Math 4107, Abstract Algebra, Spring 2008
For a copy of the course syllabus, click
Homework 1 (due Friday, Jan. 18)
Page 8-9, #4, 8, 11.
Page 16-17, #1,3,9.
Page 23-24, #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 35-36, #1,2,6,11,14,21.
Page 48-49, #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
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:
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
Page 70, #1, 5.
Click here for a
copy of an old midterm.
Homework 4, due Feb. 29
Page 75-75, #1, 5, 8.
Page 80-81, #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 3-cycles.
Page 108, #1,6,8.
Page 115, #4,6,9.
These are to be turned in next time:
Page 116-117, #2, 4, 11, 14.
Click here for
an old homework writeup, which should coincide with some of the
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.
Page 135, #3.
Page 139-140, #1, 3.
Page 142-143, #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
40-50%, 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