Math 541, Spring 2009, Tonghai Yang
Lecture Section 1, MWF 1:202:10pm, B203 VAN VLECK
Text: Abstract Algebra, by David Dummit and Richard
Foote, Third Edition, John Wiley and Sons, Inc., 2004.
Office Hours: I will be in my office 705 Van Vleck from
1011am on MF and 12:301pm on W. .
These times may change, in which case the new times will be announced
on my home page.
Other good times to talk are right before or right after the class. It
is also possible to ask questions by email, which will
be generally answered within 24 hours. The more detailed your
email question is, the more detailed the reply message will be.
My email is thyang@math.wisc.edu.
Grading: The course grades will be computed as follows.
There will be two midterms, the final and homework. Each
midterm will be graded on a scale from 0 to 100, and the final will
be graded on a scale from 0 to 150. The homework will be graded
on the scale from 0 to 150 (each homework worths 15 points), with
halfintegers allowed.
At the end of the semester, all these scores are added to give your
total score, in the range from 0 to 500. The grades are given according
to the total scores, and the average grade in the class is expected to
be slightly above B. Improvement towards the end of the semester
is not reflected in the final grade.
Two people with the same total scores will receive the same grade,
regardless of who did better at the end of the semester.
Midterm and Final Exams: We will have two 50 minute midterm
exams. They will be given in class.
There will be a
twohour final examination
given on Wednesday May 11 at 10:05pm in the location
to be announced.
You must take the
final examination at the time scheduled by the university; no final
exams
will be given earlier. In particular, examinations will not be
rescheduled because of travel arrangements. It is your responsibility
to schedule travel appropriately. Notes/textbooks will not be allowed
during the exams. Calculators will not be allowed, and will not be
needed.
Homework:
There will be eleven problem sets
with five problems each. They are the suggested problems in the table
below with *. .
Each problem will be graded on the scale from 0 to 3.
This is a proofbased course, which means that you will be expected to
write rigorous proofs to get full credit. An essence of a rigorous
proof is an airtight logical argument that establishes the
claim.
It is OK to talk to other students about homework problems. Most
exam problems will be generally a subset of the suggested
homework problems
and the practice, but they will be worth a lot more
points and will be thus graded in more detail.
Late/missed homework policy: We don't usually allow late homework unless a real good reason is given and accepted. Homework turned in after the set has been handed out will score zero. . There is no makeup for homework. However, we will drop one of lowest scores from your HWs and thus counts 10 HWs with maximal 150 points.
Missed exam policy:
There are no makeups for missed midterm exams, regardless of the reason
for absence.
However, if you can not attend the midterm due to a valid reason, for
example a
medical emergency, the rest of your exam scores will be scaled to
compensate
for the missed test. If you can not take the final exam due to a valid
reason,
you will be given the grade of Incomplete, with the makeup exam
scheduled
for the beginning of the Spring semester.
Week 
Sections 
Topics 
Suggested HW problems 
Jan. 1923 
Chapter 0, 1.1 
Preliminaries,
Definition of groups 
0.1.4, 0.1.5*, 0.1.7* 0.2.1(a, b), 0.2.3, 0.2.8, 0.2.11* 0.3.4, 0.3.8, 0.3.9, 0.3.10, 0.3.15(b*, c) 1.1.1, 1.1.6*, 1.1.12, , 1.1.15, 1.1.21, 1.1.25, 1.1.28 
Jan. 2630 
1.21.4 
Dihedral groups,
symmetric groups, matrix groups 
1.2.2*, 1.2.3, 1.2.9, 1.2.15,
1.2.17 1.3.2, 1.3.4, 1.3.5*, 1.3.7*, 1.3.11, 1.3.12, 1.3.15*, 1.3.16 1.4.1, 1.4.8*, 1.4.11 
Feb. 26 
1.51.7 
Quaternion group,
hom. and iso., group action 
1.5.3*, 1.6.1*, 1.6.2, 1.6.7*, 1.6.16, 1.6.25 1.7.1, 1.7.8*, 1.7.13, 1.7.16*, 1.7.17, 1.7.18, 1.7.19, 
Feb. 913 
2.12.3 
Subgroups,
Centralizers, normalizers, stabilizers, and kernels, cyclic
groups/subgroups 
2.1.2*, 2.1.6, 2.1.8, 2.1.9 2.2.2, 2.2.3*, 2.2.6*, 2.2.12, 2.3.3*, 2.3.8*, 2.3.10, 2.3.13, 2.3.16, 2.3.21 
Feb. 1620 
2.4, 2.5, Review 
subgroup gen. by a
subset, lattice of subgroups, review for Exam 1. 
2.4.2, 2.4.6*, 2.4.8, 2.4.10*,
2.4.11, 2.4.14*, 2.4.16 2.5.3*, 2.5.4, 2.5.9(b)*, 2.5.19 3.1.1*, 3.1.5, 3.1.9, 3.1.11, 3.1.14*, 3.1.17, 3.1.19,3.1.32, 3.1.36 
Feb. 2327 
Exam 1, 3.1 
Exam 1 is on Monday or
Wednesday, Definition of quotient groups 

Mar. 26 
3.23.3 
more on cosets,
Lagrange's theorem, and the fundamental theorems of group homomorphisms 
3.2.1, 3.2.6*, 3.2.11, 3.2.15,
3.2.18, 3.2.19, 3.2.22, 3.2.23 3.3.1, 3.3.3*, 3.3.7, 3.3.8*. 
Mar. 913 
3.5, 4.1,
4.3 
$S_n$,
$A_n$, Conjugation action and the class equation 
3.5.2, 3.5.5, 3.5.6*, 3.5.10*,
3.5.15 4.1.1, 4.1.4*, 4.1.10 4.3.2*, 4.3.9, 4.3.13*, 4.3.17, 4.3.20 
Mar. 1620 
Spring Break 

Mar. 2327 
4.4, 4.5 
Automorphisms,
Sylow's theorems 
4.4.1*, 4.4.3, 4.4.6, 4.4.13*
(can use Section 4.5),
4.4.17, 4.4.18 4.5.5*, 4.5.8*, 4.5.14*, 4.5.26, 4.5.30 
Mar. 30Apr. 3 
7.1, 7.2, 7.3 
Rings and
examples, Ring homomorphisms and quotient rings 
7.1.1, 7.1.5*, 7.1.6, 7.1.10,
7.1.11*, 7.1.18, 7.1.26 7.2.1*, 7.2.3, 7.2.9*, 7.2.12 7.3.3*, 7.3.6, 7.3.10, 7.3.15, 7.3.19, 7.3.22 
Apr. 610 
7.3, 7.4, 7.5 
Properties of ideals
and Ring of fractions 
7.4.1, 7.4.4*, 7.4.9*, 7.4.14,
7.4.15, 7.4.17*, 7.4.20 7.4.30 7.5.2*, 7.5.3*, 7.5.4 
Apr. 1317 
Review, Exam 2 
Exam 2 is on Wednesday or
Friday. 

Apr. 2024 
7.6, 8.1 
Chinese Reminder
Theorem, Euclidean Domain 
7.6.1, 7.6.2*, 7.6.3, 7.6.5*,
7.6.6, 8.1.2(a)(b), 8.1.4*, 8.1.5*, 8.1.6*, 8.1.8, 8.1.12 
Apr. 27May 1 
8.28.3 
PID, UFDs 
8.2.2*, 8.2.4*, 8.2.5*, 8.2.7,
8.2.8 8.3.1*, 8.3.3*, 8.3.5, 8.3.8 
May 4May 8 
Review  
10:05am12:05pm May 11 
Final Exam 