,8 (Read the
example on p.522),12,16,17
HW 3 (due Jan 26) 13.2:6,10,11,13,14,19,20 13.4:1,2,3
HW 4 (due Feb 2) 13.4:
4,5,6 13.5:
2,5,6,7,8,11
13.6:10
HW 5 (due Feb 9) 13.6: 1,3,4,6
Determine the Galois group of the Q[x]=polynomial (x2-2)(x2-3)(x2-5)
HW 6 (due Feb 16) 14.1:
2,3,4,5 14.2:
4,10,12,13,15(a)
To determine the Galois groups: write down the generators of the
respective groups and the complete list of equations that determine the
group multiplication. Please work through the example on p.577 in
the book on the Galois group of x8-2 before approaching
problems 14.2: 4,10;
there are more
details than I gave in the lecture.
HW 7 (due Feb 23) 14.1: 7 14.2: 6,9,15(b),16,18(abc); Also compute the Galois
group of x6-2. As before, write down the generators of the
Galois groups you compute and determine the relevant equations among
the generators.
HW 8 (Due Mar 2) 14.2:
2,3,17,18(d) Determine Galois groups of the following
polynomials over Q:
(a) x4-6x2+7
(b) x6-3
Please read these instructions.
HW 9 (Due Mar 9) 14.2: 11,27 14.3:
5,8,11 14.4: 1,2,3,5*
Also:
(a) Use the Galois group for the
polynomial (a) in HW 7 to determine all subfields
of its splitting field. Also draw the diagram inidicating the
correlations between
the subfields of the splitting field and the subgroups of the Galois
group.
HW 10 (Due Mar 16) 14.5: 1,2,4,5,10
14.6: 2
Also: Find a polynomial
in Z[x] whose Galois group is isomorphic to Z2xZ3.
HOME
Last updated: March 17,
2011