Math 4107, Abstract Algebra, Spring 2008
For a copy of the course syllabus, click
here
Homework 1 (due Friday, Jan. 18)

Page 89, #4, 8, 11.

Page 1617, #1,3,9.

Page 2324, #1,4,6,7.

Show that if a  bc, then a  ( gcd(a,b) gcd(a,c)).

Show that if ax == ay (mod N), then x == y (mod N/gcd(a,N)).
Homework 2 (due Friday, Feb. 1)

Page 3536, #1,2,6,11,14,21.

Page 4849, #2,3,4,5,6,12,13,15,19,38.

*** Your first exam will be Friday, Feb. 15. ***

I believe I said that all your problems in this last homework
can be solved in ``one line''. This is not exactly true  most will
take a couple lines perhaps. Problem #38 is the only one that might
pose some difficulty (as far as finding a short proof).
Homework 3 (due Friday, Feb. 15  before exam)

Click here for some
extra problems.

Page 53, #1,2,4,7, 12 (assume in 12 that the group is finite).
Also, show that the opposite of a group G is isomorphic to G  Recall
that G^opp = opposite of G, which is the group with operation * such
that a*b in G^opp is the same as ba in G.

Page 64  65, #1,3,6,8,10.

Here are some old homework writeups from the last time I taught
this course, which should be useful to study for the exam:
1. and
2.

Click here for a note I wrote on
group actions (handed out in class).

Extra Problem for homework: Show that if phi is an isomorphism
from a group A to a group B, and if x is in A, then order(phi(x)) equals
order(x).

Page 70, #1, 5.

Click here for a
copy of an old midterm.
Homework 4, due Feb. 29

Page 7575, #1, 5, 8.

Page 8081, #1, 2, 3, 11, 12, 18, 20.

Click here for a writeup of the proof
that A_5 is simple.
Homework 5, due March 14

Page 90, #1,4,5,14.

Page 101, #1,7,9,15.

Click here for an
old homework writeup from the last time I taught the course
(some of these coincide with some of homework 4).

Click here for a short writeup
that A_n is generated by the 3cycles.

Page 108, #1,6,8.

Page 115, #4,6,9.

These are to be turned in next time:
Page 116117, #2, 4, 11, 14.

Click here for
an old homework writeup, which should coincide with some of the
assigned problems.
Homework 6, due April 4.
Page 130, #1, 3, 7, 12.
*** Don't forget that your next midterm is on Monday, April 7. ***
Click here for a copy of a
practice midterm. Your midterm will have more material on it than this,
but will still be only 5 questions.
Click here for a study sheet
for the exam.
Homework 7.
Page 135, #3.
Page 139140, #1, 3.
Page 142143, #1, 6.
Page 149, #1, 2, 3, 5.
Page 152, #1, 2, 3, 4, 5, 6, 7.
Homework 8, due Friday, Apr. 25.
Page 158, #1, 2, 3, 4, 6.
Page 161, #1, 2, 3.
Your final exam will be Monday, Apr. 28 from 2:50  5:40.
Check back later for a list of topics to study for the final
(I will try to put it up by Saturday night.)
Click here for a copy of
the final exam study sheet.
The test will have 10 questions, and you will choose 8 to work.
The test is *very* challenging. I anticipate the median score to be around
4050%, requiring a curve; and the highest will be probably around 80%,
but those who have consistently worked the
homeworks and attended the lectures should do OK.
Click here for a copy of the
final exam.